Abstract
In many practical situations, it is necessary to have reliable evaluations of local quantities. For example, this is the case in design where dimensioning criteria nearly always involve local quantities (stresses in specified zones, Von Mises’ stresses, displacements, stress intensity factors, ...). In current industrial practice, these quantities are evaluated using F.E. analysis. Even if the mechanical model chosen is adequate (good description of the geometry, good knowledge of the material’s characteristics and of the loading), the F.E. analysis introduces errors in the quantities being calculated. For the engineer, it is essential to study and, if possible, to evaluate the quality of the calculations carried out in order to validate the results. In this work, we are concerned with the quality of a linear F.E. analysis. We propose a tool, based on the concept of error in constitutive relation, which enables one to evaluate the local quality of the stresses. We show that this approach gives good results.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Ladevèze, P. and Rougeot, P. (1997), New advances on a posteriori error on constitutive relation in f.e. analysis, Comp. Meth. in Applied Mech. and Engrg., 150: 239–249
Ladevèze, P., Rougeot, P., Blanchard, P., and Moreau, J. (1999), Local error estimators for finite element analysis, Comp. Meth. in Applied Mech. and Engrg., 176: 231–246
Peraire, J. and Patera, A. (1998), Bounds for linear-functional outputs of coercive partial differential equations: local indicators and adaptive refinement. in Advances in Adaptive Computational Methods, Ladevèze, P. and Oden, J., editors: 199–216, Elsevier
Prager, W. and Synge, J. (1947), Approximation in elasticity based on the concept of functions space, Quart. Appl. Math., 5: 261–269
Prudhomme, S. and Oden, J. (1999), On goal-oriented error estimation for elliptic problems : application to the control of pointwise errors, Comp. Meth. in Applied Mech. and Engrg., 176: 313–331
Rannacher, R. and Suttmeier, F. (1997), A feedback approach to error control in finite element methods: Application to linear elasticity, Comp. Mech., 19: 434–446
Strouboulis, T., Babuka, I., Datta, D., Copps, K., and Gangaraj, S. (2000), A posteriori estimation and adaptative control of the error in the quantity of interest. part 1: A posteriori estimation of the error in the von mises stress and the stress intensity factor, Comp. Meth. in Applied Mech. and Engrg., 180: 261–274
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Florentin, E., Gallimard, L., Pelle, JP. (2003). A Tool for Verifying the Local Quality of a 3D F.E. Analysis in Design. In: Gogu, G., Coutellier, D., Chedmail, P., Ray, P. (eds) Recent Advances in Integrated Design and Manufacturing in Mechanical Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0161-7_5
Download citation
DOI: https://doi.org/10.1007/978-94-017-0161-7_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6236-9
Online ISBN: 978-94-017-0161-7
eBook Packages: Springer Book Archive