Integrated generic resource: Numerical analysis ISO/DIS 10303-53
© ISO

Cover page
Table of contents
Copyright
Foreword
Introduction
1 Scope
2 Normative references
3 Terms, definitions and abbreviations

4 Analysis product relationships
   4.1 Introduction
   4.2 Fundamental concepts and assumptions
   4.3 Analysis product relationships entity definitions
5 Product analysis
   5.1 Introduction
   5.2 Fundamental concepts and assumptions
   5.3 Product analysis entity definitions
   5.4 Product analysis subtype constraint definition
   5.5 Product analysis function definitions
6 Analysis
   6.1 Introduction
   6.2 Fundamental concepts and assumptions
   6.3 Analysis entity definitions
   6.4 Analysis subtype constraint definition
   6.5 Analysis function definitions

A Short names of entities
B Information object registration
C Computer interpretable listings
D EXPRESS-G diagrams
Index

6 Analysis schema

The following Express declaration begins the analysis_schema and identifies the necessary external references.

EXPRESS specification:

*)
SCHEMA analysis_schema;

REFERENCE FROM analysis_product_relationships_schema    --  ISO 10303-53
  (view_relationship);

REFERENCE FROM mesh_topology_schema    --  ISO 10303-52
  (mesh);

REFERENCE FROM product_property_definition_schema    --  ISO 10303-41
  (general_property);

REFERENCE FROM support_resource_schema;    --  ISO 10303-41
(*

NOTE 1   The schemas referenced above are specified in the following part of ISO 10303:

analysis_product_relationships_schema ISO 10303-53
mesh_topology_schema ISO 10303-52
product_property_definition_schema ISO 10303-41
support_resource_schema ISO 10303-41

NOTE 2   See Annex D for a graphical representation of this schema.

6.1 Introduction

This schema defines and describes the structures for describing analyses.

6.2 Fundamental concepts and assumptions

An analysis model may assume that the temporal spatial domain is a continuum, and may also assume an analytically convenient dimension for that continuum.

NOTE    If an analysis model is a continuum, then there is a 'membership' concept which is interpreted as a place within the continuum. A field is a function from the continuum to a property space. For example a temperature field is a function from the continuum to the property space 'temperature'.

There is also a membership concept for a temporal spatial domain. In this case, the members are the physical individuals that have the properties assigned to the temporal spatial domain.

EXAMPLE 1   The temporal spatial domain may be a beam during a loading process. Different analysis models may be created as follows:

Properties of the temporal spatial domain may also be properties of the analysis model. However, simplified analytically tractable properties may be assumed for an analysis model.

EXAMPLE 2   The stress-strain behaviour of a temporal spatial domain may be very complicated. An approximate elastic behaviour may be assumed for analysis.

6.3 analysis_schema entity definition

6.3.1 behavioural_decomposition_of_numerical_model   EXPRESS-G

A behavioural_decomposition_of_numerical_model is a decomposition of a numerical_model into differnet subbehaviours.

EXPRESS specification:

*)
ENTITY behavioural_decomposition_of_numerical_model;
  parts : SET[2:?] OF numerical_model;
  whole : numerical_model;
END_ENTITY;
(*

Attribute definitions:

parts: the numerical_model that is the union of the parts

whole: the numerical_model that is the union of the parts. the set of instances of numerical_model that are subbehaviours of the whole;

6.3.2 model_action_domain   EXPRESS-G

A model_action_domain is a type of numerical_model. It is the response of a numerical_model during a period of time.

EXAMPLE    Beam type XYZ regarded as a set of cross-sections of time instants during loading procedure L1 is a model_action_domain. This model_action_domain is the domain of distributions whihc vary in two dimensions - position along the beam and time. The distributions include rotation for each instant, and bending moment for each position for each instant.

EXPRESS specification:

*)
ENTITY model_action_domain
  SUBTYPE OF (numerical_model);
  initial : model_state_domain;
  final : model_state_domain;
END_ENTITY;
(*

Attribute definitions:

initial: the model_state_domain that is a boundary of the model_action_domain for the initial time.

final: the model_state_domain that is a boundary of the model_action_domain for the final time.

6.3.3 model_product_domain   EXPRESS-G

A model_product_domain is a type of numerical_model that is only a spatial decomposition and that has an indefinite time dimension.

EXAMPLE    Beam type XYZ regarded as a set of cross sections is a model_product_domain.

EXPRESS specification:

*)
ENTITY model_product_domain
  SUBTYPE OF (numerical_model);
  temporal_parts : LIST[0:?] OF model_action_domain;
END_ENTITY;
(*

Attribute definitions:

temporal_parts: the instances of model_action_domain that are preformed by the model_product_domain.

NOTE    Each member of a model_product_domain corresponds to a physical_product. For each referenced model_action_domain there is a subset (itself a model_action_domain) that corresponds to the physical_product. This subset is a view of a physical_action performed by the physical_product.

6.3.4 model_product_domain_with_mesh   EXPRESS-G

A model_product_domain_with_mesh is a type of model_product_domain that has a mesh.

EXPRESS specification:

*)
ENTITY model_product_domain_with_mesh
  SUBTYPE OF (model_product_domain);
  model_mesh : mesh;
END_ENTITY;
(*

Attribute definitions:

model_mesh: the mesh discretizing the model_product_domain.

6.3.5 model_property_distribution   EXPRESS-G

A model_property_distribution is a function that has a numerical_model and a property space as its range. Each member of the numerical_model has a value within the property space. There can be distributions with respect to space and time for a model_action_domain. There can be distributions with respect to space for a model_product_domain.

EXPRESS specification:

*)
ENTITY model_property_distribution;
  creating_software : text;
  domain : numerical_model;
  range : general_property;
END_ENTITY;
(*

Attribute definitions:

creating_software: the name of the software used to create the model_property_distribution. The vendor, version, computer system, operating system and description shall be specified.

domain: the numerical_model that is the domain of the model_property_distribution.

range: the general_property that is the range of the model_property_distribution.

6.3.6 model_state_domain   EXPRESS-G

A model_state_domain is a type of numerical_model that has no time dimension. A model_state_domain is either independent of time, or a time slice.

For a time slice:

EXAMPLE    Beam type XYZ regarded as a set of cross-sections at the end of loading procedure L1 is a model_state_domain. This model_state_domain is the domain of distributions which vary in one dimension - position along the beam. The distributions include rotation for each position, and bending moment for each position.

EXPRESS specification:

*)
ENTITY model_state_domain
  SUBTYPE OF (numerical_model);
END_ENTITY;
(*

6.3.7 numerical_model   EXPRESS-G

A numerical_model is an aspect of a physical object relevant to a particular type of behavoir. A numerical_model takes a particular view of its domain in terms of dimensionality and continuity.

EXAMPLE 1   Examples include: 3D continuum (volume elements in FEA); 2D continuum (shell elements in FEA); 1D continuum (beam elements in FEA); lumped masses (in a many-body problem).

A numerical_model is a view of a temporal_spatial_object specificiation as a set or space. The members of the set or space may consist of:

NOTE 1   Only an object that is a set or space can be the domain of a distribution function.

EXAMPLE 2   Beam type XYZ during the loading procedure L1 regarded as a point set is a numerical_model. This numerical_model is the domain of distrubiton which vary in four dimensions - position and time. The distributions include displacement for each position for each instant and stress for each position for each instant.

EXAMPLE 3   Beam type XYZ durng loading procedure L1 regarded as a set of cross-sections for time instants is a numerical_model This numerical_model is the domain of distributions which vary in two-dimensions - position along the beam and time. The distributions include rotation for each position and for each instant, and bending moment for each position for each instant.

EXAMPLE 4   Beam type XYZ during heating procedure H1 regarded as a set of 10 segments for time instants is an numerical model. This numerical model is the domain of distributions which vary in two dimensions (one discrete and one continuous) - sub-beam and time. The distributions include average temperature for each segment for each instant, and thermal energy for each segment for each instant.

EXAMPLE 5   Beam type XYZ during heating procedure H1 regarded as a set of 10 segments for 20 time steps is an numerical model. This numerical model is the domain of distributions which vary in two dimensions (both discrete) - sub-beam and time. The distributions include average temperature for each segment for each step, and total thermal energy gain for each segment for each step.

NOTE 2   A temporal spatial object is a speci?cation or class that an individual physical object in the real world can be a member of. The members of an numerical model are instances of temporal spatial object.

EXAMPLE 6   Beam type XYZ during loading procedure L1 is a physical activity; a speci?cation that has an individual beam of type XYZ being loaded according to L1 as a member.

Beam type XYZ during loading procedure L1, regarded as a set of cross-sections for time instants is a model action domain. The cross-section at end 2 of the beam at the end of the loading procedure is a physical state that is a member of this set or space. The cross-section at end 2 of an individual beam of type XYZ that has been loaded according to procedure L1 is a member of this physical state.

EXPRESS specification:

*)
ENTITY numerical_model;
  id : identifier;
  name : label;
  description : text;
  creating_software : text;
  intended_analysis_code : SET[1:?] OF text;
  analysis_type : text;
WHERE
  wr1: temporal_spatial_domain_for_model(SELF);
END_ENTITY;
(*

Attribute definitions:

id: identifier for the numerical_model.

name: user-specified instance identifier.

description: text that provides further information about the numerical_model.

creating_software: the name of the software used to create numerical_model. The version of the software shall be specifed.

intended_analysis_code: set of one or many names of the intended analysis code that a numerical model was created for. Each intended analysis code shall have the vendor, version, computer system, operating system and descriptions specifed.

analysis_type: a description of what type of analysis is to be performed with this numerical analysis.

Formal propositions:

wr1: The numerical_model shall be associated with a temporal spatial domain via a view relationship.

6.3.8 simulation_run   EXPRESS-G

A simulation_run is an individual activity that simulates a numerical_model.

EXAMPLE    A particular run carried out on a particular computer by a particular analysis code at a particular time is a simulation run.

EXPRESS specification:

*)
ENTITY simulation_run;
  id : identifier;
  name : label;
  description : text;
  simulated : numerical_model;
  results : SET[0:?] OF model_property_distribution;
END_ENTITY;
(*

Attribute definitions:

id: the identifier for the simulation_run.

name: the words by which the simulation_run is known.

description: the text that provides further information about the simulation_run.

simulated: the numerical_model that is simulated.

results: the instances of model property distribution that result from the simulation.

6.3.9 spatial_decomposition_of_numerical_model   EXPRESS-G

A spatial_decomposition_of_numerical_model is a decomposition of a numerical_model into different subspaces.

EXPRESS specification:

*)
ENTITY spatial_decomposition_of_numerical_model;
  parts : SET[2:?] OF numerical_model;
  whole : numerical_model;
END_ENTITY;
(*

Attribute definitions:

parts: the set of instances of numerical_model that are subspaces of the whole.

whole: the numerical_model that is the union of the parts.

6.3.10 temporal_decomposition_of_model_action   EXPRESS-G

A temporal_decomposition_of_model_action is a decomposition of a model_action_domain into different time instants.

EXPRESS specification:

*)
ENTITY temporal_decomposition_of_model_action;
  parts : LIST[2:?] OF model_action_domain;
  whole : model_action_domain;
END_ENTITY;
(*

Attribute definitions:

parts: the set of instances of model_action_domain at different times.

whole: the model_action_domain that is the union of the parts.

6.4 analysis_schema subtype constraint definition

6.4.1 sc1_numerical_model

An sc1_numerical_model constrains the subtypes for the numerical_model.

EXPRESS specification:

*)
SUBTYPE_CONSTRAINT sc1_numerical_model FOR numerical_model;
  ABSTRACT SUPERTYPE;
END_SUBTYPE_CONSTRAINT;
(*

6.5 analysis_schema function definitions

6.5.1 temporal_spatial_domain_for_model

The temporal_spatial_domain_for_model function determines whether or not the given numerical_model is associated with a temporal_spatial_domain by a view_relationship.

The view_relationship can be:

The function returns true if there is an association, otherwise it returns a value of false.

EXPRESS specification:

*)
FUNCTION temporal_spatial_domain_for_model (domain : numerical_model) :BOOLEAN;
          LOCAL
            spatial_set : SET OF spatial_decomposition_of_numerical_model;
            behavioural_set : SET OF behavioural_decomposition_of_numerical_model;
            domains : SET OF numerical_model := [];
            viewing : BAG OF view_relationship;
            spatial_bag : BAG OF spatial_decomposition_of_numerical_model;
            behavioural_bag : BAG OF behavioural_decomposition_of_numerical_model;
          END_LOCAL;

          viewing := USEDIN(domain, 'ANALYSIS_PRODUCT_RELATIONSHIPS_SCHEMA.VIEW_RELATIONSHIP.VIEW');
          IF SIZEOF(viewing) > 0 THEN
            RETURN (TRUE);
          END_IF;
          spatial_bag := USEDIN(domain, 'ANALYSIS_SCHEMA.SPATIAL_DECOMPOSITION_OF_NUMERICAL_MODEL.PARTS');
          IF SIZEOF(spatial_bag) > 0 THEN
            spatial_set := spatial_bag;
            REPEAT i := 1 TO HIINDEX(spatial_set);
              domains := domains + spatial_set[i].whole;
            END_REPEAT;
          END_IF;
          behavioural_bag := USEDIN(domain, 'ANALYSIS_SCHEMA.BEHAVIOURAL_DECOMPOSITION_OF_NUMERICAL_MODEL.PARTS');
          IF SIZEOF(behavioural_bag) > 0 THEN
            behavioural_set := bag_to_set(behavioural_bag);
            REPEAT i := 1 TO HIINDEX(behavioural_set);
              domains := domains + behavioural_set[i].whole;
            END_REPEAT;
          END_IF;
          IF SIZEOF(domains) > 0 THEN
            REPEAT i := 1 TO HIINDEX(domains);
              IF temporal_spatial_domain_for_model(domains[i]) THEN
                RETURN (TRUE);
              END_IF;
            END_REPEAT;
          END_IF;
          RETURN (FALSE);
        
END_FUNCTION;
(*

Argument definitions:

domain: (input) the numerical_model to be checked.



*)
END_SCHEMA;  -- analysis_schema
(*


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