Computation of bounds for exact quantities of interest in elasticity based on FEM and SFEM

Authors:
Zhaocheng Xuan;Yaohui Li;Hongjie Wang
Affiliations:
Department of Computer Science, Tianjin University of Technology and Education, Tianjin, China;Department of Computer Science, Tianjin University of Technology and Education, Tianjin, China;Department of Computer Science, Tianjin University of Technology and Education, Tianjin, China
Venue:
HPCA'09 Proceedings of the Second international conference on High Performance Computing and Applications
Year:
2009

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Abstract

We compute lower and upper bounds for the quantities of interest that are the functions of displacements in elasticity by finite element method (FEM) and smoothed finite element method (SFEM). An important feature of FEM based on the minimum potential energy principle is that it bounds the true strain energy of the structure from below, whereas SFEM, which has been found recently, generally provides bounds from above. We use the two methods to compute outputs–local displacements, local reaction and stress intensity factor in the elastic problems, and find that they do give the lower and upper bounds for the true outputs.