A complementarity approach for elastoplastic analysis of strain softening frames under combined bending and axial force

This paper presents the elastoplastic analysis of skeletal structures that can exhibit local strain softening behavior. In particular, both nonholonomic (path-dependent) and holonomic (path-independent) formulations are developed as special instances of the well-known mathematical programming problem known as a mixed complementarity problem (MCP). The effects of combined bending and axial force are also included through a (hexagonal) piecewise linear yield locus that can accommodate either perfect plasticity or isotropic softening. Numerical examples are given to assess the ability of the nonholonomic solution scheme proposed to trace all multiple equilibrium paths, to compare the results of the nonholonomic assumption with those of its simpler approximate holonomic counterpart, and to assess the influence of combined stresses.