Limit analysis decomposition and finite element mixed method

作者：Pastor Franck^*; Loute Etienne

来源：Journal of Computational and Applied Mathematics, 2010, 234(7): 2213-2221.

DOI：10.1016/j.cam.2009.08.074

• Porous material
• Convex optimization
• Decomposition
• Limit analysis
• Finite element method
• Mixed approach

This paper proposes an original decomposition approach to the upper bound method of limit analysis. It is based on a mixed finite element approach and on a convex interior point solver, using linear or quadratic discontinuous velocity fields. Presented in plane strain, this method appears to be rapidly convergent, as verified in the Tresca compressed bar problem in the linear velocity case. Then, using discontinuous quadratic velocity fields, the method is applied to the celebrated problem of the stability factor of a Tresca vertical slope: the upper bound is lowered to 3.7776 - value to be compared to the best published lower bound 3.7752 - by succeeding in solving a nonlinear optimization problem with millions of variables and constraints.

• 出版日期2010-8-1