Keywords: geometrical simplification, accuracy, finite element, reliability, CAD, feature suppression.

The use of the CAD in design makes it possible to more and more precisely represent the mechanical systems with a great number of details. For a use in finite element computation, the obtained models are often too precise and their direct use would generate a too great number of finite elements. A preliminary step of model simplification is then necessary. Various softwares make it possible to automate this step partially. Several categories of approaches have been proposed to solve the problems involved in the the preparation of F.E. models from CAD data.

A first addresses configurations where small features must be removed to get the geometric model more compatible with the size of the F.E. required [1]. These approaches are strongly dependent on the modelling history of the part and work on the building tree of the object and the removal of selected features.

A second one starts with a polyhedral model of the part [2]. In order to adapt the model, different adaptation functions work on the initial configuration. They combine decimation processes and the suppression of topological details.

Another category of approaches is characterized by idealization treatments. Such operations are often required to transform a volume into an open surface to model a plate behaviour. Similar operations hold for transforming a volume feature into a line to model a beam belaviour of the structure.

Our paper focuses only on the errors given by the two first categories of geometric simplification and idealization process is not aborded.

The accuracy of finite element computation is one of the main concerns of the users. The causes of the errors are multiple, errors of discretization, uncertainty on the loading and the behaviour, and simplification of the geometry. During the last twenty years, much work was devoted to the errors of discretization and to the associated adaptive refinement. The quality of finite element computation can be strongly influenced by the simplifications carried out on the geometry. The choice and the control of these simplifications are thus of primary importance. When the preparation of the model is manual, quality depends on the know how of the engineer. Many industries have simplified models for their own specific applications. These models are made from experience or simulations with the complete model [3]. For an automatic process of simplifications, piloting uses geometrical criteria, curve, size, etc. In a step, a priori, geometrical criteria related to the mechanical properties of the problem can be added, variation of mass, volume, section, centre of inertia, etc.

But the a priori criteria cannot quantify the real influence of a geometrical simplification on finite element simulation. For example, the errors given by the suppression of hole will depend on the dimension of the hole but also of its position in the part. The feature can be in an area with weak or strong constraints.

A real mechanical criterion needs a posteriori process. After a simulation on the simplified part, mechanical criteria are computed for evaluate the influence of each suppressed feature. The engineer obtains information in order to validate the quality of its finite element results. He can also use the criteria in an adaptive process of simplifications and redefine the simplified part by adding some of the suppressed features. Such a process of simplification was used in [2]. The criterion used was the error of discretization on the simplified problem and the chart of size of an optimal mesh on this problem. The program suppresses detail if the size of the detail is lower than that given in this area by the chart of size. This indicator gives bad information in the area where the stresses are strong but smooth. The prescribed sizes of optimal mesh are bigger in this area.

Our criteria are a fortiori criteria and can be used in an adaptive process of geometric simplifications. After a finite element computation on the simplified structure, we propose an indicator of error allowing to quantify the influence of each simplification on the accuracy. In order to estimate the importance of a geometric modification on the global solution, we use the difference between the strain energy of the initial part and the one of the simplified part. This indicator needs a local finite element computation in the neighbourhood of each feature. With this information, the user (or the program in an automatic simplification algorithm) can define the simplified model and accept or not accept each simplification. The proposed indicators relate to problems of static analysis with linear belaviour or thermal problems for stationary linear conduction. Section 2 presents the indicator used and its efficiency is tested on different kinds of problem in section 3.

1

A.V. Mobley, M.P. Caroll, S.A. Canann, "An object oriented approach to geometry defeaturing for Finite Element Meshing", Proceeding of the 7th International Meshing Roundtable, Sandia National Laboratories, 1998.

2

P. Véron, Léon J.C., "Shape preserving polyhedral simplification with bounded error", Computer Graphic, Vol 22, 565-585, 1998. doi:10.1016/S0097-8493(98)00063-6

3

E. Livne, "Equivalent plate structural modelling for wing shape optimization including transverse shear", AIAA J, Vol 32, no6, 1278-1288, 1994. doi:10.2514/3.12130

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