A Thefftz patch recovery method for smooth stress resultants and applications to Reissner-Mindlin equilibrium plate models
Abstract
A method is proposed for smoothing approximate fields of stress-resultants in patches of finite elements. The method is based on combining Trefftz fields of stress-resultants in a p-version so as to obtain a closest fit using the strain energy norm as a measure. The local systems of equations are formulated from boundary integrals. The method is applied to a problem of a square plate modelled by hybrid equilibrium plate elements using Reissner- Mindlin theory. Results for the problem indicate that the smooth solution for stresses can be in close agreement with the analytic solution in the interior of a patch. Proposals are also included to aid the visualization of tensor and vector continuous fields as stress trajectories.
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References
[1] J .F. Debongnie, P. Beckers. On a general decomposition of the error of an approximate stress field in elasticity. CAMES, 8: 261- 270, 2001.[2] M.M. Frocht. Photoelasticity, Vol. 1. Wiley, New York, 1941.
[3] H.-C. Hege, K Polthier, eds. Mathematical Visualisation Algorithms, Applications and Numerics. Springer, Berlin, 1998.
[4] A. Hillerborg. Strip Method of Design. Viewpoint Publications, Wexham Springs, 1975.
[5] J. Jirousek, A. Venkatesh. A simple stress error estimator for hybrid Trefftz p-version elements. Int. J. Num. Meth. Engrg., 28: 211- 236, 1989.
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