Processing Geometric Models of Assemblies to Structure and Enrich them with Functional Information

Ahmad SHAHWAN

Supervised by

Jean-Claude LEON

Gilles FOUCAULT

Grenoble
August 29, 2014

In the frame of

ROMMA Project

Robust Mechanical Models for Assemblies
http://romma.lmt.ens-cachan.fr

Partners

What is a DMU?

No
explicit
and robust
relation between
CAD Models and function. Iyer et al. '05

What is a structural simulation?

Objective: assess the load distribution over the bolted junctions under prescribed external loads.
Preparation: 5 man-days.
Computation: 15'.

How to reduce simulation preparation time?

As the title implies, the starting point is the geometric model of an assembly. Collectively referred to as Digital Mock-Up (DMU).
So what is this geometric model? It is indeed a set of 3D objects, each representing a component, put up (assembled) together in a particular spacial configuration.
Is it only about geometry in a DMU? Construction tree is little use. Textual information pretty close to function, however not reliable.
What do we expect from a DMU?: manufacturing, and ...
Simulation: To study a phenomenon under given "functional" circumstances.
Assesses the compliance of a given design with initial requirements.
Thanks to the advent of digital computing, numeric simulations replaced costly physical prototypes.
Efficient calculations, that can be repeated. Costly preparation time!
This preparation time introduces a bottleneck to the PDP, and raises the urging question of how to reduce it.

Simulation model differ from CAD models

Certain hypotheses are made to produce simulation models.

Shape transformations are needed.

Simulation objectives and hypotheses refer to specific functional subsets of components.

	≠

	BoltedJunction

CAD models need to be enriched with functional knowledge and restructured accordingly.

Why do we need preparation at all?
To enable timely calculation, simplifying hypotheses are made after sim. objectives are set. The aim here is to represent components in a simple manner, while staying as faithful as possible to reality.
Shape transformations are thus required. Automated methods exist to this end.
Transformation, however, whether manual or automated, are information-intensive. This is because:
- Objectives refer to functional subsets of the DMU, e.g. a bolted junction.
- Hypotheses refer to particular geometric objects and zones with functional significance; e.g. Locker Nut, Threaded Link.
Conclusion: Before geo. preparation can be accelerated and fully-automated, the geo. model of a product represented by the DMU needs to be enriched with functional knowledge. This also implies that the geometry and structure of the DMU need to be reorganized to allow the reception of such knowledge.

Objectives

Enrich DMUs with functional knowledge required by geometric transformation for FEA preprocessing, taking into account current industrial practices and conventions.

Bottom-up approach

This define our objectives...
To enrich DMUs with functional knowledge needed by geometric preprocessing for finite element analysis purposes.
This should happen in the context of mainstream industrial practices, while taking into account the commonplace representation conventions in this domain.
The starting point is pure geometry.
Extract geometric interaction between components.
Give them potential functional interpretations based on geometry.
Qualitatively assess functional interpretations based on their behavior in a mechanical context.
Complete the functional image by gathering information bits and pieces into one coherent knowledge base.
End up with a DMU, now functionally restructured and enriched.

Overview

Function, form and behavior

Function is the semantics of a design.
Gero '90

Relationship between function and structure, i.e. form* Gero '90, Umeda '09, Qian '96, Albers '06.

Example of form-behavior-structure (FBS) model applied to a buzzer Qian & Gero '96.

Methods to apply this relationship in design suggest behavior to make the connection.

Function

Behavior

Form

* In the domain of mechanical engineering.

Challenges
of the bottom-up approach

Industrial conventions

v.s.

Restructuring of the CAD model

Level	Enrichment	Restructuring
Funct. interface	Comp. interface	Geometric
Funct. unit	Component	None
Funct. module	Comp. group	Organizational

* In this endeavor, we face certain obstacles and challenges. * The difference between real and digital shape: * A direct result of *industrial conventions*. * The example depicts a screw and a nut both bearing a threaded link, represented by a helical cut. * The threaded link is conventionally represented by means of two simple cylinders in the DMU. * Conventions are not unique, equal vs different diameters. * This makes the form-function relation in a DMU **indeterministic**. * The DMU is not yet ready to accommodate functional information: * FEA preprocessing requires functional enrichment of the DMU at different levels, now this would also imply geo. and org. restructuring of the model. * at the interface level, in order to functionally interpret an interaction, we need to isolate this interaction first, geometrically. * at the component level, no particular structuring is needed, as components are already isolated in the DMU. Even though components themselves are restructured geometrically to allow enrichment at the interface level. * at the functional group level, components of a DMU need to be regrouped in functional subsets, requiring an organizational restructuring. * Now this leads us to the first stage of our proposed approach, which is...

Form at the outset

Function stems from interactions between components De Kleer '98, Albers '02.
For mechanical components, functionality happens at the geometric interface level.
Top-down methods built on functional interaction to boost geometric design Roy & Bharadwaj '02, Kim '04.

Relationship between form and function at the interface level Roy & Bharadwaj' 02

To capture functionality, geometric interactions need to be analysed first.

Conventional Rep. of a **threaded link**

Conventional Interface

A CI is a conceptual entity that represents an interaction between two components in an assembly.

Identified by the geometric interaction of components in a DMU.
Augmented with semantics such as physical and functional properties.

CI types

Contact; curve or surface
Interference; shared volume
Clearance. play distance

* Now to seize geometric interaction between components we define a conceptual entity that we refer to as **Conventional Interface**. * Even though identified by their geometric properties, CIs can, and will, be assigned other physical and functional properties as we'll see shortly. * Because of their intrinsic geometric nature, CIs are classified into three categories: * *Contacts* that happen when components touch each others without having a common volumes. * *Interferences* happen when components penetrate each others leading to a common volume. * *Clearances* when surfaces of components keep a certain distance (play) between each others. * We observe the unrealistic, thus conventional, nature of **interferences**. * real objects cannot have commun volumes. * The detection of clearances depends on the knowledge of the play, a functional information that is not available at the outset. * This dependency prevents us from exploiting clearances, as for now.

Threaded link: a functional interaction (source ASM)	Functional Interfaces An FI is an interaction between two neighboring mechanical components that fulfills, or contributes to the fulfillment of a function. Functionally explains an CI.

Observations	One CI many FIs!
	Functional interfaces are represented through canonical surfaces.

Only geometric interactions between canonical surfaces are of significant interest.

In an attempt to functionally explain CIs, we define the Functional Interface that captures inter-component interactions that fulfil or participate to the fulfilment of a set of functions.

Observations:

A given geometric configuration, i.e. a CI, can be assigned more than one functional interpretation, i.e. FI: a result of indeterministic relation between form and function.
Now if we refer to geometric surfaces of a FI as functional surfaces, we observe that functional surfaces are represented conventionally through canonical surfaces.
This is because even when non-canonical surfaces convey functional meaning, such as helical cuts and involute profiles, they are often machined independantly from the CAD model.
Conclusion: We can then safely assume that as long as functionality is concerned, only geometric interactions between canonical surfaces are of significant interest.

Simple, yet efficient geometric interaction detection

Generation of a unique geometric representation:

Maximal edges and surfaces.

Three-level filtering:

Bounding boxes;
Geometric attributes comparison;
Boolean operators.

Efforts in the frame of ROMMA project. Jourdes et al. '14

* This allows us to develop a simple, yet efficient algorithm to detect geometric interactions. * Before any detection is made, a unique geo. rep. of shape must be obtained, unlike the one available in today's CAD models. We refer to such a representation as Maximal edges and surfaces representation. * Once such a rep is obtained (at the topological level) a three level filtering is applied to extract geometric interactions, starting by a bounding boxes check to eliminate obvious negatives. * Next, canonical surfaces of neighboring comps, according to the bb check, are compared pair-wise using their geometric properties. * Candidates of potential interactions are reported to the 3rd filter: a boolean check that eliminates false positives & precisely delimits the interaction zone. * It is worth mentioning that other efforts has been made to precisely and efficiently detect certain geo. interfaces in the frame of ROMMA. * This leads to the precise determination of geometric interactions between components.

Assembly Graph Structure

CIs connect components together.
A graph whose

nodes are the components;
edges are the CIs.

Overrides DMU tree-structure.

Conventional Interface Graph

A graph that represents geometric interactions between components in a DMU.

First step toward DMU restructuring.

Results

Centrifugal pump with 43 components.
Geo. Analysis time
Bool. Op. ≈ 8'!
3-level filtering ≈ 0.15''.
100-edge CIG:
- 87 contacts;
- 13 interferences.

Cross section in the DMU of a centrifugal pump.

Results

Root joint with 148 components.
Geo. Analysis time
3-level filtering < 0.2''.
512-edge CIG:
- 396 contacts;
- 116 interferences.

Form meets function

Objective link form to function. Gero '90, Qian '96
Problem
more than one possible interpretation. Roy '02
Need to incorporate context.


Threaded Link		Cylindric Interference		Spline Link

Spline link

Functional interpretations

Hierarchical representation of interfaces (taxonomies).
Each CI is associated multiple FIs acc. a dictionary.

Geometric and functional knowledge structuring at the interface level.

Relevant structure

	Form	Function
module	Group	?	Geometry
unit	Component	?
interface	CI	FIs	Geometry

Behavior as a broker

Can behavior Gero '90, Umeda '09, Qian '96, Albers'06 be used to mend the nexus from form to function?

Cylindric Interference	Stand point
Cylindric Interference	Geometric	Behavioral
Threaded Link	valid	valid
Spline Link	valid	invalid

Objective use a qualitative behavioral representation to deduce functional knowledge.
Reference states define behavioral validity.
- Elimination of FI that violate a given behavior.

* **Question** Can behavior, used throughout the literature to establish the link function-to-form be used to mend the yet ambiguous form-to-function link? * To illustrate this possibility we look at the example of a Cylindric Interfarence: it is valid to interpret it as a Threaded Link both geometrically and from a mechanical behavior standpoint. * However, and even though geometrically valid, a Spline Link is invalid behavior-wise: forces cannot be balanced. * This can be said intuitively as the FI Spline Link does not fit in the given context, assembly would fall apart. * **Objective** use such a behvioral judgement to narrow down multiple functional interpret per CI. * Introducing the concept of Ref. States that define what a valid behavior is. * The goal then shifts to eliminating functional interpretations that violate one or more reference states.

Reference States

Hypotheses
- Rigid bodies;
- Energy-conservative systems;
- Only mechanical interactions.

$\iint\limits_{\partial C} \vec{f_1} \; dS + \iint\limits_{\partial C} \vec{f_2} \; dS = \vec{0}$

Product at rest

Components of a product hold in place. Ref. State I

Mechanical equilibrium:

$\sum \vec{f} = \vec{0}, \; \sum \vec{m} = \vec{0}$.

$$\sum\limits_{i \in \mathcal{I}(C)} \mathsf{W}_{i} = \sum \{ \vec{f}_{i} | \vec{m}_{i} \} = \{ \vec{0} | \vec{0} \}$$

Casting a physical dimension on mere geometry.
External forces and moments on a rigid body:

can be represented using a wrench screw Poinsot 1861;
can only go through CIs of component C: $\mathcal{I}(C)$.

* Few global assumptions are made: * Components are rigid bodies. Deformations are negligeable. * Energy-conservative systems. Friction-free surfaces. * Only mechanical interactions are accounted for, i.e. all physical interactions with a component go through its CIs. * First ref. state: the product is at rest. Components of an assembly hold in place. * This can be formalized by mech. equil. eqs. * This statement casts a physical dimension on pure geometry of the DMU. * We know that a system of external forces and moment can be represented by a vector force and a vector moment, i.e. a wrench screw. * Now assigning a wrench screw to each CI according to a given FI makes the m.e.e. boil down to the statement that the sum of wrench screws over all CI of any given component is null.

Qualitative physical representation

Force and moment values are not available in a DMU!

Need for qualitative representation:

values: real intervals.

Not Null	$\odot$	$]-\infty, 0[ \: \cup \: ]0, +\infty[$
Null	$\oslash$	$[0, 0]$
Strictly Positive	$\oplus$	$]0, +\infty[$
Strictly Negative	$\ominus$	$]-\infty, 0[$
Arbitrary	$\otimes$	$]-\infty, +\infty[$

and operations: interval arithmetics.
$$ \begin{array}{l@{}l@{}l} K + L &= \{z | \exists (x, y) \in K \times L, z = x + y &\} \\ K \cdot L &= \{z | \exists (x, y) \in K \times L, z = x \cdot y &\} \end{array} $$

Elimination of statically-invalid FIs

Iterate CIG nodes until there's no more FIs to eliminate.
Heuristically pick node C.


	Coordinate alignment

CI₁		CI₂			C
$\left\{ \begin{array}{c\|c} \otimes & \otimes \\ \otimes & \otimes \\ \odot & \oslash \end{array} \right\} $ Threaded Link	+	$\left\{ \begin{array}{c\|c} \oslash & \otimes \\ \oslash & \otimes \\ \ominus & \oslash \end{array} \right\} $ Planar Support	=	$\left\{ \begin{array}{c\|c} \otimes & \otimes \\ \otimes & \otimes \\ \otimes & \otimes \end{array} \right\} $ Sum
$\left\{ \begin{array}{c\|c} \otimes & \otimes \\ \otimes & \otimes \\ \oslash & \otimes \end{array} \right\} $ Spline Link	+	$\left\{ \begin{array}{c\|c} \oslash & \otimes \\ \oslash & \otimes \\ \ominus & \oslash \end{array} \right\} $ Planar Support	=	$\left\{ \begin{array}{c\|c} \oslash & \otimes \\ \oslash & \otimes \\ \ominus & \oslash \end{array} \right\} $ Sum

$\odot$	Not Null
$\oslash$	Null
$\oplus$	Strictly Positive
$\ominus$	Strictly Negative
$\otimes$	Arbitrary

Nothing more to do at node C, close it.
Pick next component...

First level of behavioral filtering at the interface level.
Eliminate FIs that produce static invalidity.

* **The idea:** iterate CIG nodes, checking FIs validity against RS I, and eliminating FIs that violate this RS, until there's no more FIs to eliminate. * An illustrative example to show the outlines of the algo. The same principal can be generalized to more complicated models. * Heuristically pick next component to allow the algo to converge faster. * All possible solutions are evalutated. Wrench screws are borrowed from the FI taxonomy. * Screws are summed, leading to possible point of application and coord sys changes. * We know how to do it, thanks to interval arithmetics. * Sums of screws are checked for "nullability". * Does the interval contain zero? * Invalid solutions leads to the elimination of FIs. * When nothing more can be done, the component is closed. * Next! * **Conclusion:** A first level of filtering of a considerable amount of irrelevant functional interpretations at the interface level.

Reference States

R.S. I is unable to uniquely determine the FI of a given CI.
- more than one statically-valid solution.

Static Determinacy

Statically indeterminate structures must be functionally justified. Ref. State II

The solution for static equilibrium equations is unique*.
Static indeterminacy is minimized.

Unless necessary, or functionally justified, indeterminate static solutions are rejected.

Reduce the number of FIs to one per CI.

* Given one force or moment value.

Further behavioral filtering at the interface level.
Eliminate FIs that produce unnecessary static indeterminacy.

* Ambiguity still remains in CIs having multiple statically-valid FI. * **RS II** provides the necessary criterion to select the appropriate FI when multiple static solutions co-exist. * This RS considers the product in operational. * It asserts that all statically indeterminate configuration must be functionally justified, otherwise, they are eliminated. * A statically indeterminate configuration is characterized by more than one solution to the same m.e.e seen earlier in RS I. * Elimination of non-functional statically indeterminate interpretation leads to **one FI per CI**. * **Conclusion:** This consists a second and last level filtering, leading to unique function interpretation at the interface level.

Functional Group

A set of components that together deliver a coherent function or set of functions.

Each functional group is given a label (functional cluster).
Bolted junction is an example of a functional cluster.

Loads cycle goes into a bolted junctions.

Force Propagation

Loads generated by an internal load generator propagate through a cycle in a functional product. Ref. State III

A threaded link is a load generator.

* As mentioned earlier, another level at which the DMU must be functionally enriched for FEA purposes is the *functional group* level. * A **functional group** is a set of components that collaborate together to deliver a coherent set of functions. * Each functional group is labelled with a *functional cluster*. A designation that defines the set of functions it satisfies. * An example is a *bolted junction* is a functional cluster that identifies a set of components satisfying the functionality of "tightening" by means of a threaded link. * A threaded link is an internal load generator, and bolted junctions are characterized by a load cycle internal to the product. * This leads us to RS III, that again consider the product from an operational stand point. * It states that in a valid product, loads generated by a load generator, such as a threaded link, propagate in a **cyclic path**.

Internal load cycles

Force propagation graphs	One per direction.
	Subgraphs of CIG.

FIs producing static indeterminacy are eliminated.
A load cycle with a threaded link reveals a bolted junctions.

Qualitative behavioral analysis led to:

Reduction of interpretations to one FI per CI.
Functional knowledge at the component group level.

* This raises the question as how to detect internal loads cycles? * To answer this question, we first define a **Force Propagation Graph** on DMU components for each possible force propagation direction. * We know that each FPG is a sub-graph of the CIG, this is because forces can only propagate through CIs, as we only consider mechanical interactions. * This puts an upper bound on the number of force propagation graphs. * Now for each force propagation direction, dictated by a load generator, we start by eliminating FI that lead to statically indeterminate configurations. * Next, and in order to detect a load cycle, we project the CIG onto the chosen direction to produce the corresponding FPG. * Now the task of detecting *bolted junctions* reduces to cycle detection in the resulting graph. * **Conclusion** Using a qualitative behavioral study of the assembly led us to clarify ambiguity about the functional knowledge at the interface level, and to acquire new knowledge at the functional group level.

Functional knowledge

	Form	Function
module	Group	? One FC	Geometry & Behavior
unit	Component	?
interface	CI	FIs One FI	Geometry & Behavior

Functional unit

Thanks to R.S. functional knowledge is available at component interface and component group levels.
Objective Use this knowledge to functionally classify components.

Functional Designation

An FD is a denomination that functionally identifies a class of a component.

Relates the functionality to geometry through FIs and to assembly through FCs.

Observations
- Function of a component is related to functions of its interfaces and functional groups.
- Vast and dynamic diversity of component function.

FDs are organized in a taxonomy that can be *domain-specific*.

FDs need to be represented formally, and reasoned upon with dynamic rules.

How to represent functional knowledge?
How to process functional knowledge?

* First observation in this regard is that we cannot tell the function of a component by looking at it alone! Functionality of a component is determined in light of functional interfaces and the functional groups it participates to. * Another important observation is the dynamic nature of component functions. Indeed, the set of functional designation that we may describe depends on the underling domain such aeronautics or automotive industries. * This knowledge can be captured in a hierarchical structure in what is referred to as FD taxonomies. * It needs to be represented formally, yet in a dynamic and adaptive manner! * **Conclusion** So far we've been only "collecting" knowledge, now we need to consider the question as how to represent, and process functional knowledge?

Functional knowledge representation

Knowledge-based engineering (KBE)

Engineering-oriented expert systems, bottom-up approaches Chapman '01, La Rocca '07, Emberey '07.
KBE adds up to CAD systems, without changing them.
- CAD models remain unchanged!
Procedural programming. Native representation.
- Poor semantic formalism!

Ontologies

Formal semantics based on the Semantic Web paradigm.
Borrowed into assembly knowledge representation Rahmani '12, Kitamura '03 and reasoning Kim '06.
- No significant application in functional reasoning, yet!

* To answer to this question we first take a look at what the literature offers. * A common approach is Knowledge-Based Engineering (KBE) that emphasizes reuse by making knowledge available to designers. * On drawback is that KBE systems add up to CAD systems * Technological and functional information is not necessarily related to their respective geometric sets, since geometry is left intact. * Another inconvenience is the use of procedural and object-oriented programming approaches are static and do not allow generic rules. * Native representation languages hinder knowledge sharing. * Ontologies: well-defined formalism. Generic purpose, cross-domain knowledge repositories. * Existing methods didn't go beyond consistency checks, and DoF reduction when it comes to reasoning using ontologies.

Functional knowledge reasoning

A cap-screw is a component that has a threaded link and a planar support, and that participates to a bolted junction*.
In First Order Logic (FOL): Undecidable!

$$ \begin{array}{llll} Capscrew \leftarrow & Component(x) && \land \\ & ThreadedLink(i) &\land \; forms(x, i) & \land \\ & PlanarSupport(j) &\land \; forms(x, j) & \land \\ & BoltedJoint(b) &\land \; participatesTo(x, b) & \end{array} $$

In Description Logic (DL): Decidable.

$$ \begin{array}{>{\sf}l>{\sf}l>{\sf}l} \sf Capscrew \sqsupseteq & \sf Component & \sqcap \\ & \exists \sf forms.ThreadedLink & \sqcap \\ & \exists \sf forms.PlanarSupport & \sqcap \\ & \exists \sf participatesTo.BoltedJoint & \sqcap \end{array} $$

OWL DL is an ontology language that supports DL reasoning.
DL-reasoning engines with well-established algorithmic behavior (Pellet, FaCT++, Racer, ect.).

* Simplified from the real rule in use to identify cap-screws.

Captured knowledge

The romma ontology to capture domain knowledge.
Model knowledge is instantiated against romma concepts and instances are assigned to their respective geometric entities.

Ontological reasoning

Ontology romma is submitted to DL reasoner.
CIG is translated into DL fact, which are posted to reasoner.


	DIG protocol
Geometric and behavioral module		Reasoner
	DIG protocol

Components are functionally enriched down to the interface level, and geometrically restructured accordingly.

Results

Successful detection of 6 different *FDs* on an example of a centrifugal pump.

Results

Successful detection of *cap-screws*, *nuts*, and *locking nuts* on an industrial example of root joint.

Complete connection

	Form	Function
module	Group	One FC	Geometry & Behavior
unit	Component	? One FD	Expert Rules
interface	CI	One FI	Geometry & Behavior

Template-based preprocessing of DMU for FEA purposes.

Highly automated geometric pre-processing method, feeds on functional information of the DMU Boussuge et al. '14.

Templates are matched to functional groups (bolted junction).
Elements of templates are mapped to components (cap-screw, nut, locking nut).
Sub-domains are defined based on FIs.

Reduction of preparation time
from 5 man-days to 1 hour!

* A direct application of the proposed approach is introduced by Boussuge et al. in the frame of ROMMA project. * It is a highly automated geometric pre-processing method for FE simulation purposes... * based on template matching. * For example, a special template is matches to functional groups labelled as *bolted junctions*. * Locker nuts are then recognized, thanks to their Functional Designations, and removed, as the template implies. * Components bound by a threaded link, such as the capscrew and the nut in this example, are replaced by a single object. * Interaction zones are then used to define sub-domains, such as those around loose fit contacts. * This leads to the generation of the adequate simulation model. * **Conclusion:** This collaboration reduced the preparation time from 5 man-days to only one hour!

Conclusions

Geometric restructuring of components.
- CIs: components bear imprints of functional zones.
- FIs: functionality stems at the interface level.
Structural re-organization of the DMU.
- CIG: capturing functional interaction between components in a graph structure.
- FCs: grouping functionally related components in sub-graphs.
Use behavior to unambiguously bind form to function.
- RSs: qualitative behavioral assessment of function.
Apply rule-based inference to connect the dots.
- FDs: match functional patterns to restructured components.

In conclusion * Components geometry has been **restructured** with respect to function: * Geometric interactions between components have been precisely defined, components now bear imprints of those interactions thanks to their *CIs*. * Those interactions were functionally determined, each CI was assigned to a unique FI. * The DMU itself has been **reorganized** in a functionally relevant graph: * This is the *CIG*. * Components were grouped into subgraphs labelled as functional clusters. * To this end we implemented a **qualitative behavioral** assessment of function in a mechanical context. * Through *RSs*. * We also applied a **rule-based** inference to coplete the functional picture. * Building an ontology of *FDs*.

Perspectives

Other applications rather that FEA:
- Virtual and augmented reality.
- Assembly/Disassembly planning.
Future work direction:
- Take into account symmetry and repetitive geometries.
- Implement and introduce new reference states, such as kinematic chains.
- Extend existing ontology by defining new FDs and their rules.

* Other applications * Even though emphasize has been put solely on FEA preprocessing, other application can also be considered with minimal modifications to the proposed approach. * Examples are virtual and augmented reality where functional and kinematic information can be used to enhance simulations of physical phenomena. * Future work directions include * The enhancement of execution time by considering repetitive geometries and symmetries to avoid redundant reasoning. * The implementation of other reference states that account for the violation of one or more of the global hypotheses, such as friction and deformation. * The extension of current ontology by adding more rules to recognize new functional designations.

Thank you.

CI₁		CI₂			C
$\left\{ \begin{array}{c\|c} \otimes & \otimes \\ \otimes & \otimes \\ \odot & \oslash \end{array} \right\} $ Threaded Link	+	$\left\{ \begin{array}{c\|c} \oslash & \otimes \\ \oslash & \otimes \\ \ominus & \oslash \end{array} \right\} $ Planar Support	=	$\left\{ \begin{array}{c\|c} \otimes & \otimes \\ \otimes & \otimes \\ \otimes & \otimes \end{array} \right\} $ Sum
$\left\{ \begin{array}{c\|c} \otimes & \otimes \\ \otimes & \otimes \\ \oslash & \otimes \end{array} \right\} $ Spline Link	+	$\left\{ \begin{array}{c\|c} \oslash & \otimes \\ \oslash & \otimes \\ \ominus & \oslash \end{array} \right\} $ Planar Support	=	$\left\{ \begin{array}{c\|c} \oslash & \otimes \\ \oslash & \otimes \\ \ominus & \oslash \end{array} \right\} $ Sum

Bool. Op.	≈ 8'!
3-level filtering	≈ 0.15''.

Processing Geometric Models of Assemblies to Structure and Enrich them with Functional Information

Ahmad SHAHWAN

Jean-Claude LEON

Gilles FOUCAULT

ROMMA Project

What is a DMU?

What is a structural simulation?

Simulation model differ from CAD models

Objectives

Bottom-up approach

Overview

Function, form and behavior

Challenges of the bottom-up approach

Form at the outset

Conventional Interface

CI types

Functional Interfaces

Simple, yet efficient geometric interaction detection

Assembly Graph Structure

Conventional Interface Graph

Results

Results

Form meets function

Functional interpretations

Relevant structure

Behavior as a broker

Reference States

Product at rest

Qualitative physical representation

Elimination of statically-invalid FIs

Reference States

Static Determinacy

Functional Group

Force Propagation

Internal load cycles

Functional knowledge

Functional unit

Functional Designation

Functional knowledge representation

Knowledge-based engineering (KBE)

Ontologies

Functional knowledge reasoning

Captured knowledge

Ontological reasoning

Results

Results

Complete connection

Template-based preprocessing of DMU for FEA purposes.

Conclusions

Perspectives

Thank you.

Challenges
of the bottom-up approach