Elastoplastic analysis of plane stress/strain structures via restricted basis linear programming

•An automatically determined load step for nonlinear plane stress/strain analysis.•A solution for problems of unloading and twofold yield situation in PWL problems.•Less CPU time and more accurate results compared to similar existing algorithms.•Mixed FEM formulation to enable the solver to return sufficiently accurate results.•A suitable linear surface envelope definition for von-Mises yield surface.

In this paper, elastoplastic analyses of plane-stress and plane-strain structures are addressed. The traditional von Mises yield surface is assumed in the material constitutive model and its piecewise-linear (PWL) approximation is derived. An associated flow rule is adopted and a consistent linear mixed hardening rule is developed in the so called mixed formulation. The relevant mathematical programming (MP) problem, which aims at the maximization of the linear combination of plastic multipliers, is constructed. Restricted basis linear programming (RBLP) is used to solve the MP problem, while special provisions are accounted for to obtain nonholonomic solutions. In order to reduce the required storage space, the Revised Simplex method and a sifting technique are employed. The proposed algorithm is validated and its performance is illustrated by solving some classical nonlinear problems.