ࡱ> &!4 Root Entry F @ CompObjnWordDocument ObjectPoolmuYmuY u  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstvwxyz{|}~      !"#$%r()*+,-./0123456789:;<=gFbHIJKLMNOPQRST}VWXYZ[\]^_`azcdefjhiklmnopqstuvwxy{|~SummaryInformation(` th a rectangular cross section. Victoria BaileyVictoria Bailey@@Ja@Y@@y#Microsoft Word 6.016 FMicrosoft Word 6.0 Document MSWordDocWord.Document.69q_Oh+'00   4X |   More Time(C:\MSOFFICE\WINWORD\TEMPLATE\NORMAL.DOTThe Parametric_product_space 10 metre rectangular beams is the set of beams designs of length 10 metres wi      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~\ "-r/--' & &b "- $Z & &8--8p "- --' & &"Arial-.  (2 g{disjoAL_TOPOLOGY_SPACE_PARAMETERISATION (#005, #013); NOTE - The same Maths_space is used to identify cross sections and states. There is only one set of reals, but many uses of it. An individual state within a state space The final loaded state of the 10 metre beam is a State. The ARM instances that record: the existence of the final loaded state; its relationship to the set of states within the activity design; and the identification of the state by the number 1.0, are as follows: #016 = STATE (); #017 = MEMBERSHIP_OF_STATE_SPACE (#013, #016); #018 = PHYSICAL_TOPOLOGY_SPACE_PARAMETERISATION_ELEMENT (#019, #016); #019 = MATHS_VALUE (the real 1.0); #020 = ELEMENT_OF_MAPPING (#015, #018); NOTE - The entity Maths_value is a point of intersection with the Mathematical representation schema. The way in which the nature of the Maths_value is made computer interpretable, is not within the scope of this discussion. A simple value will be a direct use of the REAL type in an AIM instantiation, rather that an entity. A set of states for features within an activity design An analysis of the beam loading activity can consider the set of states that exist during the loading process for the set of cross sections of the beam. This set of states for features is a Physical_topology_space. It can be regarded as the product (i.e. () of the space of cross sections for the beam and the space of states for the loading process. There are an infinite number of states for features in the set. Each state for a feature iof the beam in an unloaded reference state. There are an infinite number of cross sections in the set. Each cross section in the set is identified by a real number in the range [0, 1]. The ARM instances that record: the existence of the one dimensional space of cross sections; its relationship to the design as a whole; and the way in which a cross section within the set is identified, are as follows: #002 = DESIGN_SURFACE_SPACE (1); #003 = FEATURE_SPACE_FOR_PRODUCT_DESIGN (#001, #002); #004 = PHYSICAL_TOPOLOGY_SPACE_PARAMETERISATION (#005, #002); #005 = MATHS_SPACE (the set of reals between 0 and 1); NOTE - The entity Maths_space is the point of intersection with the Mathematical representation schema. The way in which the nature of the Maths_space is made computer interpretable, is not within the scope of this discussion. An individual feature within a product design The mid section of the 10 metre beam is a Design_surface. The ARM instances that record: the existence of the cross section; its relationship to the set of cross sections within the beam; and the identification of the cross section by the number 0.5, are as follows: #006 = DESIGN_SURFACE (); #007 = MEMBERSHIP_OF_FEATURE_SPACE (#002, #006); #008 = PHYSICAL_TOPOLOGY_SPACE_PARAMETERISATION_ELEMENT (#009, #006); #009 = MATHS_VALUE (the real 0.5); #010 = ELEMENT_OF_MAPPING (#004, #008); NOTE - There can be alternative identification schemes for the cross sections. Identifications by the ranges [0, 1] and [-0.5, 0.5] and [-1, 1] are all possible. Also the numbering of the cross sections can start from either end. The entity Element_of_mapping indicates which scheme is used. NOTE - The entity Maths_value is a point of intersection with the Mathematical representation schema. The way in which the nature of the Maths_value is made computer interpretable, is not within the scope of this discussion. A simple value will be a direct use of the REAL type in an AIM instantiation, rather that an entity. An activity design An analyst creates the definition or design of an activity that specifies the following information: the activity is called slow loading of 10 metre beam 3 metres from one end; the activity is performed by the 10 metre beam; the 10 metre beam is simply supported throughout; the 10 metre beam is initially unloaded and unstressed; a point load is applied 3 metres from one end, and slowly increased until it is 10 kN. Using the terminology of the ARM for this part of ISO 10303, the designer creates an Activity. ASIDE - For consistency the term Activity_design could be used. Are there opinions on this? The Activity slow loading of 10 metre beam 3 metres from one end is a class that has individual activities as members. Each individual activity that slowly applies a point load 3 metres from the end of a 10 metre beam with a 4 metres by 2 metres rectangular cross section, is a member of this class, or (to put it another way) complies with the design. The ARM instances that record: the existence of the activity design; and its relationship to the product design, are as follows: #011 = ACTIVITY_DESIGN (); #012 = ACTIVITY_ASPECT_OF_PRODUCT (#011, #001); NOTE - The entity Activity is another point of intersection with the STEP product structure backbone. There are may facts to record about the activity design which are not within the scope of this discussion, including: the identification of the activity design; the classification of the activity design as a slow loading process; the possession of the simply supported boundary conditions throughout the activity design; the possession of an applied point load that increases during the activity design; the relationship with previous activity designs. A set of states within an activity design An analysis of the beam loading activity can consider the set of states that exist during the loading process. This set of states is a State_space. There are an infinite number of states in the set. Each state in the set is identified by a real number in the range [0, 1]. The ARM instances that record: the existence of the one dimensional space of states; its relationship to the activity design as a whole; and the way in which a state within the set is identified, are as follows: #013 = STATE_SPACE (1); #014 = ACTIVITY_OR_STATE_SPACE_FOR_PRODUCT_DESIGN (#013, #011); #015 = PHYSICAL_TOPOLOGY_SPACE_PARAMETERISATION (#005, #013); NOTE - The same Maths_space is used to identify cross sections and states. There is only one set of reals, but many uses of it. An individual state within a state space The final loaded state of the 10 metre beam is a State. The ARM instances that record: the existence of the final loaded state; its relationship to the set of states within the activity design; and the identification of the state by the number 1.0, are as follows: #016 = STATE (); #017 = MEMBERSHIP_OF_STATE_SPACE (#013, #016); #018 = PHYSICAL_TOPOLOGY_SPACE_PARAMETERISATION_ELEMENT (#019, #016); #019 = MATHS_VALUE (the real 1.0); #020 = ELEMENT_OF_MAPPING (#015, #018); NOTE - The entity Maths_value is a point of intersection with the Mathematical representation schema. The way in which the nature of the Maths_value is made computer interpretable, is not within the scope of this discussion. A simple value will be a direct use of the REAL type in an AIM instantiation, rather that an entity. A set of states for features within an activity design An analysis of the beam loading activity can consider the set of states that exist during the loading process for the set of cross sections of the beam. This set of states for features is a Physical_topology_space. It can be regarded as the product (i.e. () of the space of cross sections for the beam and the space of states for the loading process. There are an infinite number of states for features in the set. Each state for a feature in the set is identified by a pair of real numbers, where the first identifies the feature and the second the state. The ARM instances that record: the existence of the two dimensional space of states for features; its relationship to the space of states and to the space of features; and the way in which a state for a feature within the set is identified, are as follows: #021 = PHYSICAL_TOPOLOGY_SPACE (2); #022 = PHYSICAL_SPACE_DESIGN_FEATURE_COMPONENT (#002, #021); #023 = PHYSICAL_SPACE_ACTIVITY_OR_STATE_COMPONENT (#013, #021); #024 = PHYSICAL_TOPOLOGY_SPACE_PARAMETERISATION (#025, #021); #025 = MATHS_SPACE (the set of real pairs with each component in [0, 1]); #026 = DERIVATION_OF_PARAMETERISATION (#024, (#004, #015)); NOTE - This parameterisation of the set of states for cross sections can be used to describe any property of a cross section that varies with position along the beam, and with stage in the loading process. The description can have the form of a function as follows: the domain is the set of real pairs with each component in [0, 1], which is a parameterisation of the set of states for cross sections; and the range is the numeric space that identifies the property. An individual state for a cross section The mid section of the 10 metre beam in the final loaded state is a State for a Design_surface. This State is a member of the set of states for cross sections. The ARM instances that record: the existence of the final loaded state for the mid section; its relationship to the mid-section; its relationship to the set of states for cross sections; and the identification of the state by the pair (0.5, 1.0), are as follows: #027 = STATE (); #029 = STATE_ASPECT_OF_PRODUCT (#027, #006); #029 = CLASSIFICATION (#021, #027); #030 = PHYSICAL_TOPOLOGY_SPACE_PARAMETERISATION_ELEMENT (#031, #027); #031 = MATHS_VALUE (the real pair (0.5, 1.0)); #032 = ELEMENT_OF_MAPPING (#024, #030); NOTE - Any properties calculated or measured for the mid section of the beam in the loaded state that be associated with this state for a feature. ARM Diagrams Product feature space  Figure  SEQ Figure \* ARABIC 1: Product feature space EXPRESS-G  Figure  SEQ Figure \* ARABIC 2: Product feature space UML Activity and state space  Figure  SEQ Figure \* ARABIC 3: Activity and state space EXPRESS-G  Figure  SEQ Figure \* ARABIC 4: Activity and state space UML Product activity and state space parameterisation  Figure  SEQ Figure \* ARABIC 5: Product activity and state space parameterisation EXPRESS-G  Figure  SEQ Figure \* ARABIC 6: Product activity and state space parameterisation UML dl011_v1_param_ex.doc  PAGE 11 .Az :z*H! 1&: & &$TNPPMicrosoft PowerPoint & TNPPf & &TNPP :  1:45&8&0:- "- :"-0 & &0(H-- :"-H(0 & &-- $i/j & &8` $86` & &]lTimes New Roman4-.  : 2 C & &L"Univers-.  : 2 ms & &lL"Universw -.  : 2 my & &@Lh"Univers-.  : 2 mzs & & L"Universw -.  : 2 mFtj & &L"Univers-.  : 2 me & &L"Universw -.  : 2 mm & &L"Univers-.  : 2 ms & &d]lTimes New Roman4-.  : 2 A & &z]lTimes New Roman-.  : 2 E & &j]lTimes New Roman4-.  : 2 S & &.]lTimes New Roman-.  : 2 hA & &F]lTimes New Roman4-.  : 2 R &  & &TNPP & --"Systemn-D$XP@t(T$pazL:]E 5o'cc &7&  & &$TNPPMicrosoft PowerPoint & TNPPf & &TNPP   6345& Times New Roman-.  2 Pwhole:,($ & & x- "- "-x Times New Roman!-.  72 { feature_space_for_product_design +0 5+*0&50+*0 0+05+055+ 05+%05 & &0 8&0 8-- $0 088 88(8 "--G8h888888(8G8h8888888?` ?` ?` ?` ?` ?` 000000q0P01000000q0P010((((((y(X(9((((((y(X(9((((((y(X(9((((((y(X(9((((((y(X(9((((((y(X(9 & &08-- "- HH80(9Times New Roman-.  $2 yproduct_design_arm.5+056* 06*&0600*PTimes New Roman!-.  2 fproduct_design5+056* 06*&06 &  & &`X-- "-X`(9Times New Roman-.  %2 zdesign_feature_space5+%050 +0 5++0%50++ & &-- "-(9Times New Roman!-.  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The ARM instances that record: the existence of the two dimensional space of states for features; its relationship to the space of states and to the space of features; and the way in which a state for a feature within the set is identified, are as follows: #021 = PHYSICAL_TOPOLOGY_SPACE (2); #022 = PHYSICAL_SPACE_DESIGN_FEATURE_COMPONENT (#002, #021); #023 = PHYSICAL_SPACE_ACTIVITY_OR_STATE-- "- & &(---(h "-@--' & & Times New Roman4-.  2 pclass$( & &`- "-`@ & &h---hh "---' & &X(- "-(X & & (--  "-  --' & &&- $ "--'Hg'Hg0Op0Op0Op0Op0OppQ0pQ0hI( hI( hI( hI( hI(  Times New Roman4-.  $2 iproduct_design_arm.5+056* 06*&0600*PTimes New Roman -.  2 classification+0&% +0 05 & & H "- HHH &  & &FrTimes New Roman4-.   2 010 & & rTimes New Roman -.   2 0P 10 & & (h& (h-- $  h(h(((( "--(((('(H(g(((((('(H(`(`(`/`P`o``````/`P`o``````/`P`o``````/`P`o``````/`P`o``````/`P`o`````` ` Q 0      p Q 0      iH)iH)iH)iH)iH)iH)Times New Roman4-.  .2 Sproduct_feature_space_arm.5+056* 0 +0 5++0%50+*00+PTimes New Roman -.  *2 (physical_topology_space560%*00 0500000%60*+ & & ( "- HH(  &  & &p &p -- $pp xxx "--xxxxx(x/xHxOxhxoxxxxxxxxxxx(x/xHxOxhxoxxx '@G`g '@G`g '@G`g   ' @ G ` g            ' @ G ` g       p i P I 0 )           p i P I 0 )         x q X Q 8 1           x q X Q 8 1   xqXQ81xqXQ81xqXQ81xx)Times New Roman4-.  .2 product_feature_space_arm.5+056* 0 +0 5++0%50+*00+PTimes New Roman -.  2 fusion 5&06 & &p H "- HHH p &  & &   -- "- xTimes New Roman4-.  =2 -$activity_or_state_space_for_activity0+ 0 000+0% 0 *0&50+*0 0+00+ 0 0 & &-- "-xTimes New Roman -.  2 m state_space% 0 +0%60*+ & &PH-- "-HPxTimes New Roman4-.  2 5activity_space0+ 0 00%60*+ & &`X-- "-X`x & &X-- "-Xx & &---80  "-p--' & &}82Times New Roman4-.   2 10 & & .(---.  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(2 c{disjoint, incomplete},(,-,(-C,,,"ArialNe-.  2 Pgusage,(-,- & &P@h- "-h@P"Arialn-.  2 eClassificationE5000656"ArialNe-"Arialn-.  *2 &M(from ProductDesignARM)  5P@ 5560F5055@FP  & & H&H-- "-H & & -- "- "ArialNe-.  %2 ActivityOrStateSpace@000K @66@5605 & &---p "---' &  & &0`8(--(` "-00--' & &`(--(`p "---' & &px--??o "-oUoooo5ofoo--' & & & - "- o & & -- "- o"Arialn-.  62 \ActivityOrStateSpaceForActivity@000K @66@5605;5 @000 & & ---x 0 "-0P--' &  & &>`( "- $> ` & & --. "-`--' & &%"Arialn-.  (2 {disjoint, incomplete},(,-,(-C,,,"ArialNe-.  2 Pusage,(-,- & &p8x---??o "-oo o_oooo0o0--' & &V&V- "-Vo0 & &V-- "-Vo0"Arialn-.  -2 \(MembershipOfActivitySpaceP5P65 055K@000@5506 & &V---x0V "- --' &  & &0p"Arialn-.  2 3jmemberC,C,- & &0{"ArialNe-.   2 j* & &0>b"Arialn-.  2 jclass(,(( & &0M"ArialNe-.   2 j* & &p"Arialn-.  2 3whole:,-, & &w{"ArialNe-.   2 * & &>"Arialn-.  2 class(,(( & &wM"ArialNe-.   2 * & &P`&P - "- P & &P`(-- "-(`P"Arialn-.  2 ActivitySpace@000@5605 & &PPX---P "-PP--' &  & &P&P- "-PP & &P-- "-PP"Arialn-.  2 \ StateSpace@55@6505 & &P---x0P "---' &  & &u"Arialn-.  (2 U{disjoint, incomplete},(,-,(-C,,,"ArialNe-.  2 `8dimensionality,C,-(,-,( & &@ h- "-h @"Arialn-.  2 0Fusion;5065"ArialNe-"Arialn-.  32 &(from ProductFeatureSpaceARM)  5P@ 5560;655 5@6506@EP  & &h "-- $h & &---P "---' & &px-- "-pp--' & &x--xP "-p--' & &--X "---' & &`h- "-h`"Arialn-.  '2 S_PhysicalTopologySpace@50005;655550@6506"ArialNe-"Arialn-.  32 (from ProductFeatureSpaceARM)  5P@ 5560;655 5@6506@EP  & &-- "-"ArialNe-.  "2 DesignFeatureSpaceE6056:655 6@5506"Arialn-"ArialNe-.  32 (from ProductFeatureSpaceARM)  5P@ 5560;655 5@6506@EP  & &p (&p (-- "-( p & &p -- "- p"Arialn-.  ?2 |%PhysicalSpaceActivityOrStateComponent@50005A5506@000J @56E5P65565 & &p --- Pp "-p--' &  & &p &p - "- pp & &p -- "- pp"Arialn-.  <2 <#PhysicalSpaceDesignFeatureComponent@50005A5506E5056:655 5F5P56565 & &p ---X p "-p--' &  & &x--??pp "-5fFp--' & &@--@P "---' & &=P"Arialn-.  2 *whole:,-, & &["ArialNe-.   2 ** & &""Arialn-.  2 c*class(,(( & &k "ArialNe-.   2 ** & &PxX---??ppO "-O5OfOOOOFOpO--' & &--P "-`@--' & &=`"Arialn-.  2 #*whole:,-, & &P@X---@ "-P P--' & &"Arialn-.   2 ** & &n""ArialNe-.  2 *class(,(( & &+"Arialn-.   2 ** & &E-F"ArialNe-.  (2 `%{disjoint, incomplete},(,-,(-C,,,"Arialn-.  2 K membershipC,C,-(-, & &(h "-- $(`p & &Ppx---P "-pp--' & & X--X( "-  --' & & --(  "-@--' & & --8 "-`  --' & & P X--  "-P` P --' & &TNPP & --"::` Ho6(TT B9&  & &$TNPPMicrosoft PowerPoint & TNPPf & &TNPP   V345& (H& (H- "- $ H(H(((( "--(('(H(g(((((('(@0@O@p@@@@@@0@O@p@@@@@@0@O@p@@@@@@0@O@p@@@@@@0@O@p@@@@@@0@O@p@@@@@0      p Q 0    iH)iH)iH)iH)iH)iH)Times New Roman -.  .2 cproduct_feature_space_arm.5+056* 0 +0 5++0%50+*00+PTimes New Roman-.  *2 (physical_topology_space560%*00 0500000%60*+ & & ( "- HH( &  & & ((-- "-(( )Times New Roman -.  +2 sphysical_topology_space_560%*00 0500000%60*+0Times New Roman-.  2 parameterisation50+0P+ *+&0 06 & &P-- "-P)Times New Roman -.  !2 Tbsubset_of_mapping%65&* 00 0P05660 & & (-- "-( )Times New Roman-.  +2 sphysical_topology_space_560%*00 0500000%60*+0Times New Roman -.  +2 parameterisation_element50+0P+ *+&0 060*+P*6  & &P  -- "- P)Times New Roman-.  '2 mapping_element (ABS)P056600*+P*6  E@5  & & H& H-- $H H  "--'Hg'@@@0@O@p@@@@@@0@O@p@@@@@@0@O@p@@@@@@0@O@p@@@@@ @0 @O @p @ @ @ @ @ @0 @O @p @ @ @ 0      p Q 0       i H )      i H )  iH)iH)iH)iH))Times New Roman -.  $2 c)product_design_arm.5+056* 06*&0600*PTimes New Roman-.  +2 class_of_physical_object+0&%00 0560%*0005 ++  & &  "- HH  &  & &`-- "-`Times New Roman -.  2 +derivation_of_5++00 0500 0Times New Roman-.  2 parameterisation50+0P+ *+&0 06 & &dTimes New Roman -.  2 PBL[2,?] sources5(((,$#$ & &`-- "-`Times New Roman-.  .2 tcomponent_parameterisation+0P505+5 060*0P+ *+%0 05 & &mTimes New Roman -.  2 03 component$(B-(,$, & &h}Times New Roman-.  2 @parameterisation,($(C##$((- & &hmTimes New Roman -.  2 0$derived,$$(#- & &px&px-- $pxxpx "--8Wx ?` ?` ?` ?` ?` ?` ?`ppppqpPp1ppppppxpxpxixHx)xxxxxxixHx)xxxxxxixHx)xxxxxxixHx)xxxxxxixHx)xxxxxxixHx)xxxxxxixHx)xxTimes New Roman-.  2 4state_arm.state% 0 +00+O& 0 * & &x "- <<x &  & &a(Times New Roman -.  2 imageC((# & &--"Systemn-@ "-@` --' & &A( Times New Roman -.  2 domain,(C(- & & @X - "-X @ ` & & ( --- "-@ ` --' & &a( Times New Roman -.  2  imageC((# & & `X - "-X ` ` & & ( h---h  "-  --' & &p - "- p Times New Roman -.  2  mapping (ABS)P05660 E@6  & &`(-- "-(` & & ---   "-`--' & &`- "-`` & &--  "-0--' & &@- "-@0 & &px--   "-p0p--' & &`(- "-(`0p & &h--hxp  "---' & &8(- "-(8 & &`--`  "- --' & &xH&xH- $HxHx "--8Wx8@@@@ @?@`@@@@@@ @?@`@@@@@@ @?@`@@@@@@ @?@`@@@@@@ @?@`@@@@@@ @?@`@@@@@@ @?@`@p@p1ppppppqpPp1ppppiH)iH)iH)iH)iH)iH)iH) Times New Roman -.  '2 activity_arm.activity0+ 0 000+O0+ 0 0 & & x "- <<x  &  & &px&px-- $pxxpx "--8Wx ?` ?` ?` ?` ?` ?` ?`ppppqpPp1ppppppxpxpxixHx)xxxxxxixHx)xxxxxxixHx)xxxxxxixHx)xxxxxxixHx)xxxxxxixHx)xxxxxxixHx)xxTimes New Roman-.  92 44!product_design_arm.product_design5+056* 06*&0600*P6*065+ 05+%05 & &x "- <<x &  & &h---Xh "---' & & 0- "-0  & &`hh--h "-``@--' & &@(- "-(@`@ & &p`x-- `  "-p p--' & &8- "-8 p & &--` "-`--' & &`8- "-8` & &h--h` "-@--' & & H- "-H  & &x--xp "-`--' & &phx--h "-pp--' & &p8- "-8pp & &8 --8   "-p --' & &pP- "-Pp & &8 --8   "-p --' & &p8- "-8p & &8 --8   "-p --' & &0 @8 -- @  "-0 0 --' & &AnTimes New Roman -.  2 *domain,(C(- & &`- "-`0 & & h---h @ "---' & &@- "-@ & &` -- "- `Times New Roman -.  "2 Relement_of_mapping++P*6 00 0P05660 & &-- "- & &LhTimes New Roman-.  2 class$( & &---X "-@P--' & &X- "-XP & &8Times New Roman -.  2 memberC#C,$# & &`h&`h-- $``hhhhh "--7hXhwhhhhhh7hXh`h`h`````` `?```````` `?```````` `?```````` `?```````` `?``````A `A hI( hI( hI( hI( hI( hhPTimes New Roman-.  $2 Iproduct_design_arm.5+056* 06*&0600*PTimes New Roman -.  2 classification+0&% +0 05 & &`@8 "- <<8@` &  & &P h&P h-- $PPh h XXX "--7XXXwXXXXXX7XXX`X`X`o``````/`P`o``````/`P`o``````/`P`o``````/`P`o````` `/ `P `o ` ` ` A       ` A    y X 9  yX9yX9yX9yX9yXXhTimes New Roman-.  $2 9product_design_arm.5+056* 06*&0600*PTimes New Roman -.  2   individual550560 & &P@ 8 "- <<8 @P &  & & & -- $   "--'Hg ?` ?` ?`_COMPONENT (#013, #021); #024 = PHYSICAL_TOPOLOGY_SPACE_PARAMETERISATION (#025, #021); #025 = MATHS_SPACE (the set of real pairs with each component in [0, 1]); #026 = DERIVATION_OF_PARAMETERISATION (#024, (#004, #015)); NOTE - This parameterisation of the set of states for cross sections can be used to describe any property of a cross section that varies with position along the beam, and with stage in the loading process. The description can have the form of a function as follows: the domain is the se ?` ? `       ? `          ` A         i H )      i H )  iH)iH)iH)iH)XTimes New Roman-.  2 KLmaths_value_arm.P0 5&0006*00+PTimes New Roman -.  2  maths_valueP0 5&0006* & &  "- <<  &  & & & -- $  ((( "--(('(H(g((((((((?` ?` ?` ?` ?` ?``A iH)iH)iH)iH)iH)iH)Times New Roman-.  2 Kmaths_space_arm.P0 5&0%50++00*PTimes New Roman -.  2  maths_spaceP0 5&0%50++ & &  "- << &  & &`8&`8-- $``88hhh "--hh'hHhghhhhhhhh ?` ?` ?` ?` ?` 0000000`0A0 00000)iH)iH)iH)iH)iH)i)Times New Roman-.  02 Kproducct_feature_space_arm.5+056*+ 0 +0 5+*0%60*+00+PTimes New Roman -.  2 fusion 5&06 & &`8 "- <<8` &  & &p(&p(-- $pp((xxx "--xx7xXxwxxxxxx x x      0 O p      0 O p      0 O p      0 O p      0 O p    `A xY8xY8xY8xY8xY8xxiTimes New Roman-.  $2 [Yproduct_design_arm.5+056* 06*&0600*PTimes New Roman -.  2 class+0&% & &p "- <<p &  & &P&P-- $PPXXX "--XXX8XWXxXXXXXXXo/Po/Po/Po/Po/Poa@!yX9yX9yX9yX9yX9yXXxTimes New Roman-.  $2 ;9product_design_arm.5+056* 06*&0600*PTimes New Roman -.  *2 %specialisation_of_class%6*+0%0 0500 0+0%% & &P "- <<P &  & &9}MTimes New Roman-.  2 swhole:,($ & &x(-- "-(xX & &@H--- "-@@--' & &MTimes New Roman -.   2 #part,($ & &((- "-((@ & &---P "---' & &TNPP & --hz[:` Ho6(TT -3& F & &$TNPPMicrosoft PowerPoint & TNPPf & &TNPP   V345&- "- "-Times New Roman-.  !2 subset_of_mapping%65&* 00 0P05660 & &(--"Systemn-(@ "-0--' & &X--X@ "- --' & &X--X@ "---' & &X--X8 "---' & &@H--8H@ "-@@--' & &(--(` "-@--' & &@H--(H@ "-@@--' & &`- "-`@"ArialNe-.  2 cClassificationE5000656"ArialNe-"Arial-.  *2 (from ProductDesignARM)  5P@ 5560F5055@FP  & & H-- "-H @"Arial-.  2 pFusion;5065"Arial-"Arial-.  12 E(from ProductFeatureSpaceARM  5P@ 5560;655 5@6506@EP & & (H-- "-H(  @"Arial-.  2  MathsSpaceP550@6506"Arial-"Arial-.  %2 (from MathsSpaceARM)  5PP550@5605@FP  & &  H-- "-H @"Arial-.  2  MathsValueP550@665"Arial-"Arial-.  %2 (from MathsValueARM)  5PP550@556@EP  & &-- "-@"Arial-.  '2 S]SpecialisationOfClass@56060655KE600"Arial-"Arial-.  *2 (from ProductDesignARM)  5P@ 5560F5055@FP  & &P@ h-- "-h @P@"Arial-.  2 % Individual550655"Arial-"Arial-.  *2 &(from ProductDesignARM)  5P@ 5560F5055@FP  & &p-- "-p@"Arial-.  2 CClassE500"Arial-"Arial-.  *2 (from ProductDesignARM)  5P@ 5560F5055@FP  & &&-- "-@ & &-- "-@"Arial-.  2 lSubsetOfMapping@5605KP65555 & &---@ "-P--' &  & &--` "-0@--' & &--?? "-/Po--' & &n"ArialNe-.  2 whole:,-, & &G}"Arial-.   2 @* & &n"Arial-.   2 part,- & &}"Arial-.   2 @1* & &"Arial-.  2 cclass(,(( & &kK "Arial-.   2 * & &X"Arial-.  2 cmemberC,C,- & &kR "Arial-.   2 * & &`(&`(- "-(` & &`-- "-`"Arial-.  2 |eElementOfMapping@6P56KO65656 & &`---P` "- --' &  & & --??  "-?` --' & &@"ArialNe-.  2 zimageB-,- & &{M"Arial-.   2 * & &>b"Arial-.  2 domain,-C,, & &+{"Arial-.   2 * & & (- "-(  "Arial-.  '2 cPhysicalTopologySpace@50005;655550@6506"Arial-"Arial-.  32 U(from ProductFeatureSpaceARM)  5P@ 5560;655 5@6506@EP  & &---?? "- ?`--' & & ( (--(  "- 0 --' & &r "ArialNe-.  2 imageB-,- & & ( M"Arial-.   2  * & &>( "Arial-.  2 domain,-C,, & & +( "Arial-.   2 * & & - "- 0 "Arial-.  '2 cXClassOfPhysicalObjectE500K@60006K560"Arial-"Arial-.  *2 (from ProductDesignARM)  5P@ 5560F5055@FP  & &pPx&px-- "-xp0 & &pP-- "-Pp0 "Arial-.  2 XMappingP56565 & &p@H---p "-@0@--' &  & &PP x&P x- "-x P@ & &PP -- "- PP@"ArialNe-.  2 MappingElementP56565@5P56 & &P@ H--- P "-@@--' &  & & ( --??  "- @ _        --' & &` &P - "- P & &` X-- "-X ` "ArialNe-.  '2 _PhysicalTopologySpace@50005;655550@6506"Arial-.  *2 .EParameterisationElement@5 6P55 0556@5P65 & & ---(  "-@--' &  & &`H&PH- "-HP@ & &`HX-- "-XH`@"ArialNe-.  '2 PhysicalTopologySpace@50005;655550@6506"Arial-.  2 .5Parameterisation@5 6P55 0556 & &H---(H "---' &  & &- "-"ArialNe-.  2 0State@55"Arial-"Arial-.  2 8(from StateARM)  5P@66@EP  & &-- "-"Arial-.  2 cActivity@000"Arial-"Arial-.  "2 (from ActivityARM)  5P@000@EP  & &@h-- "-h@"Arial-.  2 e ProductDesign@ 5650E6056"Arial-"Arial-.  *2 &m(from ProductDesignARM)  5P@ 5560F5055@FP  & &0x&0x-- "-x0 & &0x-- "-x0"Arial-.  12 \[DerivationOfParameterisationE6 0565K@5 5P66 0565 & &0x---xx00 "---' &  & &@H-- "-p@@--' & &@"ArialNe-.  2 sz 1 derived,,-(-, & &@Q"Arial-.  2 cz 2..* source,(,-(- & &M"Arial-.   2 :* & &"Arial-.   2 s:1, & &@---??@@@ "-_--' & &--?? "-0Op--' & &p--p` "---' & & 0~- "- $v(v  & &K  "ArialNe-.  (2 p{disjoint, incomplete},(,-,(-C,,,"Arial-.  2 usage,(-,- & &X---X@ "-0--' & &`- "- $` & &k[]"ArialNe-.  (2 {disjoint, incomplete},(,-,(-C,,,"Arial-.  2 nature,--- & &0`8---` "-00--' & &`t- "- $lXl00 & &{"ArialNe-.  (2 `{disjoint, incomplete},(,-,(-C,,,"Arial-.  2 usage,(-,- & &h---h@ "-@--' & &p- "- $p & &kkm"ArialNe-.  (2 {disjoint, incomplete},(,-,(-C,,,"Arial-.  2 0nature,--- & & (h---h "-@  --' & &jP- "- $H j & &kkm"ArialNe-.  (2 {disjoint, incomplete},(,-,(-C,,,"Arial-.  2 0 membershipC,C,-(-, & &PX---XP` "-PP--' & &0d- "- $\(\P & &K"ArialNe-.  (2 P{disjoint, incomplete},(,-,(-C,,,"Arial-.  2 membershipC,C,-(-, & &7-- "- $7||`P & &{ "Arial-.  (2 `{disjoint, incomplete},(,-,(-C,,,"Arial-.  2  membershipC,C,-(-, & 't of real pairs with each component in [0, 1], which is a parameterisation of the set of states for cross sections; and the range is the numeric space that identifies the property. An individual state for a cross section The mid section of the 10 metre beam in the final loaded state is a State for a Design_surface. This State is a member of the set of states for cross sections. The ARM instances that record: the existence of the final loaded state for the mid section; its relationship to the mid-section; its relationship to the set of states for cross sections; and the identification of the state by the pair (0.5, 1.0), are as follows: #027 = STATE (); #029 = STATE_ASPECT_OF_PRODUCT (#027, #006); #029 = CLASSIFICATION (#021, #027); #030 = PHYSICAL_TOPOLOGY_SPACE_PARAMETERISATION_ELEMENT (#031, #027); #031 = MATHS_VALUE (the real pair (0.5, 1.0)); #032 = ELEMENT_OF_MAPPING (#024, #030); NOTE - Any properties calculated or measured for the mid section of the beam in the loaded state that be associated with this state for a feature. ARM Diagrams Product feature space  Figure  SEQ Figure \* ARABIC 1: Product feature space EXPRESS-G  Figure  SEQ Figure \* ARABIC 2: Product feature space UML Activity and state space  Figure  SEQ Figure \* ARABIC 3: Activity and state space EXPRESS-G  Figure  SEQ Figure \* ARABIC 4: Activity and state space UML Product activity and state space parameterisation  Figure  SEQ Figure \* ARABIC 5: Product activity and state space parameterisation EXPRESS-G  Figure  SEQ Figure \* ARABIC 6: Product activity and state space parameterisation UML dl011_v1_param_ex.doc  PAGE 7 .Az :z*H! 1&: & &$TNPPMicrosoft PowerPoint & TNPPf & &TNPP :  1:45&8&0:- "- :"-0 & &0(H-- :"-H(0 & &-- $i/j & &8` $86` & &]lTimes New Roman4-.  : 2 C & &L"Univers-.  : 2 ms & &lL"Universw -.  : 2 my & &@Lh"Univers-.  : 2 mzs & & L"Universw -.  : 2 mFtj & &L"Univers-.  : 2 me & &L"Universw -.  : 2 mm & &L"Univers-.  : 2 ms & &d]lTimes New Roman4-.  : 2 A & &z]lTimes New Roman-.  : 2 E & &j]lTimes New Roman4-.  : 2 S & &.]lTimes New Roman-.  : 2 hA & &F]lTimes New Roman4-.  : 2 R &  & &TNPP & --"Systemn-D$XP@t(T$zL:]E 5o'cc &7&  & &$TNPPMicrosoft PowerPoint & TNPPf & &TNPP   6345& Times New Roman-.  2 Pwhole:,($ & & x- "- "-x Times New Roman!-.  72 { feature_space_for_product_design +0 5+*0&50+*0 0+05+055+ 05+%05 & &0 8&0 8-- $0 088 88(8 "--G8h888888(8G8h8888888?` ?` ?` ?` ?` ?` 000000q0P01000000q0P010((((((y(X(9((((((y(X(9((((((y(X(9((((((y(X(9((((((y(X(9((((((y(X(9 & &08-- "- HH80(9Times New Roman-.  $2 yproduct_design_arm.5+056* 06*&0600*PTimes New Roman!-.  2 fproduct_design5+056* 06*&06 &  & &`X-- "-X`(9Times New Roman-.  %2 zdesign_feature_space5+%050 +0 5++0%50++ & &-- "-(9Times New Roman!-.  "2 tdesign_point_space5+%050606 0%60*+ & &0(-- "-(0(9Times New Roman-.  "2 design_curve_space5+%050+5+0+0%50++ & &x-- "-x(9Times New Roman!-.  %2 design_surface_space5+%050&5+ 0*+0%60*+ & &@ -- "- @(9Times New Roman-.  2  fusion (ABS) 5&06 E@6 & &ph-- "-hp(9 & &`--"Systemn-H` "-@--' & &=Times New Roman-.  2 class$( & &ph- "-hp & &p---Hp "---' & & H- "-H  & &(--(   "-@--' & &Times New Roman-.  2 F1memberC#C,$# & &`x- "-x`@Times New Roman!-.  02 membership_of_feature_spaceP+P5+*&5500 0 +06*+0%60*+ & &h-- "-h@ & &`---h` "-@--' & &=Times New Roman-.  2 class$( & &h- "-h & &Root Entry F8iY@)_ DCompObjnWordDocumentH ObjectPoolmuYmuY      !"#$%r()*+,-./0123456789:;<=gACFbHIJKLMNOPQRST}VWXYZ[\]^_`azcdefjhiklmnopqstuvwxy{|~ u  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstvwxyz{|}~SummaryInformation(` th a rectangular cross section. Victoria BaileyVictoria Bailey@@Ja@Y@+ @(EMicrosoft Word 6.015 FMicrosoft Word 6.0 Document MSWordDocWord.Document.69q_Oh+'00   4X |  (C:\MSOFFICE\WINWORD\TEMPLATE\NORMAL.DOTThe Parametric_product_space 10 metre rectangular beams is the set of beams designs of length 10 metres wits state, so that a full statement would be: each member of the class that is Product_design to specification ABC, when unloaded and at 20 degrees Celsius; is also a member of the class that is Property 10 metre long bridge beam. However if this precision is not required, a direct association between the Product_design and the Property implies that a each member of the Product_design has the property at each state throughout its life. It is possible to record that the beam has an average density of 4000 Kg m-3. In reality, this property also depends upon the state of the beam. If the average density is more or less independent of state, then it is possible to make an imprecise statement by a direct association between the Product_design and the Property. It is possible to record that the beam has a density 4000 Kg m-3. In reality, this property varies from point to point within the beam and from state to state of the beam. If the beam is more or less homogenous (at the scale of interest) and the de-HHQ "-b/--' & &LH- $LLHHTTT "--TTTT T$T+TDTKTdTkTTTTTTTTTT T$T+T@X@_@x@@@@@@@@@@@@8@?@X@_@x@@@@@@@@@@@@8@?@X@_@x@@@@@@@@@@@@8@?@X@_@x@@@@@@@@@@@@8@?@X@_@x@@@@@@@@@@@@8@?@X@_@x@4- tmTM4- |u\U<5|u\U<5|u\U<5|u\U<5|u\U<5|u\U/Times New Roman0-.  .2 aproduct_feature_space_arm.5+056* 0 +0 5++0%50+*00+PTimes New Roman!-.  2 nfusion 5&06 & &L "- IIL & &\\-- "-\\UTimes New Roman0-.  62 space_for_property_distribution%60*+0 0+05+05+* 006& *56 06 & &l-- "-lU & &9---M9E  "-r--' & &Z Times New Roman0-.   2 10 & &P - $P PX "--w7Xw'Hg'Hg'Hg'Hg'Hg'HgqP1qXXXXX|X]X<XXXXXX|X]X<XXXXXX|X]X<XXXXXX|X]X<XXXXXX|X]X<XXXXXX|X]X<XTimes New Roman!-.  .2 product_feature_space_arm.5+056* 0 +0 5++0%50+*00+PTimes New Roman0-.  '2 h+product_feature_space5+056* 0 +0 5++0%50+* & & "- HH & &$ -- $$  $, "--Kl ,Kl<[|<[|<[|<[|<[|<[||]<|]<,,,,,,,u,T,5,,,,,,u,T,5,,,,,,u,T,5,,,,,,u,T,5,,,,,,u,T,5,,,,,,u,T,5,,XTimes New Roman!-.  32 activity_and_state_space_arm.0+ 0 000560% 0 +0%50++00*P- "- $p & &kkm"ArialNe-.  (2 {disjoint, incomplete},(,-,(-C,,,"Arial-.  2 0nature,--- & & (h---h "-@  --' & &jP- "- $H j & &kkm"ArialNe-.  (2 {disjoint, incomplete},(,-,(-C,,,"Arial-.  2 0 membershipC,C,-(-, & &PX---XP` "-PP--' & &0d- "- $\(\P & &K"ArialNe-.  (2 P{disjoint, incomplete},(,-,(-C,,,"Arial-.  2 membershipC,C,-(-, & &7-- "- $7||`P & &{ "Arial-.  (2 `{disjoint, incomplete},(,-,(-C,,,"Arial-.  2  membershipC,C,-(-, & &`ph---p "-`0`--' & &h--(h "- --' & &0h8--h "-00 --' & &h--xh0 "- --' & &TNPP & -- ACTIVITY_OR_STATEACTIVITY39374142VqsP^es-AOqƥϧݧ(ϩv~έZe#$Ͱٰڰ,4Dp2@LMȴд:HQY|  GIDR^_߹źB>NbpݾmoU]cUJ]h`{:?FNrs*n /0;CGLXj|>I1CNITCDx#(/=EJFhUJU]c`FGPQghij   67@AWXYZ2345no/6FG^prU]cuP uDPuDXuDuDuD$uDDuDuDQ   <=QRSTUVW^ijoқMN!"p p p p p p p Kp Kp Kp p p p p p p p lIIIIII3Y$"Ld|Aɞ`a̠͠-.9¢-.?գp p p p p p p p p p p p p p p p p p 7 4  4 գ%&*+pq8)  grLMjp p p p p p p p p p p p p p p p p p p p  7 4  4 -lέϭde3CDpq @ֹ :;Zp p p p p p p p p p p p p p p p p p p p p p p p p p   4&nsity is more or less independent of state, then it is possible to make an imprecise statement by a direct association between the Product_design and the Property. If the beam is not homogenous (being reinforced concrete, say), then a direct association makes an untrue statement. A property variation with position T to specification ABC reinforced concrete. The density at a point within the product design is: 7000 Kg m-3 for a point within the reinforcement; and 2500 Kg m-3 for a point within the concrete. 16DESIGN_POINT_SPACE #107 = ,,,, 18PROPERTY_DISTRIBUTION 19SPACE_FOR_DISTRIBUTION (#106, #108); #110 = PROPERTY_FUNCTION (# , 4.AFEATURE_ 4.A physical function; and.lifetime of bridge beam the description of the range by the real interval from 100 to infinity; #104 = MATHS_VALUE (the real interval from 100 to infinity); #105 = IDENTIFICATION_OF_PROPERTY (#103, #104);61made computer interpretable, is supported by the Maths value application module, and NOTE - ^^^^^^^^_____ _F_G_H_K_S_Y_[_^______ `` `!`?``````````````````aa a,a/a5a6aCaEaPaQaRaWa\agawaxa~aaaaaab(b)bbbbbbbbbbbbbbb ccPcTcXcYcccccUU]cbccccccdd dddUdVdYdidzddddddddddddddddeee!e#eWeXebecegeheiejeoepeqere|eeeeeee!f"f>fOfPfVf^fiffffffffffff%g*gZg[gggrgsgtgug}ggggggggggggh!h(h)hU]cUb)h>h^h_h`hhhhhhhhhhhhhhhiii/i0iQi_i`iaidiriuiviiiiiiiiiiiiiiiii5jCjRjSjVjdjgjhjijjj7k8k9k:kikkklkmkkkkkkkkkkkkkkk lllll-lNl\l]l^lalolrlslllllU]cUbp---hp "---' & & X- "-X  & & ((--(  "- @ --' & & & - $  ( "--Gh(Gh0Op0Op0Op0Op0OpqP1qP1(((h(I((( (((((h(I((( (llllllllll m8mFmOmWmfmgmzmmmmmmmmmmmmmmmmnnnnn n nn8nq?qBqPqSqTqUqzq{qqqqqqqqhUdqqqqqqrrrrrrr&r'r(r)r>r?r@rArYr\rcrerfrrrrrrrrrrrrrrrrrrrrrrrrs!s"s)s6s7s]s^sasssssssssssssssss6cstxyz{|ق݂ނ%&'*?uPU]cha^ ___?`@```DaEaabbbccccddXece=f>ffh0iiii8k9kkkp p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p   4 7 4 kk-lllmooq=qqqrrrr'r?rfrrrrrrrrrr"sass|r΃<p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p   4&relationship between the identification of the propertby the real interval from 100 to infinity and the concept of year 7 The ARM instances that record: the density distribution is with respect to points within the beam; and each point within the distribution corresponds to a density value (i.e there is a function from the distribution space to the density space), are as follows: 89FEATURE_SPACE_FOR_PRODUCT_DESIGN (#108, #101);1011PROPERTY_102110, #113); #113 = PROPERTY_SPACE (density);The property function can be described by a mathematical function that has: a domain that is a parameterisation of the points within the beam, such as a 3D mesh; and a range that is an identification of the density space (i.e. the set of positive reals). The ARM instances that record: the description of the property function by the mathematical function; and the existence of the mathematical function, are as follows: 14MAPPING_OF_PHYSICAL_FUNCTION (#112, #115); #115 = MATHS_FUNCTION (my function over my mesh); functionfunctionmade computer interpretable is supported by the Maths function application module, and NOTE - relationship between the mapping of the physical function to the mathematical function and: the parameterisation (or identification) of points within the beam by the mesh; and the identification of density values with respect to the Kg m-3 scale, Physical function mapping Possession of a property distribution by a product design or by a state The ARM instance that records: the loose statement that the each beam manufactured to the design has the density distribution throughout out its life, is as follows: 17POSSESSION_OF_PROPERTY (#101, #110); Alternatively, it is possible to record the precise statement that: each beam manufacture to the design, has the density distribution in its as supplied state, when unstressed and at 20 degrees Celsius, by ARM instances as follows: 18STATE (as supplied, unstresses and at 20 degrees Celsius); #119 = STATE_ASPECT_OF_PRODUCT_DESIGN (#118, #101); #120 = POSSE&`ph---p "-`0`--' & &h--(h "- --' & &0h8--h "-00 --' & &h--xh0 "- --' & &TNPP & -- Properties of psies and states20thuse of the EACM modules to record information about the properties of a product, activity or state. A property can be a property of a whole product, activity or state. Alternatively, a property can be somethHKfhu v    W q g{h^p('Ya=it b!t!!@"E"##$ $z$$/&F&t&u&(*T,Y,`,n,v,{,-.w/x////////uDuD>U]cUJ]hU]cU]c uD@2U////////00%0&0<0=0>0?0g0h0q0r0000000000111B1C1L1M1c1d1e1f11'2(2.2/212225262CCCC C"C$Ch\I Z k  U   V W q r [ p p p p p p p p p p p p p p p p p p p p   4 [ } ./Y,-I.ghMN|>yp p p p p p p p p p p p p p p p p p p p p p   4 7 4 y@hiV>TU,<=Xgp p p p p p p p p p p p p p p p p p p p p  4#Z1AB`>??@_׽NOrsۿ0w:p p p p p p p p p p p p p p p p p p p  7 4  4 :6SPKLp -vw45Pp p p p p p p p p p p p p p p p p p p  7 4  4 P}'XSqr`%Vgp p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p   4&Times New Roman0-.  *2 B#activity_or_state_space0+ 0 000+0% 0 *0&50+* & &b  "- HH b & & L-- "-L , & &---  "-_"--' & &--xp  "-_"--' & & 8- "-8 " & &,| -- "- |,"Times New Roman0-.  !2 D%physical_function560%*00 56* 05 & &|L-- "-L|" & &A8---P8A "-R --SSION_OF_PROPERTY (#118, #110); statethe identification of the state; classification of the state as an as supplied state;temperature distribution property possessed by the state; stress distribution property possessed by the state; the relationship of the state to the manufacturing activity; the relationship with previous specifications or designs of the state. Possession of a property by a state A designer or analyst can specify or predict information about the reinforced concrete beam after 50 years ' & & :Times New Roman0-.  2 domain,(C(- & &lL- "-Ll & &A8---@8A "-R --' &ܥe= e62H ]XnXn^ ^ ^ ^ ^ j _ x x x x Dy j CVz z { { { { { { | | | | &| ~ / 5 T M ^ { "$({ { { { M { ^ ^ { 8z etermining that a bridge beam has reached the end of its life. Using the terminology of the ARM for this part of ISO 10303, the standardisation body defines a Property_space. The Property_space lifetime of bridge beam is a class that has individual properties, such as a bridge beam lifetime of 100 years, as members. perty space12PERTYSPACEperty_spacea dictionary of property types.perty spaceproperty space a text definition of the property space with references;source of the property space definition; previous versions of the property space.This information is addressed by ISO 13584, and is accessed from the EACM by the Property dictionary application module. Length of bridge beam is a Property_space. This property space is defined by a standardisation body that specifies: the features of the beam that are used to measure the length (is it the overall length of the beam or the distance between the bearing surfaces?); the state of the beam when the length is measured (e.g. at what temperature). Density is a Property_space. This property space has a fundamental physical definition. A point within a volume of matter at a state possesses a density. Average density is a Property_space. This property space has a fundamental physical definition. A quantity of matter, curve, surface or volume, at a state possesses an average density. A property The Property bridge beam lifetime greater that 100 years is a class which has individual bridge beams as members. A bridge beam is a member of the class if it has, or is predicted to have, a life time in the range. NOTE - The distinction between properties that are predicted and those that are actually observed can be made using the Possession of property validity application module. range of bridge beam lifetimes from 100 years to infinity; andthe relationship of the range to the concept of lifetime of bridge beam13PROPERTY_RANGE104MEMBERSHIP_OF_PROPERTY_SPACE123property range is described by the instance of valuethat is the real interval from 100.0 to infinity. The description of a property is supported by the Property identification application module, and is not within the scope of this discussion. Possession of a property by a product designA to specification ABC has a bridge beam lifetime greater that 100 years. This statement means that: each member of the class that is Product_design to specification ABC; is also a member of the class that is Property bridge beam lifetime greater that 100 years. NOTE - The specification that each has the property may not be true. It may be that 99% of beams that are members of to specification ABC have a lifetime longer than 100 years. Statistical and probabalistic information about the possession of a property is supported by the Possession of property statistics and probability application module. seach member of the beam design has the property, 15POSSESSION_OF_PROPERTY#101, #103It is possible to record that the beam has a length of 10 metres. In reality the length of the beam depends upon i &8Times New Roman0-.  2 t3range$(,($ & &,\ - $,\,  \44d4 "--44444$4C4d4444444St((((h(I((( (((((h(I((( (((((h(I((( ((((@ Times New Roman-.  $2 iproduct_design_arm.5+056* 06*&0600*PTimes New Roman!-.int, incomplete},(,-,(-C,,,"Arial-.  2 dimensionality,C,-(,-,( & &9L- "-L9 & &L-- "-L"Arial  2 fclassification+0&% +0 05 & & "- HH &  & &p-- "-p( & &&-- $ "--'Hg'Hg0Op0Op0Op0Op0OppQ0pQ0hI( hI( hI( hI( hI( (Times New Roman-.  $2 iproduct_design_arm.5+056* 06*&0600*PTimes New Roman!-.  *2 FUspecialisation_of_class%6*+0%0 0500 0+0%% & &` "- HH` &  & &x---Hx@  "- --' & &- "-Times New Roman-.  $2 ddesign_volume_space5+%050005P+0%60*+ & & 0-- "-0  & & H-- "-H  & & -- "-  & & @-- "-@  & &0P8h---hP  "-@0p 0--' & &fm"Times New Roman-.   2 10 & &`X- "-X`p 0Times New Roman!-.  *2 (physical_topology_space560%*00 0500000%60*+ & &Xh-- "-hXp 0 & & @(---@  "-  --' & &@h- "-h@ & &@PHx--????P? "-o??????/?of use. The State that is after fifty years of useis a class that has individual reinforced concrete beams after 50 years of use as members. This State has a Property that is 50 year of use. The ARM instances that record: the existence of the state and its relationship to the product design; the existence of the property, its description by the number 50, and its membership of the length of use property space; and the possession of the property by the state, are as follows: 21STATE (after 50 years of use); #122 = STATE_ASPECT_OF_PRODUCT_DESIGN (#121, #101); #123 = PROPERTY_SPACE (length of use); #124 = PROPERTY (); #125 = MEMBERSHIP_OF_PROPERTY_SPACE (#123,#124); #126 = IDENTIFICATION_OF_PROPERTY (#124, #127); #127 = MATHS_VALUE (the real 50); #128 = POSSESSION_OF_PROPERTY (#121, #124); Possession of property by an 13.A,,HP DeskJet 870C Series7 d,,4St4St4St4St4St 4 S t          d E $      d d d d d d dt dU d4 d dddddtdUd4ddddddtdUd4ddddddtdUd4ddddddtdUd4ddddddtdUd4ddddddtdUd4d4 Times New Roman!-.  ?2 _%product_activity_and_state_space_arm.5+056* 00+ 0 000650% 0 +0%60*+00+OTimes New Roman0-.  2 vmappingP05660 & &,  "- II , & & \ X-- "-X\ d4 & &  (---(h `  "-/  --' & & m Times New Roman0-.   2 Y10 & &  - $    "--3Ts3Ts'Hg'Hg'Hg'Hg'Hg'HgmL- mL- time. A strength of bridge beam property is possessed by a particular state of a bridge beam. The definition of a property may specify some information about the environment in which it is measured, but this does not remove the need to be precise about the state of the object that possesses the property. A prediction of the strength of a beam after 50 years implies a prediction of a test on an individual beam that is simultaneously: in the state after 50 years use; and in the state specified for the property strength of bridge beam. The state specified for the property is implicit in the definition of the property, but the state after 50 years of use must be recorded. This give a complete possession of property statement of the form:when in state after 50 years of use50 tonne bridge beam strength It would be correct to insist that a length of bridge beam property cannot be possessed by a Product_design that is a beam, but only by a State. However, in practice engineers make looser statements such as: , is 5tonne bridge beam strength for all parts of its life of current interest. In order to support such a looser statement, a Possession_of_property is valid between a Product_design and a Property, even if that property is defined only for a State. Neglecting variation with position An is possessed by the beam as whole for a particular state. As indicated in the preceding paragraphs, a possession of property between: the Product_design that is the beam; and the Property that is the average density of 4000 Kg m-3, indicates that the beam has the average density for all parts of its life of current interest. An average density property is possessed by a state of as a whole, and so does not vary from point to point within it. A density property is possessed by a state of a point within the beam. It would be correct to insist that a density property cannot be possessed by a Product_design that is a beam or by a State of a beam, but only by a State of a point within a beam. However, in practice engineers make looser statements such as: point within the beam at 20 degrees Celsius has the density of ; This is supported by a Possession_of_property between the State and the density Property. each point within the beam has a density of 4000 Kg for all states of interest. This is supported by a Possession_of_property between the Product_design and the density Property. both these statements are untrue. Instead the State or Product_design must be associated with a density Property_distribution. NOTE - The concept of density at a point is itself a loose statement at the next level of precision, because matter is not a continuum if your scale is small enough. This discussion is not yet within the scope of the EACM. distribution with respect to re is a property distribution with respect to position such that the density is: The Property_distribution density variation in 5.Apredicted is a class that has individual beams as 6!8!Z!_!d!x!!!!!!!!!!!!!!!" " " "#"$"&"'":""""""""""""#######8#9#:#;#>#G#`#a#v#w############$$$$/$0$1$6$8$=$>$J$L$M$S$^$_$`$a$$$$$$$$$%% % %.%/%Ud/%1%2%B%E%N%j%m%p%%%%%%%%%%%%%&&&&&<&D&|&~&&&&&&&&&&&&&&&&&&&''')'5'?'A'D'M'f'g'n'o'''''''''''''''''(( ( (6(7(8(N(d(s(w(x(y(z(((((((((((hUd s within the distribution and the states within the loading activity; the correspondence between points within the distribution and points within the loading beam; the existence of the stress space; and the mapping between each state for a point in the distribution and a stress value (i.e. the function from the distribution space to the stress space), are as follows: #151 = PROPERTY_DISTRIBUTION (); #152 = SPACE_FOR_PROPERTY_DISTRIBUTION (#151, #153); #153 = PROPERTY_DISTRIBUTION_SPACE (4); -- complete space #154 = PROPERTY_DISTRIBUTION_SPACE (3); -- spatial component #155 = PHYSICAL_SPACE_DESIGN_FEATURE_COMPONENT (#154, #153); #156 = PROPERTY_DISTRIBUTION_FOR_FEATURE_SPACE (#154, #108); #157 = PROPERTY_DISTRIBUTION_SPACE (1); -- state component #158 = PHYSICAL_SPACE_DESIGN_FEATURE_COMPONENT (#157, #153); #159 = PROPERTY_DISTRIBUTION_FOR_FEATURE_SPACE (#157, #140); #160 = PROPERTY_SPACE (6); - stress #161 = PROPERTY_DISTRIBUTION_FUNCTION (#153, #160); The Property_distribution_space has 4 dimensions - 3 spatial dimensions within the beam, and 1 state dimension within the activity. These two components of the Property_distribution_space are separated. The spatial component is mapped by a Property_distribution_for_feature_space on to the set of points within the beam. The state component is mapped by a Property_distribution_for_feature_space on to the set of states within the activity. The property distribution function can be described by a mathematical function that has: a domain that is a Cartesian product of the parameterisation of the points within the beam (perhaps a unit cube or a finite element mesh) and a parameterisation of the states within the loading activity (perhaps a unit interval); and a range that is an identification of the stress space (perhaps the set of real 6-tuples or the set of symmetric 3(3 matrices). The ARM instances that record: the description of the property function by the mathematical function; and the existence of the mathematical function, are as follows: #162 = MAPPINP?o?p?--' & &\K7Times New Roman-.  2  dimension,B$,(, & &`&`- "-`p?Times New Roman!-.  2 INTEGER%F@@J@F & &08--- "- 00--' &  & &0p(x--(0  "-pp@--' & &0(--(0  "-@--' & &0(--H(@0  "-@--' & &0`(h--(0  "-``@--' & &bTimes New Roman-.   2 `10 & &F]Times New Roman!-.   2 10 & &FTimes New Roman-.   2 10 & &6Times New Roman!-.   2 p10 & &@px---??o@ "-o_ooooooo@--' & &- "-o@Times New Roman-.  2 H subset_of_%65&* 00 0Times New Roman!-.  *2 (physical_topology_space560%*00 0500000%60*+ & &Times New Roman-.  2 Vwhole:,($ & &P-- "-Po@ & &---x0 "-p--' & &yTimes New Roman-.   2 Vpart,($ & &PP- "-PPp & &---( "-p--' & &`H&`H- $`HH`h "--(Gh(@@@@@@@@0@O@p@@@@@@0@O@p@@@@@@0@O@p@@@@@@0@O@p@@@@@@0@O@p@@@@1qP1qhhhhhIh(h hhhhhhhIh(h hhhhhhhIh(h hhhhhhhIh(h hhhhhhhIh(h hhhhpTimes New Roman-.  $2 3iproduct_design_arm.5+056* 06*&0600*PTimes New Roman!-.  2 class+0&% & & "- HH &  & &(H-- "-H(h & &@---x@p  "---' & &]Times New Roman-.   2 P10 & &TNPP & ---E:v^bFfX5']] m"3&P  & &$TNPPMicrosoft PowerPoint & TNPPf & &TNPP P l145&- "- "-"Arial-.  2 ce ProductDesign@ 5650E6056"Arial-.  *2 m(from ProductDesignARM)  5P@ 5560F5055@FP  & &x "-- $x & &--"Systemn-h  "-P--' & &);="Arial-.  (2 c{disjoint, incomplete},(,-,(-C,,,"Arial-.  2 gusage,(-,- & &P- "-PP"Arial-.  2 ceClassificationE5000656"Arial-"Arial-.  *2 M(from ProductDesignARM)  5P@ 5560F5055@FP  & &@&@p-- "-p@P & &@x-- "-x@P"Arial-.  "2 ,DesignFeatureSpaceE6056:655 6@5506 & &@---H@ "- --' &  & &08-- "-p0P 0--' & &--p "-pP --' & & (--?? "-U5f--' & & &P - "- P & & X-- "-X "Arial-.  12 FeatureSpaceForProductDesign;555 6@5605;5 @ 5650E6056 & & ---(  "-0P--' &  & & & - "- P & & -- "- P"Arial-.  2 l0Fusion;5065 & & --- @ "-0P--' &  & &> "- $> & &--. "-P--' & &;%="Arial-.  (2 {disjoint, incomplete},(,-,(-C,,,"Arial-.  2 usage,(-,- & & 8(---?? "- _00--' & &V&VP- "-PV0 & &VX-- "-XV0"Arial-.  +2 MembershipOfFeatureSpaceP5P65 055K:655 5@6506 & &V---(V "- --' &  & &0~ "Arial-.  2 jmemberC,C,- & &0+"Arial-.   2 j* & &0bp"Arial-.  2 3jclass(,(( & &0;"Arial-.   2 j* & &~ "Arial-.  2 whole:,-, & &w+"Arial-.   2 * & &p"Arial-.  2 3class(,(( & &w;"Arial-.   2 * & &Pp- "-pP"Arial-.  2 ClassE500"Arial-"Arial-.  *2 VM(from ProductDesignARM)  5P@ 5560F5055@FP  & &>X "-- $>PP & &%"Arial-.  (2 {disjoint, incomplete},(,-,(-C,,,"Arial-.  2  membershipC,C,-(-, & &@@HH---H@ "-@@@@--' & & 8& 8- "-8 @@ & & -- "- @@"Arial-.  2  DesignPointSpaceE6056@55@5506 & & --- ` "-P--' &  & & &P - "- P & & X-- "-X "Arial-.  2 DesignCurveSpaceE6056E6 05@5605 & & ---(  "-P--' &  & & 8& 8- "-8  & & -- "- "Arial-.  "2 DesignSurfaceSpaceE6056@5 506@5506 & & --- ` "-P--' &  & & &P - "- P & & X-- "-X "Arial-.  !2 DesignVolumeSpaceE6056@55P5@6506 & & ---(  "-P--' &  & &X "- $X & &--H "-@0--' & &E"Arial-.  (2 `%{disjoint, incomplete},(,-,(-C,,,"Arial-.  2 %dimensionality,C,-(,-,( & &P---.P "---' & &V&V- "-V"Arial-.  "2 Ldimension: Integer5P550565556  & &V-- "-V"Arial-.  '2 PhysicalTopologySpace@50005;655550@6506 & &V-- "-V &  & & "-- $F & &"Arial-.  (2 P{disjoint, incomplete},(,-,(-C,,,"Arial-.  2  membershipC,C,-(-, & &FNH---H "-FF--' & &pX--Xhp  "-0 --' & &px-- "-pp@--' & & (-- "-  @--' & &--H "-@--' & &PX-- "-PP@--' & &--@ "---' & &H--HX "-@ --' & &H--H` "-@ --' & &@H-- "-@`@P--' & &."Arial-.  2 whole:,-, & &K}"Arial-.   2 @* & &."Arial-.   2 :part,- & &}"Arial-.   2 @:* & &---?? "-Ev%V--' & & H&H- "-H & & -- "- "Arial-.  32 SubsetOfPhysicalTopologySpace@5605K@60005:656560@5506 & &---p "- @--' &  & &- "-@"Arial-.  '2 3SpecialisationOfClass@56060655KE600"Arial-"Arial-.  *2 }(from ProductDesignARM)  5P@ 5560F5055@FP  & &n "-- $n & &U"Arial-.  (2 5{disjoint, incomplete},(,-,(-C,,,"Arial-.  2 `5 membershipC,C,-(-, & &@---^@ "---' & &TNPP & --zR:] HV%5(bb )F&  & &$TNPPMicrosoft PowerPoint & TNPPf & &TNPP  VB345& -Times New Roman4-.  2 whole:,($ & &08&08- "- $0088888 "--88'8H8g888888'8H8g8888?` ?` ?` ?` ?` ?` 000p0Q00000000p0Q000000yX9yX9yX9yX9yX9yX9 & &0 8H-- "- HHH8 09Times New Roman -.  2  activity_arm.0+ 0 000+OTimes New Roman4-.  2 activity0+ 0 0 &  & &08-- "-809Times New Roman -.  *2 TSactivity_or_state_space0+ 0 000+0% 0 *0&50+* & &p-- "-p9 & &(--"Systemn-(H "-@--' & & Times New Roman4-.  2 pclass$( & &p`- "-`p@ & &h---hH "---' & & Ph - "-h P  & & --x p  "-  --' & &#Times New Roman4-.  2 1memberC#C,$# & &` - "- ` Times New Roman -.  12 membership_of_activity_spaceP+P5+*&5500 00+ 0 00%60*+ & &-- "- & &(---(h "-@--' & & Times New Roman4-.  2 pclass$( & &`- "-`@ & &h---hh "---' & &X(- "-(X & & (--  "-  --' & &&- $ "--'Hg'Hg0Op0Op0Op0Op0OppQ0pQ0hI( hI( hI( hI( hI(  Times New Roman4-.  $2 iproduct_design_arm.5+056* 06*&0600*PTimes New Roman -.  2 classification+0&% +0 05 & & H "- HHH &  & &FrTimes New Roman4-.   2 010 & & rTimes New Roman -.   2 0P 10 & & (h& (h-- $  h(h(((( "--(((('(H(g(((((('(H(`(`(`/`P`o``````/`P`o``````/`P`o``````/`P`o``````/`P`o``````/`P`o`````` ` Q 0      p Q 0      iH)iH)iH)iH)iH)iH)Times New Roman4-.  .2 Sproduct_feature_space_arm.5+056* 0 +0 5++0%50+*00+PTimes New Roman -.  *2 (physical_topology_space560%*00 0500000%60*+ & & ( "- HH(  &  & &p &p -- $pp xxx "--xxxxx(x/xHxOxhxoxxxxxxxxxxx(x/xHxOxhxoxxx '@G`g '@G`g '@G`g   ' @ G ` g            ' @ G ` g       p i P I 0 )           p i P I 0 )         x q X Q 8 1           x q X Q 8 1   xqXQ81xqXQ81xqXQ81xx)Times New Roman4-.  .2 product_feature_space_arm.5+056* 0 +0 5++0%50+*00+PTimes New Roman -.  2 fusion 5&06 & &p H "- HHH p &  & &   -- "- xTimes New Roman4-.  =2 -$activity_or_state_space_for_activity0+ 0 000+0% 0 *0&50+*0 0+00+ 0 0 & &-- "-xTimes New Roman -.  2 m state_space% 0 +0%60*+ & &PH-- "-HPxTimes New Roman4-.  2 5activity_space0+ 0 00%60*+ & &`X-- "-X`x & &X-- "-Xx & &---80  "-p--' & &}82Times New Roman4-.   2 10 & & .(---.  "- : --' & &P--P  "---' & &P--80P  "---' & &008&008- $0008808888 "--W8x88888888W8x8888888?` ?` ?` ?` ?` ?` 0000000`0A0 000000`0A0888888y8X89888888y8X89888888y8X89888888y8X89888888y8X89888888y8X89Times New Roman4-.  .2 product_feature_space_arm.5+056* 0 +0 5++0%50+*00+PTimes New Roman -.  %2 vzdesign_feature_space5+%050 +0 5++0%50++ & &08 "- HH80 &  & &  -- "- 89Times New Roman4-.  F2 4x*physical_space_activity_or_state_component560%*00%60*+00+ 0 000+0% 0 *0+0P506*6  & & P H-- "-H P 89Times New Roman -.  B2 'physical_space_design_feature_component560%*00%60*+05+%050 +0 5++0*0P605+5  & & Times New Roman4-.  2 pwhole:,($ & &p-- "-p89 & &---H "-0--' & &-Times New Roman4-.  2 class$( & &p - "- p0 & &(---(H "---' & &; Times New Roman4-.  2 whole:,($ & &p`- "-`p & &X---XH "-0--' & &]Times New Roman4-.  2 class$( & &p8- "-8p & &@---H@ "-`--' & &` -- `  "- --' & & h 8- "-8h  & &` -- `  "- --' & & h - "-h   & &`  --8 0`  "- --' & &8- "-8 & &88-- "-88 & &--  "-P --' & &p(x--(  "-pp@--' & &|(RTimes New Roman4-.   2 10 & &TNPP & ---z>:];%5!bb ?&J@  & &$TNPPMicrosoft PowerPoint & TNPPf & &TNPP @J  B345&@h- "- "-h@"Arialn-.  2 Activity@000"ArialNe-"Arialn-.  "2 &(from ActivityARM)  5P@000@EP  & &x`( "-- $`x  & & --"Systemn-h  "-`--' & &)"Arialn-.  (2 c{disjoint, incomplete},(,-,(-C,,,"ArialNe-.  2 Pgusage,(-,- & &P@h- "-h@P"Arialn-.  2 eClassificationE5000656"ArialNe-"Arialn-.  *2 &M(from ProductDesignARM)  5P@ 5560F5055@FP  & & H&H-- "-H & & -- "- "ArialNe-.  %2 ActivityOrStateSpace@000K @66@5605 & &---p "---' &  & &0`8(--(` "-00--' & &`(--(`p "---' & &px--??o "-oUoooo5ofoo--' & & & - "- o & & -- "- o"Arialn-.  62 \ActivityOrStateSpaceForActivity@000K @66@5605;5 @000 & & ---x 0 "-0P--' &  & &>`( "- $> ` & & --. "-`--' & &%"Arialn-.  (2 {disjoint, incomplete},(,-,(-C,,,"ArialNe-.  2 Pusage,(-,- & &p8x---??o "-oo o_oooo0o0--' & &V&V- "-Vo0 & &V-- "-Vo0"Arialn-.  -2 \(MembershipOfActivitySpaceP5P65 055K@000@5506 & &V---x0V "- --' &  & &0p"Arialn-.  2 3jmemberC,C,- & &0{"ArialNe-.   2 j* & &0>b"Arialn-.  2 jclass(,(( & &0M"ArialNe-.   2 j* & &p"Arialn-.  2 3whole:,-, & &w{"ArialNe-.   2 * & &>"Arialn-.  2 class(,(( & &wM"ArialNe-.   2 * & &P`&P - "- P & &P`(-- "-(`P"Arialn-.  2 ActivitySpace@000@5605 & &PPX---P "-PP--' &  & &P&P- "-PP & &P-- "-PP"Arialn-.  2 \ StateSpace@55@6505 & &P---x0P "---' &  & &u"Arialn-.  (2 U{disjoint, incomplete},(,-,(-C,,,"ArialNe-.  2 `8dimensionality,C,-(,-,( & &@ h- "-h @"Arialn-.  2 0Fusion;5065"ArialNe-"Arialn-.  32 &(from ProductFeatureSpaceARM)  5P@ 5560;655 5@6506@EP  & &h "-- $h & &---P "---' & &px-- "-pp--' & &x--xP "-p--' & &--X "---' & &`h- "-h`"Arialn-.  '2 S_PhysicalTopologySpace@50005;655550@6506"ArialNe-"Arialn-.  32 (from ProductFeatureSpaceARM)  5P@ 5560;655 5@6506@EP  & &-- "-"ArialNe-.  "2 DesignFeatureSpaceE6056:655 6@5506"Arialn-"ArialNe-.  32 (from ProductFeatureSpaceARM)  5P@ 5560;655 5@6506@EP  & &p (&p (-- "-( p & &p -- "- p"Arialn-.  ?2 |%PhysicalSpaceActivityOrStateComponent@50005A5506@000J @56E5P65565 & &p --- Pp "-p--' &  & &p &p - "- pp & &p -- "- pp"Arialn-.  <2 <#PhysicalSpaceDesignFeatureComponent@50005A5506E5056:655 5F5P56565 & &p ---X p "-p--' &  & &x--??pp "-5fFp--' & &@--@P "---' & &=P"Arialn-.  2 *whole:,-, & &["ArialNe-.   2 ** & &""Arialn-.  2 c*class(,(( & &k "ArialNe-.   2 ** & &PxX---??ppO "-O5OfOOOOFOpO--' & &--P "-`@--' & &=`"Arialn-.  2 #*whole:,-, & &P@X---@ "-P P--' & &"Arialn-.   2 ** & &n""ArialNe-.  2 *class(,(( & &+"Arialn-.   2 ** & &E-F"ArialNe-.  (2 `%{disjoint, incomplete},(,-,(-C,,,"Arialn-.  2 K membershipC,C,-(-, & &(h "-- $(`p & &Ppx---P "-pp--' & & X--X( "-  --' & & --(  "-@--' & & --8 "-`  --' & & P X--  "-P` P --' & &TNPP & --::` Ho6(TT B9&  & &$TNPPMicrosoft PowerPoint & TNPPf & &TNPP   V345& (H& (H- "- $ H(H(((( "--(('(H(g(((((('(@0@O@p@@@@@@0@O@p@@@@@@0@O@p@@@@@@0@O@p@@@@@@0@O@p@@@@@@0@O@p@@@@@0      p Q 0    iH)iH)iH)iH)iH)iH)Times New Roman -.  .2 cproduct_feature_space_arm.5+056* 0 +0 5++0%50+*00+PTimes New Roman-.  *2 (physical_topology_space560%*00 0500000%60*+ & & ( "- HH( &  & & ((-- "-(( )Times New Roman -.  +2 sphysical_topology_space_560%*00 0500000%60*+0Times New Roman-.  2 parameterisation50+0P+ *+&0 06 & &P-- "-P)Times New Roman -.  !2 Tbsubset_of_mapping%65&* 00 0P05660 & & (-- "-( )Times New Roman-.  +2 sphysical_topology_space_560%*00 0500000%60*+0Times New Roman -.  +2 parameterisation_element50+0P+ *+&0 060*+P*6  & &P  -- "- P)Times New Roman-.  '2 mapping_element (ABS)P056600*+P*6  E@5  & & H& H-- $H H  "--'Hg'@@@0@O@p@@@@@@0@O@p@@@@@@0@O@p@@@@@@0@O@p@@@@@ @0 @O @p @ @ @ @ @ @0 @O @p @ @ @ 0      p Q 0       i H )      i H )  iH)iH)iH)iH))Times New Roman -.  $2 c)product_design_arm.5+056* 06*&0600*PTimes New Roman-.  +2 class_of_physical_object+0&%00 0560%*0005 ++  & &  "- HH  &  & &`-- "-`Times New Roman -.  2 +derivation_of_5++00 0500 0Times New Roman-.  2 parameterisation50+0P+ *+&0 06 & &dTimes New Roman -.  2 PBL[2,?] sources5(((,$#$ & &`-- "-`Times New Roman-.  .2 tcomponent_parameterisation+0P505+5 060*0P+ *+%0 05 & &mTimes New Roman -.  2 03 component$(B-(,$, & &h}Times New Roman-.  2 @parameterisation,($(C##$((- & &hmTimes New Roman -.  2 0$derived,$$(#- & &px&px-- $pxxpx "--8Wx ?` ?` ?` ?` ?` ?` ?`ppppqpPp1ppppppxpxpxixHx)xxxxxxixHx)xxxxxxixHx)xxxxxxixHx)xxxxxxixHx)xxxxxxixHx)xxxxxxixHx)xxTimes New Roman-.  2 4state_arm.state% 0 +00+O& 0 * & &x "- <<x &  & &a(Times New Roman -.  2 imageC((# & &--"Systemn-@ "-@` --' & &A( Times New Roman -.  2 domain,(C(- & & @X - "-X @ ` & & ( --- "-@ ` --' & &a( Times New Roman -.  2  imageC((# & & `X - "-X ` ` & & ( h---h  "-  --' & &p - "- p Times New Roman -.  2  mapping (ABS)P05660 E@6  & &`(-- "-(` & & ---   "-`--' & &`- "-`` & &--  "-0--' & &@- "-@0 & &px--   "-p0p--' & &`(- "-(`0p & &h--hxp  "---' & &8(- "-(8 & &`--`  "- --' & &xH&xH- $HxHx "--8Wx8@@@@ @?@`@@@@@@ @?@`@@@@@@ @?@`@@@@@@ @?@`@@@@@@ @?@`@@@@@@ @?@`@@@@@@ @?@`@p@p1ppppppqpPp1ppppiH)iH)iH)iH)iH)iH)iH) Times New Roman -.  '2 activity_arm.activity0+ 0 000+O0+ 0 0 & & x "- <<x  &  & &px&px-- $pxxpx "--8Wx ?` ?` ?` ?` ?` ?` ?`ppppqpPp1ppppppxpxpxixHx)xxxxxxixHx)xxxxxxixHx)xxxxxxixHx)xxxxxxixHx)xxxxxxixHx)xxxxxxixHx)xxTimes New Roman-.  92 44!product_design_arm.product_design5+056* 06*&0600*P6*065+ 05+%05 & &x "- <<x &  & &h---Xh "---' & & 0- "-0  & &`hh--h "-``@--' & &@(- "-(@`@ & &p`x-- `  "-p p--' & &8- "-8 p & &--` "-`--' & &`8- "-8` & &h--h` "-@--' & & H- "-H  & &x--xp "-`--' & &phx--h "-pp--' & &p8- "-8pp & &8 --8   "-p --' & &pP- "-Pp & &8 --8   "-p --' & &p8- "-8p & &8 --8   "-p --' & &0 @8 -- @  "-0 0 --' & &AnTimes New Roman -.  2 *domain,(C(- & &`- "-`0 & & h---h @ "---' & &@- "-@ & &` -- "- `Times New Roman -.  "2 Relement_of_mapping++P*6 00 0P05660 & &-- "- & &LhTimes New Roman-.  2 class$( & &---X "-@P--' & &X- "-XP & &8Times New Roman -.  2 memberC#C,$# & &`h&`h-- $``hhhhh "--7hXhwhhhhhh7hXh`h`h`````` `?```````` `?```````` `?```````` `?```````` `?``````A `A hI( hI( hI( hI( hI( hhPTimes New Roman-.  $2 Iproduct_design_arm.5+056* 06*&0600*PTimes New Roman -.  2 classification+0&% +0 05 & &`@8 "- <<8@` &  & &P h&P h-- $PPh h XXX "--7XXXwXXXXXX7XXX`X`X`o``````/`P`o``````/`P`o``````/`P`o``````/`P`o````` `/ `P `o ` ` ` A       ` A    y X 9  yX9yX9yX9yX9yXXhTimes New Roman-.  $2 9product_design_arm.5+056* 06*&0600*PTimes New Roman -.  2   individual550560 & &P@ 8 "- <<8 @P &  & & & -- $   "--'Hg ?` ?` ?` ?` ? `       ? `          ` A         i H )      i H )  iH)iH)iH)iH)XTimes New Roman-.  2 KLmaths_value_arm.P0 5&0006*00+PTimes New Roman -.  2  maths_valueP0 5&0006* & &  "- <<  &  & & & -- $  ((( "--(('(H(g((((((((?` ?` ?` ?` ?` ?``A iH)iH)iH)iH)iH)iH)Times New Roman-.  2 Kmaths_space_arm.P0 5&0%50++00*PTimes New Roman -.  2  maths_spaceP0 5&0%50++ & &  "- << &  & &`8&`8-- $``88hhh "--hh'hHhghhhhhhhh ?` ?` ?` ?` ?` 0000000`0A0 00000)iH)iH)iH)iH)iH)i)Times New Roman-.  02 Kproducct_feature_space_arm.5+056*+ 0 +0 5+*0%60*+00+PTimes New Roman -.  2 fusion 5&06 & &`8 "- <<8` &  & &p(&p(-- $pp((xxx "--xx7xXxwxxxxxx x x      0 O p      0 O p      0 O p      0 O p      0 O p    `A xY8xY8xY8xY8xY8xxiTimes New Roman-.  $2 [Yproduct_design_arm.5+056* 06*&0600*PTimes New Roman -.  2 class+0&% & &p "- <<p &  & &P&P-- $PPXXX "--XXX8XWXxXXXXXXXo/Po/Po/Po/Po/Poa@!yX9yX9yX9yX9yX9yXXxTimes New Roman-.  $2 ;9product_design_arm.5+056* 06*&0600*PTimes New Roman -.  *2 %specialisation_of_class%6*+0%0 0500 0+0%% & &P "- <<P &  & &9}MTimes New Roman-.  2 swhole:,($ & &x(-- "-(xX & &@H--- "-@@--' & &MTimes New Roman -.   2 #part,($ & &((- "-((@ & &---P "---' & &TNPP & --z[:` Ho6(TT -3& F & &$TNPPMicrosoft PowerPoint & TNPPf & &TNPP   V345&- "- "-Times New Roman-.  !2 subset_of_mapping%65&* 00 0P05660 & &(--"Systemn-(@ "-0--' & &X--X@ "- --' & &X--X@ "---' & &X--X8 "---' & &@H--8H@ "-@@--' & &(--(` "-@--' & &@H--(H@ "-@@--' & &`- "-`@"ArialNe-.  2 cClassificationE5000656"ArialNe-"Arial-.  *2 (from ProductDesignARM)  5P@ 5560F5055@FP  & & H-- "-H @"Arial-.  2 pFusion;5065"Arial-"Arial-.  12 E(from ProductFeatureSpaceARM  5P@ 5560;655 5@6506@EP & & (H-- "-H(  @"Arial-.  2  MathsSpaceP550@6506"Arial-"Arial-.  %2 (from MathsSpaceARM)  5PP550@5605@FP  & &  H-- "-H @"Arial-.  2  MathsValueP550@665"Arial-"Arial-.  %2 (from MathsValueARM)  5PP550@556@EP  & &-- "-@"Arial-.  '2 S]SpecialisationOfClass@56060655KE600"Arial-"Arial-.  *2 (from ProductDesignARM)  5P@ 5560F5055@FP  & &P@ h-- "-h @P@"Arial-.  2 % Individual550655"Arial-"Arial-.  *2 &(from ProductDesignARM)  5P@ 5560F5055@FP  & &p-- "-p@"Arial-.  2 CClassE500"Arial-"Arial-.  *2 (from ProductDesignARM)  5P@ 5560F5055@FP  & &&-- "-@ & &-- "-@"Arial-.  2 lSubsetOfMapping@5605KP65555 & &---@ "-P--' &  & &--` "-0@--' & &--?? "-/Po--' & &n"ArialNe-.  2 whole:,-, & &G}"Arial-.   2 @* & &n"Arial-.   2 part,- & &}"Arial-.   2 @1* & &"Arial-.  2 cclass(,(( & &kK "Arial-.   2 * & &X"Arial-.  2 cmemberC,C,- & &kR "Arial-.   2 * & &`(&`(- "-(` & &`-- "-`"Arial-.  2 |eElementOfMapping@6P56KO65656 & &`---P` "- --' &  & & --??  "-?` --' & &@"ArialNe-.  2 zimageB-,- & &{M"Arial-.   2 * & &>b"Arial-.  2 domain,-C,, & &+{"Arial-.   2 * & & (- "-(  "Arial-.  '2 cPhysicalTopologySpace@50005;655550@6506"Arial-"Arial-.  32 U(from ProductFeatureSpaceARM)  5P@ 5560;655 5@6506@EP  & &---?? "- ?`--' & & ( (--(  "- 0 --' & &r "ArialNe-.  2 imageB-,- & & ( M"Arial-.   2  * & &>( "Arial-.  2 domain,-C,, & & +( "Arial-.   2 * & & - "- 0 "Arial-.  '2 cXClassOfPhysicalObjectE500K@60006K560"Arial-"Arial-.  *2 (from ProductDesignARM)  5P@ 5560F5055@FP  & &pPx&px-- "-xp0 & &pP-- "-Pp0 "Arial-.  2 XMappingP56565 & &p@H---p "-@0@--' &  & &PP x&P x- "-x P@ & &PP -- "- PP@"ArialNe-.  2 MappingElementP56565@5P56 & &P@ H--- P "-@@--' &  & & ( --??  "- @ _        --' & &` &P - "- P & &` X-- "-X ` "ArialNe-.  '2 _PhysicalTopologySpace@50005;655550@6506"Arial-.  *2 .EParameterisationElement@5 6P55 0556@5P65 & & ---(  "-@--' &  & &`H&PH- "-HP@ & &`HX-- "-XH`@"ArialNe-.  '2 PhysicalTopologySpace@50005;655550@6506"Arial-.  2 .5Parameterisation@5 6P55 0556 & &H---(H "---' &  & &- "-"ArialNe-.  2 0State@55"Arial-"Arial-.  2 8(from StateARM)  5P@66@EP  & &-- "-"Arial-.  2 cActivity@000"Arial-"Arial-.  "2 (from ActivityARM)  5P@000@EP  & &@h-- "-h@"Arial-.  2 e ProductDesign@ 5650E6056"Arial-"Arial-.  *2 &m(from ProductDesignARM)  5P@ 5560F5055@FP  & &0x&0x-- "-x0 & &0x-- "-x0"Arial-.  12 \[DerivationOfParameterisationE6 0565K@5 5P66 0565 & &0x---xx00 "---' &  & &@H-- "-p@@--' & &@"ArialNe-.  2 sz 1 derived,,-(-, & &@Q"Arial-.  2 cz 2..* source,(,-(- & &M"Arial-.   2 :* & &"Arial-.   2 s:1, & &@---??@@@ "-_--' & &--?? "-0Op--' & &p--p` "---' & & 0~- "- $v(v  & &K  "ArialNe-.  (2 p{disjoint, incomplete},(,-,(-C,,,"Arial-.  2 usage,(-,- & &X---X@ "-0--' & &`- "- $` & &k[]"ArialNe-.  (2 {disjoint, incomplete},(,-,(-C,,,"Arial-.  2 nature,--- & &0`8---` "-00--' & &`t- "- $lXl00 & &{"ArialNe-.  (2 `{disjoint, incomplete},(,-,(-C,,,"Arial-.  2 usage,(-,- & &h---h@ "-@--' & &pG_OF_PHYSICAL_FUNCTION (#161, #163); #163 = MATHS_FUNCTION (my function from R4 to R6); NOTE - The relationship between the mapping of the physical function to the mathematical function and: the parameterisation (or identification) of points within the beam; the parameterisation (or identification) of states within the activity; and the identification of stress values with respect to the MPa scale and using a vector encoding as ((xx, (yy, (zz, (xy, (yz, (zx,), is supported by the Physical function mapp-.  2 >] PropertyRange@ 565 0E6556 & &H---\H "---' & &Q08--Q "-00--' & &Ping application module, and is not within the scope of this discussion. NOTE - The definition of mathematical functions between multi dimensional mathematical spaces is a speciality of the mathematical representation schema. The ARM instance that records: each loading activity carried out according to the specification gives rise to the variation of stress with position and state , is as follows: #164 = POSSESSION_OF_PROPERTY (#138, #151); ARM Diagrams Product feature space  Figure  SEQ Figure \* ARABIC 1: Product feature space EXPRESS-G  Figure  SEQ Figure \* ARABIC 2: Product feature space UML Activity and state space  Figure  SEQ Figure \* ARABIC 3: Activity and state space EXPRESS-G  Figure  SEQ Figure \* ARABIC 4: Activity and state space UML Product activity and state space parameterisation  Figure  SEQ Figure \* ARABIC 5: Product activity and state space parameterisation EXPRESS-G  Figure  SEQ Figure \* ARABIC 6: Product activity and state space parameterisation UML dl012_v1_prop_ex.doc  PAGE 15 .Az :z*H! 1&: & &$TNPPMicrosoft PowerPoint & TNPPf & &TNPP :  1:45&8&0:- "- :"-0 & &0(H-- :"-H(0 & &-- $i/j & &8` $86` & &]lTimes New Roman4-.  : 2 C & &L"Univers-.  : 2 ms & &lL"Universw -.  : 2 my & &@Lh"Univers-.  : 2 mzs & & L"Universw -.  : 2 mFtj & &L"Univers-.  : 2 me & &L"Universw -.  : 2 mm & &L"Univers-.  : 2 ms & &d]lTimes New Roman4-.  : 2 A & &z]lTimes New Roman-.  : 2 E & &j]lTimes New Roman4-.  : 2 S & &.]lTimes New Roman-.  : 2 hA & &F]lTimes New Roman4-.  : 2 R &  & &TNPP & --"Systemn-D$XP@t(T$zL:]E 5o'cc &7&  & &$TNPPMicrosoft PowerPoint & TNPPf & &TNPP   6345& Times New Roman-.  2 Pwhole:,($ & & x- "- "-x Times New Roman!-.  72 { feature_space_for_product_design +0 5+*0&50+*0 0+05+055+ 05+%05 & &0 8&0 8-- $0 088 88(8 "--G8h888888(8G8h8888888?` ?` ?` ?` ?` ?` 000000q0P01000000q0P010((((((y(X(9((((((y(X(9((((((y(X(9((((((y(X(9((((((y(X(9((((((y(X(9 & &08-- "- HH80(9Times New Roman-.  $2 yproduct_design_arm.5+056* 06*&0600*PTimes New Roman!-.  2 fproduct_design5+056* 06*&06 &  & &`X-- "-X`(9Times New Roman-.  %2 zdesign_feature_space5+%050 +0 5++0%50++ & &-- "-(9Times New Roman!-.  "2 tdesign_point_space5+%050606 0%60*+ & &0(-- "-(0(9Times New Roman-.  "2 design_curve_space5+%050+5+0+0%50++ & &x-- "-x(9Times New Roman!-.  %2 design_surface_space5+%050&5+ 0*+0%60*+ & &@ -- "- @(9Times New Roman-.  2  fusion (ABS) 5&06 E@6 & &ph-- "-hp(9 & &`--"Systemn-H` "-@--' & &=Times New Roman-.  2 class$( & &ph- "-hp & &p---Hp "---' & & H- "-H  & &(--(   "-@--' & &Times New Roman-.  2 F1memberC#C,$# & &`x- "-x`@Times New Roman!-.  02 membership_of_feature_spaceP+P5+*&5500 0 +06*+0%60*+ & &h-- "-h@ & &`---h` "-@--' & &=Times New Roman-.  2 class$( & &h- "-h & &p---hp "---' & & X- "-X  & & ((--(  "- @ --' & & & - $  ( "--Gh(Gh0Op0Op0Op0Op0OpqP1qP1(((h(I((( (((((h(I((( (((((h(I((( (((((h(I((( (((((h(I((( ((((@ Times New Roman-.  $2 iproduct_design_arm.5+056* 06*&0600*PTimes New Roman!-.  2 fclassification+0&% +0 05 O)*>no68Y-Myp p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p   4'}KL Y126_p p p p p p p p p p p p p p p p p p p p p p p p p p p  4 7 4 *p?tu"gwxWyp p p p p p p p p p p p p p p p p p p p p p p p p p p p 7 4  4 y?@Ay2c !/EFHIp p p p p p p p p p p p p p p p p p p p p p p p p p "  4 7 44689znol-/p p p p p p p p p p Vp p p Vp p p p p p p p  4 ACTIVITY_OR_STATE413943424444maximum deflectionstates loading activity,load factor from 0 to 1maximum deflection45434646the [0, 1] load factor domainstatesactivitymaximum deflectionmetre loading activity that is carried out according to the specification gives rise to the variation of maximum deflection with state473741property variation with position and state 14.Aropertyroperty space property distribution;possession of that records: the existence of ; and :::<<<===>Y?rtvx}~;=?AJklnx-./GUempq+,089>?NUVuvxy      " # $ ` a c u v   $!6!UuPU]cathe fact that this space is one dimensional, 1 Some other instances of Property_space are as follows:strength: Tthe way in which the beam is loaded to failurestrength; and the necessary precision of the measurementd:a: An average density can be possessed by a curve, surface or volume of matter. Precise and loose possession of propertyNeglecting variation with state A lifetime of bridge beam property is possessed by a bridge beam throughout out its life, and is not something that changes from time to& & "- HH &  & &p-- "-p( & &&-- $ "--'Hg'Hg0Op0Op0Op0Op0OppQ0pQ0hI( hI( hI( hI( hI( (Times New Roman-.  $2 iproduct_design_arm.5+056* 06*&0600*PTimes New Roman!-.  *2 FUspecialisation_of_class%6*+0%0 0500 0+0%% & &` "- HH` &  & &x---Hx@  "- --' & &- "-Times New Roman-.  $2 ddesign_volume_space5+%050005P+0%60*+ & & 0-- "-0  & & H-- "-H  & & -- "-  & & @-- "-@  & &0P8h---hP  "-@0p 0--' & &fm"Times New Roman-.   2 10 & &`X|]<|]<|]<|]<|]<|]< Times New Roman!-.E"  $2 Iproperty_space_arm.5+05++ 00%50++00*PTimes New Roman0-.  2 $property_space5+05++ 00%50++ & &< f "- HHf < & &---d\  "---' & & - "-  & & -- "-  & &X`--  "-XqX4--' & &,  l- "-l ,X4Times New Roman0-.  42  property_distribution_function5+05++ 005% +65 050 56* 05 & &\\-- "-\\X4 & &---   "-?--' & &ll- "-ll & &8@Times New Roman0-.  2 3range$(,($ & &a088---8a "-00--' & &l- "-l0 & &p8x--8 "-pRp--' & &:Times New Roman0-.  2 Ddomain,(C(- & &a---h a "---' & &x--xh "---' & &,L - "- L,?Ukprƒǃ΃:<Mg}̈́U\ƅɅʅ݅ޅ )3:<@DEFH[\abjkƆdžˆ܆ AUU]cbAY[c|}~ŇƇʇ  ^_mnopq{ÈĈֈ܈%abc !&+-.EFGijuv}ˊ̊)WpqU]chb‹؋  '4YÌČnj-lmڍ  579BDFGIYZghijk~ӎ܎ݎ/01MNOQ[SVU]cU]c uDuPU]cU[\ƅbdžc}~Ƈ_no܈c !Gp p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p  7 4  4 )pq -ڍBk01Op p p p p p p p p p p p p p p p p p p p p p p p p p p p p   4 7 4 Properties of products and activities and states A usage of the EACM AuthorDavid LealDate20th September 1999Version1.0CirculationDerek Pashley, Chris Vaughan, Steve Chilcott, Ray Goult, PDES Inc. EA team The production of this document was funded by Rolls-Royce plc as a contribution to tasks 3.46 Engineering Analysis and 3.47 Application Module Development within the PDES Inc. Work Program. Introduction Purpose of the document This document explains use of the EACM modules to record information about the properties of a product, activity or state. A property can be a property of a whole product, activity or state. Alternatively, a property can be something that varies from position to position within a product and from state to state within an activity. The modules covered by this document are: possession of property; physical function; and property. A simple example A product design A designer creates a design for a product that specifies the following information: the product is a beam; the product has a rectangular cross section; the product has a length of 10 metres, depth of 4 metres and breadth of 2 metres; the design is called 10 metre 4(2 rectangular beam; the use of the ABC manufacturing specification. Using the terminology of the ARM for this part of ISO 10303, the designer creates a Product_design. The Product_design 10 metre 4(2 rectangular beam to specification ABC is a class that has individual beams as members. Each individual beam that is 10 metres long, that has a 4 metres by 2 metres rectangular cross section, and that is manufactured according to specification ABC, is a member of this class, or (to put it another way) complies with the design. The ARM instance corresponding to this product design is as follows: #101 = PRODUCT_DESIGN (); NOTE - The entity Product_design is the principal point of intersection with the STEP product structure backbone. There are may facts to record about the product design which are not within the scope of this discussion, including: the identification of the design; the classification of the design as a beam with a rectangular cross section; the possession of the length, breadth and depth properties; the relationship of the design to the manufacturing specification; the relationship with previous designs. A property space A standardisation body defines the concept of a life time for a bridge beam. This concept includes: a specification of what happens during the life; a criterion for determining that a bridge beam has reached the end of its life. Using the terminology of the ARM for this part of ISO 10303, the standardisation body defines a Property_space. The Property_space lifetime of bridge beam is a class that has individual properties, such as a bridge beam lifetime of 100 years, as members. The ARM instance corresponding to this property space is as follows: #102 = PROPERTY_SPACE (lifetime of bridge beam); NOTE - The entity Property_space is the point of intersection with a dictionary of property types. There are may facts to record about the property space which are not within the scope of this discussion, including: the identification of the property space; a text definition of the property space with references; the source of the property space definition; previous versions of the property space. This information is addressed by ISO 13584, and is accessed from the EACM by the Property dictionary application module. Length of bridge beam is a Property_space. This property space is defined by a standardisation body that specifies: the features of the beam that are used to measure the length (is it the overall length of the beam or the distance between the bearing surfaces?); the state of the beam when the length is measured (e.g. at what temperature). Density is a Property_space. This property space has a fundamental physical definition. A point within a volume of matter at a state possesses a density. Average density is a Property_space. This property space has a fundamental physical definition. A quantity of matter, curve, surface or volume, at a state possesses an average density. A property The Property bridge beam lifetime greater that 100 years is a class which has individual bridge beams as members. A bridge beam is a member of the class if it has, or is predicted to have, a life time in the range. NOTE - The distinction between properties that are predicted and those that are actually observed can be made using the Possession of property validity application module. The ARM instances that record: the existence of the range of bridge beam lifetimes from 100 years to infinity; the description of the range by the real interval from 100 to infinity; and the relationship of the range to the concept of lifetime of bridge beam, are as follows: #103 = PROPERTY_RANGE (); #104 = MATHS_VALUE (the real interval from 100 to infinity); #105 = IDENTIFICATION_OF_PROPERTY (#103, #104); #106 = MEMBERSHIP_OF_PROPERTY_SPACE (#102, #103); NOTE - The entity Maths_value is a point of intersection with the Mathematical representation schema. The way in which the nature of the Maths_value is made computer interpretable, is supported by the Maths value application module, and is not within the scope of this discussion. NOTE - The relationship between the identification of the property range by the real interval from 100 to infinity and the concept of year is supported by the Property identification application module, and is not within the scope of this discussion. Possession of a property by a product design A 10 metre 4(2 rectangular beam to specification ABC has a bridge beam lifetime greater that 100 years. This statement means that: each member of the class that is Product_design 10 metre 4(2 rectangular beam to specification ABC; is also a member of the class that is Property bridge beam lifetime greater that 100 years. NOTE - The specification that each has the property may not be true. It may be that 99% of beams that are members of 10 metre 4(2 rectangular beam to specification ABC have a lifetime longer than 100 years. Statistical and probabalistic information about the possession of a property is supported by the Possession of property statistics and probability application module. The ARM instance that records: each member of the beam design has the property, are as follows: #107 = POSSESSION_OF_PROPERTY (#101, #103); It is possible to record that the beam has a length of 10 metres. In reality the length of the beam depends upon its state, so that a full statement would be: each member of the class that is Product_design 10 metre 4(2 rectangular beam to specification ABC, when unloaded and at 20 degrees Celsius; is also a member of the class that is Property 10 metre long bridge beam. However if this precision is not required, a direct association between the Product_design and the Property implies that a each member of the Product_design has the property at each state throughout its life. It is possible to record that the beam has an average density of 4000 Kg m-3. In reality, this property also depends upon the state of the beam. If the average density is more or less independent of state, then it is possible to make an imprecise statement by a direct association between the Product_design and the Property. It is possible to record that the beam has a density 4000 Kg m-3. In reality, this property varies from point to point within the beam and from state to state of the beam. If the beam is more or less homogenous (at the scale of interest) and the density is more or less independent of state, then it is possible to make an imprecise statement by a direct association between the Product_design and the Property. If the beam is not homogenous (being reinforced concrete, say), then a direct association makes an untrue statement. A property variation with position The Product_design 10 metre 4(2 rectangular beam to specification ABC is reinforced concrete. The density at a point within the product design is: 7000 Kg m-3 for a point within the reinforcement; and 2500 Kg m-3 for a point within the concrete. The ARM instances that record: the density distribution is with respect to points within the beam; and each point within the distribution corresponds to a density value (i.e there is a function from the distribution space to the density space), are as follows: #108 = DESIGN_POINT_SPACE (); #109 = FEATURE_SPACE_FOR_PRODUCT_DESIGN (#108, #101); #110 = PROPERTY_DISTRIBUTION (); #111 = FEATURE_SPACE_FOR_PROPERTY_DISTRIBUTION (#110, #108); #112 = PROPERTY_FUNCTION (#110, #113); #113 = PROPERTY_SPACE (density); The property function can be described by a mathematical function that has: a domain that is a parameterisation of the points within the beam, such as a 3D mesh; and a range that is an identification of the density space (i.e. the set of positive reals). The ARM instances that record: the description of the property function by the mathematical function; and the existence of the mathematical function, are as follows: #114 = MAPPING_OF_PHYSICAL_FUNCTION (#112, #115); #115 = MATHS_FUNCTION (my function over my mesh); NOTE - The entity Maths_function is a point of intersection with the Mathematical representation schema. The way in which the nature of the Maths_function is made computer interpretable is supported by the Maths function application module, and is not within the scope of this discussion. NOTE - The relationship between the mapping of the physical function to the mathematical function and: the parameterisation (or identification) of points within the beam by the mesh; and the identification of density values with respect to the Kg m-3 scale, is supported by the Physical function mapping application module, and is not within the scope of this discussion. Possession of a property variation with position The ARM instance that records: the loose statement that the each beam manufactured to the design has the density distribution throughout out its life, is as follows: #117 = POSSESSION_OF_PROPERTY (#101, #110); Alternatively, it is possible to record the precise statement that: each beam manufacture to the design, has the density distribution in its as supplied state, when unstressed and at 20 degrees Celsius, by ARM instances as follows: #118 = STATE (as supplied, unstresses and at 20 degrees Celsius); #119 = STATE_ASPECT_OF_PRODUCT_DESIGN (#118, #101); #120 = POSSESSION_OF_PROPERTY (#118, #110); NOTE - There are may facts to record about the state which are not within the scope of this discussion, including: the identification of the state; the classification of the state as an as supplied state; the temperature distribution property possessed by the state; the stress distribution property possessed by the state; the relationship of the state to the manufacturing activity; the relationship with previous specifications or designs of the state. Possession of a property by a state A designer or analyst creates the definition or design of a state as follows: it is possessed by a 10 metre 4(2 rectangular beam to specification ABC; it occurs after fifty years of use. A designer or analysis can specify or predict properties for this state. The State that is 10 metre 4(2 rectangular beam to specification ABC after fifty years of use is a class that has individual reinforced concrete beams after 50 years of use as members. This State has a Property that is 50 year of use. The ARM instances that record: the existence of the state and its relationship to the product design; the existence of the property, its description by the number 50, and its membership of the length of use property space; and the possession of the property by the state, are as follows: #121 = STATE (after 50 years of use); #122 = STATE_ASPECT_OF_PRODUCT_DESIGN (#121, #101); #123 = PROPERTY_SPACE (length of use); #124 = PROPERTY (); #125 = MEMBERSHIP_OF_PROPERTY_SPACE (#123,#124); #126 = IDENTIFICATION_OF_PROPERTY (#124, #127); #127 = MATHS_VALUE (the real 50); #128 = POSSESSION_OF_PROPERTY (#121, #124); Possession of property by an activity A designer or analyst creates the definition or design of an activity as follows: it is possessed by a 10 metre 4(2 rectangular beam to specification ABC; it consists of 106 cycles of a 10000 Kg uniformly distributed load. The Activity 106 cycles of 10000Kg UDL on 10 metre beam is a class that has individual activities carried out on individual beams as members. The ARM instances that record: the existence of the activity, and its relationship to the product design; the existence of the property, its description by the number 106, and its membership of the number of cycles property space; and the possession of the property by the activity, are as follows: #129 = ACTIVITY (); #130 = ACTIVITY_ASPECT_OF_PRODUCT (#129, #101); #131 = PROPERTY_SPACE (number of cycles); #132 = PROPERTY (); #133 = MEMBERSHIP_OF_PROPERTY_SPACE (#131,#132); #134 = IDENTIFICATION_OF_PROPERTY (#132, #135); #135 = MATHS_VALUE (the real number 10E6); #136 = POSSESSION_OF_PROPERTY (#129, #132); A property variation with state An analyst creates the definition or design of an activity that specifies the following information: the activity is called slow loading of 10 metre beam 3 metres from one end; the activity is performed by the 10 metre beam; the 10 metre beam is simply supported throughout; the 10 metre beam is initially unloaded and unstressed; a point load is applied 3 metres from one end, and slowly increased until it is 10 kN. The ARM instances that record: the existence of the activity design; and its relationship to the product design, are as follows: #137 = ACTIVITY (); #138 = ACTIVITY_ASPECT_OF_PRODUCT (#137, #101); The maximum in-space deflection for the beam increased during the activity. The ARM instances that record: the distribution of maximum deflection is with respect to states within the activity; and each point within the distribution corresponds to a maximum deflection value (i.e there is a function from the distribution space to the maximum deflection space), are as follows: #139 = STATE_SPACE (); #140 = FEATURE_SPACE_FOR_PRODUCT_DESIGN (#108, #101); #110 = PROPERTY_DISTRIBUTION (); #111 = FEATURE_SPACE_FOR_PROPERTY_DISTRIBUTION (#110, #108); #112 = PROPERTY_FUNCTION (#110, #113); #113 = PROPERTY_SPACE (density); The property function can be described by a mathematical function that has: a domain that is a parameterisation of the points within the beam, such as a 3D mesh; and a range that is an identification of the density space (i.e. the set of positive reals). The ARM instances that record: the description of the property function by the mathematical function; and the existence of the mathematical function, are as follows: #114 = MAPPING_OF_PHYSICAL_FUNCTION (#112, #115); #115 = MATHS_FUNCTION (my function over my mesh); NOTE - The entity Maths_function is a point of intersection with the Mathematical representation schema. The way in which the nature of the Maths_function is made computer interpretable is supported by the Maths function application module, and is not within the scope of this discussion. NOTE - The relationship between the mapping of the physical function to the mathematical function and: the parameterisation (or identification) of points within the beam by the mesh; and the identification of density values with respect to the Kg m-3 scale, is supported by the Physical function mapping application module, and is not within the scope of this discussion. A set of states within an activity design An analysis of the beam loading activity can consider the set of states that exist during the loading process. This set of states is a State_space. There are an infinite number of states in the set. Each state in the set is identified by a real number in the range [0, 1]. The ARM instances that record: the existence of the one dimensional space of states; its relationship to the activity design as a whole; and the way in which a state within the set is identified, are as follows: #013 = STATE_SPACE (1); #014 = ACTIVITY_OR_STATE_SPACE_FOR_ACTIVITY (#013, #011); #015 = PHYSIC- "-X`p 0Times New Roman!-.  *2 (physical_topology_space560%*00 0500000%60*+ & &Xh-- "-hXp 0 & & @(---@  "-  --' & &@h- "-h@ & &@PHx--????P? 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(2 {disjoint, incomplete},(,-,(-C,,,"Arial-.  2 usage,(-,- & & 8(---?? "- _00--' & &V&VP- "-PV0 & &VX-- "-XV0"Arial-.  +2 MembershipOfFeatureSpaceP5P65 055K:655 5@6506 & &V---(V "- --' &  & &0~ "Arial-.  2 jmemberC,C,- & &0+"Arial-.   2 j* & &0bp"Arial-.  2 3jclass(,(( & &0;"Arial-.   2 j* & &~ "Arial-.  2 whole:,-, & &w+"Arial-.   2 * & &p"Arial-.  2 3class(,(( & &w;"Arial-.   2 * & &Pp- "-pP"Arial-.  2 ClassE500"Arial-"Arial-.  *2 VM(from ProductDesignARM)  5P@ 5560F5055@FP  & &>X "-- $>PP & &%"Arial-.  (2 {disjoint, incomplete},(,-,(-C,,,"Arial-.  2  membershipC,C,-(-, & &@@HH---H@ "-@@@@--' & & 8& 8- "-8 @@ & & -- "- @@"Arial-.  2  DesignPointSpaceE6056@55@5506 & & --- ` "-P--' &  & & &P - "- P & & X-- "-X "Arial-.  2 DesignCurveSpaceE6056E6 05@5605 & & ---(  "-P--' &  & & 8& 8- "-8  & & -- "- "Arial-.  "2 DesignSurfaceSpaceE6056@5 506@5506 & & --- ` "-P--' &  & & &P - "- P & & X-- "-X "Arial-.  !2 DesignVolumeSpaceE6056@55P5@6506 & & ---(  "-P--' &  & &X "- $X & &--H "-@0--' & &E"Arial-.  (2 `%{disjoint, incomplete},(,-,(-C,,,"Arial-.  2 %dimensionality,C,-(,-,( & &P---.P "---' & &V&V- "-V"Arial-.  "2 Ldimension: Integer5P550565556  & &V-- "-V"Arial-.  '2 PhysicalTopologySpace@50005;655550@6506 & &V-- "-V &  & & "-- $F & &"Arial-.  (2 P{disjoint, incomplete},(,-,(-C,,,"Arial-.  2  membershipC,C,-(-, & &FNH---H "-FF--' & &pX--Xhp  "-0 --' & &px-- "-pp@--' & & (-- "-  @--' & &--H "-@--' & &PX-- "-PP@--' & &--@ "---' & &H--HX "-@ --' & &H--H` "-@ --' & &@H-- "-@`@P--' & &."Arial-.  2 whole:,-, & &K}"Arial-.   2 @* & &."Arial-.   2 :part,- & &}"Arial-.   2 @:* & &---?? "-Ev%V--' & & H&H- "-H & & -- "- "Arial-.  32 SubsetOfPhysicalTopologySpace@5605K@60005:656560@5506 & &---p "- @--' &  & &- "-@"Arial-.  '2 3SpecialisationOfClass@56060655KE600"Arial-"Arial-.  *2 }(from ProductDesignARM)  5P@ 5560F5055@FP  & &n "-- $n & &U"Arial-.  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