Keywords: reverse engineering, mesh generation, geometry adaptation, vertex removal, triangulations, conformity.

Currenlty, FE meshes and analysis models are generated from CAD models during the product design phase. Such a preparation phase often requires the use of geometric treatments for adapting or idealizing the model to fit the hypotheses and requirements of the FE analysis forseen. Either based on CAD models preparation [1,2] or on FE mesh modifications [3], model adaptation and idealization are necessary to fit the FE analysis requirements. Recently, new approaches have been proposed to generate meshes from models prepared for rapid prototyping manufacture, namely STL files [4], to be able to handle new sources of data. However, CAD models of products and constructions as well as FE meshes are not always available if the objective is the study either of products "as-manufactured" or of constructions "as-built". Hence, reverse engineering methods are required to produce a FEA model.

The proposed approach focuses on the direct use of the triangulation obtained from the digitizing phase to avoid the construction of a CAD model from the digitized points and provide directly the FE model required for the analysis or the adapted geometry [5] required to generate the FE mesh.

A first step analyses the input triangulation to check its conformity and correct it to remove degenerate faces, unwanted gaps, self intersecting areas that can be generated during the generation phase of this input triangulation. Most of these operations are automated through specific operators to ease the generation of a conform triangulation and tools are provided to analyse the conformity of this triangulation.

Basically, the method set up uses a polyhedron decimation approach to remove vertices from the digitized model input after the clean up phase of this digitized model which has produced a conform triangulation. Then, combining shape triangle constraints, geometry adaptation constraints, FE element size gradient, FE element sizes, an adapted FE mesh of the structure can be obtained directly from the digitized data. Depending on the digitizing technique (3D laser sensor, tomography), complementary operators may be applied to generate an adequate initial triangulation and the FE model generation may requires two distinct stages to produce the adapted model and then the FE mesh generation. A two stages approach is required when detail removal operations are required with respect to the desired analysis model.

In this case, the first stage is used to perform noise and detail removal from the input triangulation. Noise is inherited from the scanning phase and needs to be removed to produce a smooth triangulation. This operation is performed using a shape preserving decimation algorithm based on a vertex removal operator. The maximum geometric deviation between the initial triangulation and the smoothed one is controlled by a distance criterion. From this triangulation a detail removal process takes place to adapt the object geometry to the hypotheses of the analysis and the requirements of the FE mesh.

Then, the second stage is the generation of the FE mesh onto the adapted triangulation representing the domain of study.

In order to speed up further the process the first and second stages described above can be merged together when the geometry adaptation phase does not need to large geometry changes or topological changes. In this configuration, a single process used to remove the digitizing noise, perform surface adaptation of the part and generate the target FE mesh can be directly applied on the conform triangulation.

Results are provided to illustrate this approach with historical constructions: elements of a statue of Ptolemy found at Alexandria (input triangulation with 700 000 faces), elements of a roman column digitized by a laser sensor ; as well as industrial components: aerospace crankcase digitized by tomography (input triangulation with 400 000 faces).

1

A. Sheffer, T.D. Blacker, M. Bercovier, Clustering: Automated detail suppression using virtual topology, Proc. 1st Symp. On Trends in Unstructured Mesh Generation, Joint ASME/ASCE/SES Summer Meeting, (1997), 57-64.

2

M. Reyzayat, Midsurface abstraction from 3D Solid Models: general theory and applications, CAD, 28, (1996), 905-915.

3

S. Dey, M.S. Shephard, M.K. Georges, Elimination of the adverse effects of small model features by the local modification of automatically generated meshes, Eng. With Computers, (1997), 134-152. doi:10.1007/BF01221211

4

E. Béchet, J.-C. Cuillière and F. Trochu, Generation of a finite element MESH from stereo-lithography (STL) files, CAD, 34 (1), (2002), 1-17

5

L. Fine, L. Rémondini, J-C. Léon, Automated Generation of FEA models through idealization operators, Int. J. Num. Meth. In Eng., 49, (2000), 83- 108. doi:10.1002/1097-0207(20000910/20)49:1/2<83::AID-NME924>3.0.CO;2-N

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