Keywords: finite element, quality control, design of experiments, h-adaptivity.

The use of finite element analysis (FEA) in engineering simulation requires the management of hypotheses in order to analyze a real complex system. This paper proposes a framework based on the design of experiments method [4] and a multi-objective optimization method to help in choosing the physical model hypotheses. The procedure is coupled with a mesh adaptive method based on the use of an h-adaptive scheme in combination with an error estimator in order to choose the mesh for the simulation model [1]. From a reference case and for a similar analysis case [2], this method allows us to choose the simplification hypotheses for both the physical model and the simulation model while conforming to the prescribed cost and quality of the whole FEA.

Nowadays, in an industrial context, cost and delay reduction, as well as quality improvement are of major interest in engineering design. Therefore, in order to make decision as soon as possible and according with the product specifications, FEA is commonly used as a design-aided tool for product design. In FEA, two modelling steps require hypotheses to be able to carry out the computations and to obtain some results: the building of the physical model (mathematical model, domain simplifications, materials properties, boundary conditions and loads) and the building of the simulation model (adaptive mesh). The simplification hypotheses made on the system analysed in these two steps two kinds of errors can be generated: the physical modelling errors and the mesh discretization errors. The physical modelling errors result from the simplification of the real complex problems in order to solve them using FEA. According to the real system, the physical model consists of the whole simplification hypotheses. Therefore, in the physical modelling process, the main source of errors arise from the choice of the simplification hypotheses categories such as: the mathematical model (the elasticity theory, the Reissner one for plates, plastic strains, etc.), the geometrical simplifications (suppression of geometrical details such as some small size holes, chamfers, etc.), the materials properties, the boundary conditions and the loading. The mesh discretization error results from the difference between the analytical results and those obtained from the discretized calculation. In this work, we only consider the spatial mesh discretization error. Adaptive mesh strategies are a necessary tool to make FEA applicable to engineering practice [3]. This study focuses on the assessment and the control of physical modelling and the discretization errors in FEA. From a reference case and a similarity hypothesis, the automated method enables us to obtain an indication of the simplification hypotheses for a new similar case of structural analysis in order to control the cost and the quality of the whole FEA. The method presented in this paper supports the choice of the physical and simulation models.

1

E. Bellenger, P. Coorevits, Adaptive mesh refinement for the control of cost and quality in finite element analysis, Finite Elements in Analysis and Design, vol. 41, pp. 1413-1440, 2005. doi:10.1016/j.finel.2005.04.002

2

Y. Benhafid, N. Boudaoud, N. Troussier, F. Pourroy, Towards the use of the design of experiments method to control the quality of structural analysis, Proceedings of the 8 International Conferences on Quality, Reliability, Maintainability, 2002.

3

A. Huerta, A. Rodríguez-Ferran, P. Díez, J. Sarrate, Adaptive finite element strategies based on error assessment, Int. J. Numer. Methods Eng., vol. 46, pp. 1803-1818, 1999. doi:10.1002/(SICI)1097-0207(19991210)46:10<1803::AID-NME725>3.3.CO;2-V

4

G. Taguchi, S. Konishi, Orthogonoal arrays and linear graphs, Dearborn: American supplier institute, 1987.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £105 +P&P)