Topology optimization methods enable designers to find the best structural layout for required structural performances. Most papers have been concerned with the optimization of structures with linear material. However, there are several structures involving nonlinear material. Evolutionary structural optimization (ESO) is based on the simple concept of systematically removing inefficient material from the structure after each finite element analysis, so that the resulting design is gradually evolved to an optimum. This method has been successfully applied to optimum material distribution problems for continuum structures and has been extended to a wide range of structural optimization problems. Huang and Xie in 2007 applied this method to the topology optimization for maximizing stiffness of nonlinear structures by removing and adding elements, based on the strain energy criterion. This paper is concerned with optimization of elastic and elasto-plastic bodies when isotropic strain hardening takes place, based on the von Mises stress criterion using the classical ESO method. The optimum design has a more uniform stress level. Also, the optimization process has been carried out based on the stiffness criterion. In this case, the material with the least contribution to the overall stiffness should be removed from the structure and the optimum design has a uniform stiffness. Several examples are presented to verify the proposed optimization methods. Results are compared for these two criteria and against elastic and elasto-plastic material and also with that of the adaptive method. It is concluded that in elastic analysis the stress criterion is more suitable with respect to the stiffness criterion and the optimum shapes have a better stress ratio as well as a better strain energy ratio outcome. For elasto-plastic bodies, the behavior of the both criteria is more or less the same and can be used alternatively.

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