Keywords: simplification detail, adaptive modelling, error estimation, structural simulation.

To perform a mechanical simulation on a component, a geometric model needs, in general, to be simplified through several steps of shape adaptation and idealization [1,2,3]. The choice and evaluation of the simplifications to perform are a critical element to take in account, since they could strongly affect the quality of the finite element (FE) computation. Most approaches developed about this topic are centred on some a priori criteria [4,5]. These criteria act before performing a FE analysis, and drive and control the shape changes occurring on the component. Nevertheless, a priori criteria are not able to quantify accurately the real influence of a shape simplification on the FE simulation output. An efficient mechanical criterion would need an a posteriori process. In such a case, this criterion is applied after a FE simulation of a simplified model and is assessed using the results coming from a first FE computation on a simplified model. In this way, the user obtains objective information about the quantities produced by the FE computation, which validate the quality of FE analysis results.

We developed an a posteriori criterion [6] that can be applied to linear static FE analysis or thermal problems for stationary linear conduction. It uses an approximation in terms of the energy norm of the difference between the FE solutions over the initial and simplified models, and it is able to evaluate the influence that geometric sub-domain removal has on simulation results. The a posteriori indicator developed is integrated into an automatic adaptive process of geometric simplifications.

The shape adaptation process for the detail simplification takes place in a software environment using polyhedral models, in order to access a wider range of possible shape modifications. We consider as a single detail, that we name "simplification detail", each sub-domain of an object shape whose removal has no influence on the physical phenomenon of the problem considered. Therefore, the removal of a "simplification detail", while shortening meshing and simulation processes, should not significantly modify the analysis results. Although we focus on the application of an a posteriori criterion to estimate the influence of each shape simplification, at first sub-domains are removed according to an a priori estimation of their influence on the simulation results. Therefore, each time we refer to a "simplification detail" at this stage of the process, we are actually referring to an a priori "simplification detail". Details stored during this phase will be subjected to the a posteriori evaluation, and some of them could prove to have an influence on simulation results, and so be reinserted into the simulation model. The concept of "simplification detail" can be associated to any kind of shape input. If we input CAD models, CAD data are attached to the geometry of the polyhedron model. Even when no CAD data are available, geometric operators are able to identify and store the information about all the removed sub-domains.

After the simplification process, the FE mesh of the simplified model is generated and the mechanical problem is solved using this model. Then, a local FE problem is set up around each shape detail removed, in order to apply the a posteriori indicator to it. A FE mesh is generated for each sub-domain removed and another sub-domain surrounding it is built. Boundary conditions are applied on each local FE problem that come from the FE results on the simplified model. The influence indicator is computed using the FE results from the simplified model and from each sub-domain, and gives a feedback about the contribution of each sub-domain relative to the FE solution for the simplified model. The accuracy threshold value is prescribed by the user. Values of the indicator lower than the threshold validate the corresponding user shape detail removal; otherwise the corresponding shape detail needs to be reinserted in the simplified model.

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, Dearborn, USA, 1998.

2

P. Dabke, V. Prabhakar, S. Sheppard, "Using features to support Finite Element idealization", International Conference ASME, Minneapolis, Volume 1, 183-193, 1994.

3

V. Francois, J-C. Cuillière, "Automatic remeshing applied to model modification", Computer Aided Design, Vol. 32, 377-388, 2000. doi:10.1016/S0010-4485(00)00028-2

4

L. Fine, J-C, Léon "A new approach to the Preparation of models for F.E. analyses", International Journal of Computer and Applications, Vol. 23, No.2/3/4, pp. 166 - 184, 2005

5

G. Foucault, P. Marin, J-C. Léon, "Mechanical criteria for the preparation of finite element model", Proceeding of the 13^o International Meshing Roundtable, Williamsburg, USA, 2004.

6

P.M. Marin, R. Ferrandes, "Adaptive modelling of CAD model for linear static computation", Proc. of ADMOS Conference, Barcelona, Sept. 2005.

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