Topology Optimization for Structures With Nonlinear Behavior Using the Equivalent Static Loads Method

Abstract

Many structures in the real world show nonlinear responses. The nonlinearity may be due to some reasons, such as nonlinear material (material nonlinearity), large deformation of the structures (geometric nonlinearity), or contact between the parts (contact nonlinearity). Conventional optimization algorithms considering the nonlinearities are fairly difficult and expensive because many nonlinear analyses are required. It is quite difficult to perform topology optimization considering nonlinear static behavior because of the many design variables. In the current element density based topology optimization considering nonlinear behavior, low-density finite elements cause serious numerical problems due to excessive mesh distortion. Updating the material of the finite elements based on the density is considerably complicated because of the relationship between the element density and structural material. The equivalent static loads method for nonlinear static response structural optimization (ESLSO) has been proposed for size and shape optimization. The equivalent static loads (ESLs) are defined as the linear static load sets which generate the same displacement field from nonlinear static analysis. In this research, a new algorithm is proposed for topology optimization considering all kinds of nonlinearities by modifying the existing ESLSO. The new ESLSO can overcome the difficulties which may occur in topology optimization with nonlinear static behavior. A nonlinear static response optimization problem is converted to cyclic use of linear static response optimization with ESLs. Therefore, the new ESLSO can generate results of nonlinear static response topology optimization by using well established nonlinear static analysis and linear static response topology optimization methods. Four structural examples are demonstrated using the finite element method. Different kinds of nonlinearities are involved in each example.