CAD model simplification using a removing details and ...€¦ · CAD model simplification using a...

Journal of Mechanical Science and Technology 26 (11) (2012) 3539~3548

www.springerlink.com/content/1738-494x

DOI 10.1007/s12206-012-0869-6

CAD model simplification using a removing details and merging faces technique

for a FEM simulation†

Hamdi Mounir, Aifaoui Nizar* and Benamara Abdelmajid

LGM, ENIM, University of Monastir, Av Ibn Eljazzar 5019 Monastir, Tunisia

(Manuscript Received December 1, 2011; Revised May 13, 2012; Accepted June 15, 2012)

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Abstract

The simulation process is currently used in the design and dimensioning of mechanical parts. With the progress of computer materials,

the finite elements method (FEM) becomes the most used approach in the simulation of mechanical behaviour. The simulation process

needs multiple Design-FEM loops. In order to accelerate those analysis loops, an adaptation of computer aided design (CAD) model is

necessary. The adaptation step consists in the simplification of the CAD model geometry by eliminating details (holes, chamfers, fillet,

etc.) and faces. In this paper, a novel technique of simplification of the CAD geometry is developed. This technique is a hybrid method

based on a combination of the elimination details and merging faces. The merging of faces is based on the energetic method. With this

approach, the computing time is reduced by the elimination of geometric details which do not boundary conditions. An implementation

of the proposed algorithm on the Open Cascade platform is also presented. The results of the developed method are compared with a

previous publication. The reduction of the computing time and the amelioration of the result precision highlight the efficiency of the

presented method.

Keywords: CAD model; Analysis model; Simplification model; Simulation; Hybrid method

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1. Introduction

For a long time, design and mechanical analysis were con-

sidered two independent activities. Our research tasks aim at

the improvement of the CAD models preparation's phase even

before starting the mesh stage. The preparation of a CAD

model consists in idealizing or cleaning the geometry by

eliminating details (holes, chamfer, fillet, etc), considered

superfluous for the simulation [1]. Then, these details are

zones where the mesh will be automatically refined, which

will generate a very important computing time without bring-

ing more precision to the results of simulation.

The simplified models are used in many simulation do-

mains: for dynamic analysis of satellite [2]; modeling flow

conditions in the tunnel [3]; vibration of penetration beam-

plate coupled structures [4]; aircraft icing simulation [5];

structural optimization of an automobile transmission [6] and

for analyze the difference of 3-D CAD model by feature ex-

traction [7], etc.

The generation of an analysis model using the CAD geome-

try is based on some analysis assumptions. These assumptions

are related to the material behavior, solicitations and the ge-

ometry definition of the part. In the bibliography [8-10], sev-

eral research tasks were interested in the CAD geometry adap-

tation problems to analysis models dedicated to the mechani-

cal analysis by the finite elements method.

Thakur et al. [11] studied existing model simplification

techniques that are useful from the physics based simulation

and classified them broadly into four main categories based

upon the type of simplification operators used in the respec-

tive techniques, i.e. surface entity, volumetric entity, explicit

feature and dimensional reduction.

Dabke et al. [12] uses an identification method of entities

(features) to carry out the adaptation and the simplification of

geometrical models by suppression, in CSG models. This

technique is based on expert system implementing heuristic

rules resulting from the analyst experience.

Belaziz et al. [13] proposes an adaptation method of geome-

try based on the features’ recognition approach. In this ap-

proach, the recognition is carried out by a morphological

analysis of the CAD geometry, that’s why this method is more

flexible than the Dabke’s method. The adapted and idealized

geometry is generated by the removal of some form features

considered as being non characteristic for the considered me-

chanical analysis.

Sheffer et al. [14] develops a suppression procedure of de-

tails and "cleaning" of the CAD geometry using the principles

*Corresponding author. Tel.: +216 98 901 839, Fax.: +216 73 500 514

E-mail address: [email protected] † Recommended by Associate Editor Ki-Hoon Shin

© KSME & Springer 2012

3540 H. Mounir et al. / Journal of Mechanical Science and Technology 26 (11) (2012) 3539~3548

of virtual topology. This topology is based on regrouping the

faces constituting the B-Rep model in areas admitting the

same characteristics of curve and dimension.

Armstrong et al. [15] and Donaghy [16] use the Medial

Axis Transform (MAT) to carry out the adaptation and the

simplification of B-Rep geometry. The MAT method builds

the skeleton of a geometrical representation in order to obtain

the median axis. A circle with a variable diameter sweeps the

interior of the structure remaining constantly in contact, in at

least 2 points with the structure. The skeleton is obtained by

building the places of the center of the circle. For a 3D geome-

try, the circle is replaced by a sphere and the places of its cen-

Table 1. Summary of the simplification techniques.

Method Input formatFeatures

simplified

Simplification

criterionAdvantages Limitations Application domain

Finite element

based feature

removal [12]

B-Rep Axis-symmetric,

plane, solid

Interactive FE based features used FE features like beam,

pipe, shell, etc. not defined

FEM model

preparation

Medial axis

transform [15, 16]

B-Rep Shell based

features

Automatic or semi-

automatic

High aspect ratio regions can be

identified; simplified models

computationally efficient and

comparable with original model

w.r.t. FEA results

Only applicable for shells FEM model

preparation

Decimation-

Idealization

operators based on

vertex removal and

spherical error zone

[6, 18]

Polygonal Mesh Holes Error measure based

on a posteriori

analysis using

tetrahedral finite

elements and

Interactive

Takes care of large

transformations and

simplification of complex areas

of polyhedron such as saddle

points

Only for polyhedral

models; error estimator for

hexahedral elements not

developed

FEM model

preparation

Face clustering

[14]

Gambit pre-

processor

(Fluent™)

Chamfers,

fillets, rounds

and spherical

surface based

features

Metric based on

boundary

preservation, region

size, region

smoothness and

simplicity of region

boundary shape

Applicable to both faceted and

free form geometries;

curved regions can be handled;

geometry is retained, only

topology changes

face clustering may not be

optimal

FEM model

preparation

Cellular topology

progressive

modeling [17]

Feature based

model

Freeform

features

Based on ascending

order of progressive

volumes

Applicable for NURBS

surfaces; computationally

efficient

Application specific

feature complexity not

considered

Network

transmission; FEM

model preparation

Edge decimation

based approach

[20]

Polygonal Mesh Protrusions and

depressions

Error measure based

on overall geometry

error, mesh size and

mesh shape

Mesh quality based error

metrics are used

Not applicable for

assembly models

Mesh generation for

FEM analysis

Feature

simplification using

wrap-around,

thinning and

smoothing

operators [21]

B-Rep Blends,

chamfers,

passages and

concave regions

Based on summation

of area of faces

contained by features

Applicable to assembly models;

interoperability and portability

to commercial system

Rule based feature

recognition results in

overhead;

mating information not

preserved while

simplifying assembly

models

FEM model

preparation, network

model transmission

and multi-

resolution viewing

Decimation-Cell

transformation

based technique

[10]

B-Rep Holes, fillets and

narrow regions

The features are

selected manually by

the user for

simplification

Analysis history useful for

simplification strategy

comparison;

Handles narrow regions

Post processing needed for

mesh generation of desired

density;

Lack of automation

FEM model

preparation

Feature

simplification using

wrap-around,

thinning and

smoothing

operators

[21]

B-Rep Blends,

chamfers,

passages and

concave regions

Based on summation

of area of faces

contained by features

Applicable to assembly models;

interoperability and portability

to commercial system

Rule based feature

recognition results in

overhead;

mating information not

preserved while

simplifying assembly

models

FEM model

preparation, network

model transmission

and multi-

resolution viewing

Decimation-MCT

based technique

[22]

B-Rep Freeform Interactive Preserves topology and creates

new geometry adapted to

various mesh quality constraints

Lack of automation FEM model

preparation

Removing details

[25]

B-Rep Freeform

Chamfers,

fillets, rounds

and holes

Automatic or semi-

automatic

Simplification of CAD models

based on the criterion of size

and boundary conduction

Does not take account the

location of details

FEM model

preparation

H. Mounir et al. / Journal of Mechanical Science and Technology 26 (11) (2012) 3539~3548 3541

ter represent a surface. This skeleton is then used to carry out

an analysis of the geometry in order to characterize the set of

details which composes the 3D geometry. Then, the geometri-

cal representation is adapted or idealized by the means of the

Euler operators.

Lee et al. [17] present a method to generate progressive

solid models (PSM) from feature-based models using a cellu-

lar topology-based approach. Here, cellular topology is used to

generate the PSM, and then the surface entity based operators

are developed to simplify the model. The main concept in this

paper is to start with a feature based model as input and gener-

ate a sequence of solid models representing the underlying

object with various levels of details. The intended purpose of

the PSM is to stream models over a network efficiently.

Fine et al. [18] introduced simplification operators for the

Finite Element Analysis. The operators are based on the ver-

tex removal and spherical error zone concept.

Mobley et al. [19] reported an object-oriented approach to

develop surface-based disfeaturing operators to suppress small

features for the FEA model preparation.

Date et al. [20] reported vertex and an edge collapse-based

technique for the mesh model simplification and refinement.

They defined three metrics based on the overall geometry

error, face size and face shape. The metrics are evaluated

for the edges to determine their priority index for simplifica-

tion.

Kim et al. [21] reported a system for a multi-resolution fea-

ture simplification using three operators, namely wrap-around,

smooth out and thinning. The method is applied to the finite

element model preparation and network transmission multi-

resolution modeling. The features are first recognized using

rule-based techniques and then various operators are applied

to suppress them. In the case of the wraparound operator, the

model is considered to be wrapped by a thin plastic cover. The

parts of the model hidden by the cover are considered for sim-

plification or removal.

Foucault et al. [22] reported a topology simplification tech-

nique for the finite element mesh generation. The authors have

developed a Mesh Constraint Topology (MCT) based on the

model simplification scheme to address the sharp corner

matching requirements. MCT entities are defined as compos-

ite topological entities created to suit the mesh generation

requirements stated before. The MC face is a poly-surface,

defined as the union of Riemannian surfaces constituting the

reference model. The MC edge is a poly-curve, defined as a

union of Riemannian curves constituting the reference model.

Woo et al. [23] presented a method that is mainly focused

on the mechanical parts that will be created by machining.

That is, the most simplified result of a solid model will be the

solid model of stock material. Independently of user-specified

design features, this method simplifies the solid model by

removing the detailed geometry by using these subtractive

features. If a solid model is not appropriate to be represented

in terms of machining features, unnatural simplification may

happen for the solid model.

Hamdi et al. [24], CAD/CAE interoperability, an automatic

generation of Analysis Model based on the simplification of

CAD geometry is implemented using the Open Cascade plat-

form. In this work, the simply size criteria is integrated, and in

Ref. [25], a simplification algorithm of CAD models for a

simulation by the finite element method is presented. The

algorithm proposed consists in reading the B-rep model of the

CAD geometry in order to identify, and then remove the de-

tails considered to be superfluous for the mechanical analysis,

using two criteria of size and boundary condition. In this work,

the creation tree of CAD model (CSG) is not taken into ac-

count not only because it is not unique but also it is easily lost

by a simple CAD model transfer between the different work-

ing tools. Table 1 summarizes and compares the simplification

techniques.

Based on the bibliography previously presented, the contri-

bution of this works is positioned in the: “model simplification

technique for surface entity based operators” [11].

The objective of this paper is to propose an original method

which can guide the designer in the phase of the CAD model's

preparation for a simulation by the finite elements method

(FEM). According to the suggested approach, the elimination

of the details is based on a representation by Iso-zones ena-

bling the designer to visualize the details which are candidates

for elimination or fusion if they are positioned in the stress

concentration zone.

This paper can be divided in to three sections. The first one

has presented a state of the art on the principal techniques used

to eliminate details from the CAD geometry. In the second

section, the proposed method of simplification is proposed. In

order to highlight the efficiency in the reduction of the design

time and the cost of the product, an example of a mechanical

part has been studied using the proposed approach, and pre-

sented in the third section.

2. Algorithm of simplification with hybrid method

The proposed algorithm composed of three principal inter-

dependent phases is represented in Fig. 1. Each phase implies

overlapping stages.

2.1 Principle

In order to be independent of the CAD/CAM systems, the

proposed algorithm relies on a neutral file (Standard for Ex-

change of Product: STEP) to import the data of the part to be

idealized. To use various tools of simulation, the idealized

CAD geometry will be also stored under the same neutral

format (STEP). The phase (A) of the algorithm consists in a

step of pre-treatment of the CAD model. It allows restructur-

ing the Boundary Representation (B-rep) model of the part to

a data base. The structured information in this data base relates

to the faces, the normal of the faces, the wires, the edges and

the vertex which includes the geometry model of the part.

Phase (B) consists in identifying the details candidates for


simplification. That implies the implementation of algorithms

of identification based on criteria (forms, sizes, function, posi-

tion…). The result of this phase is a representation of Iso-

zones targets for simplification. These Iso-zones are entities

(edges, faces) coloured according to the specificity of each

face. This original vision enables the designer to visualize the

least influential zones (high order of criticality) on the compu-

tation results, giving him the possibility either to inter-actively

eliminate the entities which have a high order of criticality, or

to apply the automatic algorithms of simplification. The stage

(7) consists in the creation of Boundary Conditions (BC) de-

limited box. And the phase (C) allows the reconstruction of

the simplified model. Stage (9) consists in removing the iden-

tified details, if they are outside the BC delimited box, then in

rebuilding the geometric model after suppression. Stage (10)

consists in the fusion of the identified details with the adjacent

faces if they are inside the Box (the details represent the con-

centrator’s stress). The result of stage (12) is an idealized

CAD model whose elementary topology is validated in stage

(13). At the exit of the algorithm, the designer has at his dis-

posal an idealized model saved in the STEP format for a simu-

lation by finite elements.

2.2 Stage A: Restructuration of CAD model

The restructuration of the CAD model aims at exploring

and making it easy to handle the topological and geometrical

data associated with the part. Fig. 2, presents all the stages of

the restructuration of the initial CAD model.

Reading the STEP file led to determine the characteristics

of each element of the B-rep model, namely

• Vertex: (coordinates),

• Edge: (associated vertex, length),

• Wire: (associated edges, orientation, length),

• Face: (associated wires, normal, area).

This information will be stored in a data-base allotted to the

part. Any geometrical handling on the part implies the proc-

essing of information indexed in the data-base. For a given

face, it is evident to know the associated wires, the participat-

ing edges and also the list of vertex appearing in the face.

Geometrical information such as the perimeter and the surface

of the face are directly deduced.

2.3 Stage B: Identification of details

Fig. 3, presents the stages of the second phases that are the

identification of details and the region of fused faces, based on

the three criteria. The basic criterion used by the majority of

authors in the simplification field is the size criterion. A sec-

ond criterion of geometry simplification which takes account

of the detail function in this case is that of the boundary condi-

tions, a BC surface is kept. The third criterion which is most

original is that of the detail site in the structure, if the detail is

located in the loading zone area then this detail should not be

removed but fused with the adjacent faces.

In the example of Fig. 3, if we take into account only the

size criterion, we notice that all the details (holes, leave,

groove and chamfer) will be removed. And when we consider

2. Restructuration of CAD model

3. Identification of details: Di

12. Reconstruction of the idealized model

15. STEP file of idealized CAD model

1. STEP file of init ial CAD model

13. Topology validation

4. Eliminate cri terion

11. Fuse criterion

9. Elimination of details

5. Boundary Conditions

7. Creation of BC delimited Box: B

8. If (Di ? B )

10. Fusion of face with the adjacent fac es

Non

14. Non

Yes

Yes

6. Identification of BC detai ls: BCD j

A

B

C

Fig. 1. Algorithm of idealization with a hybrid method.

Phase A: Restructuration of CAD model

1.1. Reading the STEP file

1.2. Exploration of topological data

1.3. Conversion of topological

elements to geometric elements

1.4. Determination of each

element characteristics

1.5. Information storage

Face: Fi

Vertex: Vk

Wire: Wi

Edge: Ej

- Area of faces Fi

- Length of edges Eij

- Normal Ni

- …

Normal: Ni

Fig. 2. Restructuration of CAD Model.


the second criterion (Boundary Condition), the holes and the

groove will be kept. But if we take into account the third crite-

rion (detail position), we notice that only the chamfer will be

removed and the face of the leave will be fused with the two

adjacent faces.

2.4 Stage C: Treatment of details and rebuilding of idealized

CAD model

Fig. 4 details the reconstruction process of the simplified

model. This process is composed of four steps:

• The CAD model decomposition

• The reconstruction of fused faces

• Reconstruction of faces after details suppression

• Reconstruction of simplified CAD model.

Each step of the algorithm is composed of a number of op-

erations applied according to an order, to lead at the algorithm

exit a simplified model, which takes account of the three crite-

ria fixed in this work.

So, after the stage of the CAD model decomposition, the

energetic method: it is about rebuilding a surface that interpo-

lates the region and that adheres to the curves of the loops of

the faces that will be fused. The process is stopped when the

error between the calculated surface and each constraint point

is less than a distance fixed by the user or when the maximum

number of iterations is reached. The result of the energetic

Phase B: Identification of details

2.1. Choice of the idealization criteria

1. Size criterion

2. Boundary conditions criterion

3. Position criterion

2.2. Detection of faces to be eliminated

1. Display of Iso-zones

2. Location of the faces

2.4. Possible intervention of the user

1. Add or remove faces

2. Re-specify criteria of idealization

(a)

(b)

(c)

1 : Small, suppressible

2 : Average, suppressible

3 : Large, suppressible

4 : Small, non suppressible

5 : Average, non suppress

6 : Large, non suppressible

7 : Carrier of BC

8 : Can be fused2.3. Detection of faces to be fused

1. Display of Iso-zones

2. Location of the regions

(d)

Fig. 3. Identification of details and regions.

(d)

Phase C: Reconstruction of idealized model

3.3.1. Detection of adjacent faces

3.3.2. Prolongation of the kept faces

3.3.3. Determination of intersection curves

3.3.4. Determination of limiting points

3.3.5. Adjustment of curves by limiting points

3.3.6. Reconstruction of contours

3.3.7. Reconstruction of faces

3.4.1. Reconstruction of solid

3.4.2. Validation of the idealized model

3.4.3. Writing of a STEP file

(e)

(f)

(g)

3.3. Reconstruction of faces after

details suppression3.2. Reconstruction of fused faces

3.2.1. Detection of fusion region

3.2.2. Fusion using

energetic method

3.2.3. Reconstruction

of fused face

(c)

(k)

(j)

(l)

3.1. Decomposition of Model

(b) (a)

3.4. Reconstruction of model

(h)(m)

(i)

Fig. 4. Reconstruction of idealized model.


method is a NURBS surface.

As for the procedure of CAD model’s rebuilding after the

elimination of faces, it consists, firstly, in detecting the adja-

cent faces to the removed entities. The detection of adjacent

faces is based on the database part processed in the first stage.

Secondly, it consists in prolonging these faces in all directions.

That will lead to detecting intersections curves due to the pro-

longation of faces. The vertex ‘limit’ will be determined from

curves, then the edges will be delimited by the vertex. The

CAD model is regenerated by rebuilding faces associated to

new wires. A new database of the idealized part is thus com-

pleted. The designer has the B-rep model of the part before

and after simplification. A file ‘STEP’ is finally generated in

order to use the idealized CAD model by an analysis tool.

The proposed algorithm of simplification is adjudicated

universal because it is based only on the B-rep model of the

CAD geometry. This algorithm is completely independent of

the CAD geometry creation tree, because of the non-

uniqueness of this tree. In addition, the CAD model, once

exported, loses any information in its manner of creation.

3. Data-processing implementation and validation on

example

3.1 Data-processing implementation

The data-processing implementation of the simplification

algorithm was carried out on a development's platform: 'Open

Cascade'. Open Cascade is an environment dedicated to the

development of 3D applications of CAD-CAM multi-

platforms. This platform is available and free on Internet. It is

based on a bookstore of C++ classes and tools developed and

available in open source.

3.2 Example of validation

In this section, one example of validation will allow validat-

ing the principal functionalities of the simplification algorithm.

Fig. 5 presents a stair climber machine. The part “support”

was selected because they have a broad variety of mechanical

parts in terms of its forms, the boundary conditions, and also

the details which they contain. The validation example is pre-

sented in Ref. [25]. The CAD model simplified using the hy-

brid method will be compared to those published in Ref. [25]

in which the method of detail removal is developed. The com-

parison is carried out on the following points:

• Number of topological entities

• Computation time

• Precision of results.

Fig. 6 presents the illustration of the principal stages to pass

from a CAD model of the “support” (Fig. 6(a)), to a model of

analysis whose geometry is idealized (Fig. 6(k)) using an hy-

brid method or to the second model (Fig. 6(l)) using only the

size criterion [25]. A very important stage (Fig. 6(c)) repre-

sents the casing by Iso-zones. These iso-zones give to the

designer a very clear idea of the details candidates to the

elimination by sharp colors, according to the level of critical-

ity, details function and position (Fig. 6(d)), the Boundary

Conditions (BC) are defined (loading and fixing) (Fig. 6(e)),

this information allows to identify the BC faces (Fig. 6(f)) and

to create the BC box (Fig. 6(g)), the (Fig. 6(h)) present the

region of faces that can be fused, in (Fig. 6(i)) is presented the

model after the stage of details elimination, (Fig. 6(j)) presents

the simplified model using all the criteria (hybrid method).

Finally, the simplified model was saved at a neutral format

(Fig. 6(k)).

Fig. 7 represents two Open Cascade windows in which are

Fig. 5. Example of validation: “support of stair climber machine”.

(f)

(l)(g) (h)

(j)(i) (k)

B

(d)(a)

Face: Fi

Wire: Wi

Vertex: Vk

1:Small, suppressible

2:Average, suppressible

3:Large, suppressible

4:Small, non suppressible

5:Average, non suppressible

6:Large, non suppressible

7:Carrier of BC

8:Can be fused

(b) (c)

(e)

Fig. 6. Stages of CAD Model simplification using a hybrid method.


represented the idealized CAD models of the models 2, and 3.

These models will be saved in 'STEP' format to be simulated

by the finite element method.

Table 2 represents the number of the B-rep entities of the

model, before and after simplification. It has been shown that

the number of entities after simplification is lower than that

before simplification. That generates a reduction of the mesh

and computation times of the idealized model.

The graph presented in Fig. 8, shows that the hybrid method

provides a gain in terms of topological entities compared to

the method published in Ref. [25] and a gain from the initial

model.

Fig. 9 represents the computation results by the FEM simu-

lation of the initial model, model 2 after simplification using

only the size criterion (the most used criterion in the state of

the art) and model 3 after simplification using the hybrid

method. Figs. 9(a-1) - 9(b-1) represent respectively the states

of stress and the displacements of the part before the applica-

tion of the simplification algorithm. Figs. 9(a-2) - 9(b-2) re-

spectively show the states of parts stress and displacements

after simplification using only a size criterion. And Figs. 9(a-

3) - 9(b-3) represent respectively the states of stress and the

displacements of a simplified model after simplification using

the hybrid method. For model 2, we notice that the saving

time of computation is 62.5%. The error relating to the values

of displacements is 2.18%, while that of the equivalent stress

is 1.36%. And for model 3, it is noted that the saving of com-

putation time is 50% and the error relating to the values of

displacements is only 0.54%, while that of the equivalent

stress is only 0.40%.

The graphs presented in Fig. 10, show that the hybrid

method provides a gain in precision of the results more

important than the method published in Ref. [25].

For a preliminary dimensioning analysis, the error of the

first method is considered to be acceptable. If the designer

aims to have a much more precise analysis in order to check

the chosen dimensions, he can apply stricter criteria of sim-

plification to dimensions of the details to be removed or to

the site of the details compared to the loading using the hy-

brid method. This won’t allow the removal of the forms

which are concentrators of the constraint. In all cases, the

taking into account of the simplification link in the "design-

analysis" chain brings an important saving of the computing

time without any significant loss on the quality of the results.

We must notice that this procedure of simplification requires

a negligible execution time compared to the total simulation

time.

Table 2. The B-rep entities before and after idealization.

Models Number

of faces

Number

of wires

Number

of edges

Number

of vertexes

Model 1 209 223 590 385

Model 2 143 156 407 268

Model 3 135 148 391 260

% of Model 2 1

1

100in n

n

−= i 31.58% 30.05% 31.017% 30.39%

% of Model 3 1

1

100in n

n

−= i 34.51% 33.63% 33.73% 32.47%

(a) Model 2: using size criterion (presented in Ref. [25])

(b) Model 3: using hybrid method

Fig. 7. Result of the idealization algorithm implemented by Open

Cascade.

Fig. 8. Comparison between the B-rep entities of idealized model using

size criterion and idealized model using hybrid method.


4. Conclusion

This study has presented a hybrid method of simplification

of the CAD model. The proposed approach consists in reading

the B-rep model of the CAD geometry in order to identify the

details. Then, the identified details were removed or fused if

they are localized in the concentrator’s stress zones.

A comparison of the size’s criterion method [25] and the

hybrid method with the CAD model before simplification was

conducted. The results of this comparison illustrate the major

advantage of the hybrid method compared to the method

based only on the size criterion since it gives a model better

adapted to the need for the FEM simulation.

For a preliminary dimensioning analysis, the error of the

method published in Ref. [25] is considered to be acceptable.

If the designer aims to reach more analysis precision (in order

to check the chosen dimensions), stricter simplification criteria

of to dimensions are needed which is available in the hybrid

method.

The simulation results presented in a treated example high-

light the efficiency of the proposed method.

The proposed method presents the following advantages:

• In the simplification process, the input and output files are

in a STEP format, which is a neutral format (used by the total-

ity of CAD and Analysis tools and systems).

• The simplification process is based on a hybrid method,

to ensure the quality of simulation the result.

• The simplification process is interactive. After treatment,

the CAD part is presented by an iso-zone model, so the de-

signer can intervene in the choice of details to be deleted using

some criteria.

• The simplification process is based on a CAD model, the

reconstruction process is performed without approximation.

• A hierarchic link is saved between the initial model and

the adapted model, to allow a perfect CAD/Analysis integra-

tion.

To improve even more the simplification method, it can

also take into account the orientation of the details compared

to the loadings, this criterion will be a subject of future

work.

Acknowledgment

These research works were developed in the Mechanical

Engineering Laboratory at the National Engineering School of

Monastir, University of Monastir, Tunisia.

a-1

b-1

a-2

b-2

a-3

b-3

Model 1 : Initial model

Model 2 : Simplified model (preliminary dimensioning analysis)

Model 3 : Simplified model (checking analysis)

t : simulation time

S : stress Max

d : displacement Max

% t : time percentage

% S : stress percentage

% d : displacement percentage

Model 1 Model 2 Model 3

t (s) 32 12 16

C (Mpa) 5.438 5.364 5.416

d (µm) 0. 1469 0. 1501 0.1461

% t 62,5 % 50 %

% S 1,36 % 0.40 %

% d 2,18 % 0.54 %

1

1

100it t

t

−= •

1

1

100is s

s

−= •

1

1

100id d

d

−= •

Fig. 9. Computation results.

Fig. 10. Comparison between the computation results of idealized model using size criterion and idealized model using hybrid method.


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Mounir Hamdi is a teacher of Me-

chanical Design at the Higher Institute

of Technological Studies of Sousse,

Tunisia. Hi is currently a Ph.D student

in the National Engineering School of

Monastir, University of Monastir. In

2000 he received his Mechanical engi-

neering degree from National Engineer-

ing School of Monastir. In 2004 he received his Mechanical

master degree from National Engineering School of Tunis.

His main research interests include knowledge-based Com-

puter Aided Design, interoperability and the application of

geometric and solid model Simplification in CAD/CAE.


Nizar Aifaoui is an Associate Professor

of Mechanical Engineering at Prepara-

tory Institute for Engineers of Monastir

in Tunisia. He obtained his Master De-

gree in Mechanical Engineering and

Computer Science and Automation from

Valenciennes University (France) in

1998 and Ph.D in Mechanical Engineer-

ing and Computer Science and Automation, respectively, from

National Engineering School of Monastir (Tunisia) and

Valenciennes University (France) in 2003. Dr. Aifaoui’s re-

search areas include: CAD/CAM/CAE integration and Me-

chanical Design Methodology.

Abdelmajid BenAmara is a Professor

of Mechanical Engineering at National

Engineering School of Monastir in Tunisia.

He obtained his Master Degree in Me-

chanical Engineering from National En-

gineering School of Tunis (Tunisia) in 1992

and Ph.D in Mechanical Engineering and

Computer Science and Automation,

respectively, from National Engineering School of Tunis (Tunisia)

and Valenciennes University (France) in 1998. After an academic

career, he integrated the Mechanical Engineering Department at the

National Engineering School of Monastir in Tunisia. He contributes

to the teaching of CAD, CAM, CAE and manufacturing technologies.

Dr. BenAmara’s research areas include CAD/CAM/CAE integration,

Manufacturing Technologies and Mechanical Design Methodology.

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