A “poor-man’s” deformation plasticity based approach to topology optimization of elastoplastic structures

Abstract

This paper presents a topology optimization framework utilizing a deformation plasticity model to approximate the isotropic hardening von-Mises incremental elastoplasticity model under monotone proportional loading. One advantage of the model is that it is based on a yield surface allowing for precise matching to uniaxial elastoplastic isotropic hardening response. The deformation plasticity model and the incremental plasticity model coincides for proportional loading and since the deformation plasticity model is path-independent, the computational cost and implementation complexity reduce significantly compared to the conventional incremental elastoplasticity. To investigate the deformation plasticity model combined with topology optimization, we compare three common elastoplastic optimization objectives: stiffness, strain energy and plastic work. The possibility to limit the peak local plastic work while maximizing the strain energy is also investigated. The consistent analytical sensitivity analysis which only requires the terminal state is derived using adjoint method. Numerical examples demonstrate that the proportionality assumption is reasonable and the deformation plasticity model combined with topology optimization is a competitive alternative to cumbersome incremental elastoplasticity.