TOPOLOGY OPTIMIZATION OF PLASTIC STRUCTURES USING FINITE ELEMENT LIMIT ANALYSIS

Abstract

This paper is concerned with topology optimization of plastic structures under large deformation using finite element limit analysis. The topology optimization allows designers to get a solution independent of the initial guess enhancing the required structural performances such as stiffness or eigenfrequency of structures. Due to the advantage, the topology optimization has been used in many applications very successfully since its introduction. However, most applications have been limited to optimization of structures with assumption of linear elastic material and finite deformation behavior which are not always valid especially in the cases of compliant design and energy absorption design. It is well known that the structural analysis considering a nonlinear plastic material and large deformation to evaluate the performance measure with respect to the design variation is very time consuming and the computing time of the conventional elasto-plastic analysis is generally dependent on the number of unknowns. Also it is extremely difficult to derive an analytic formulation of the design sensitivity for the objective and cost functions for plastic deformation problems. So, it is very crucial to employ an efficient and alternative structural analysis technique for the optimization to solve those obstacles. The topology optimization of plastic structures, hence, still remains inapplicable except a few ones. Finite element limit analysis could be one of promising solutions for nonlinear topology optimization. Finite element limit analysis predicts sequential collapse modes and collapse loads of a structure considering not only plastic material behavior but also large deformation with moderate computing cost. In this paper, the optimum topologies of structures under large plastic deformation are obtained using finite element limit analysis. Optimizations are performed to maximize the plastic work under displacement-controlled loadings. The SIMP method and the MMA are employed for parameterization of the design domain and minimization of the objective functional respectively. Comparisons between elastic design and limit analysis design are made for verification of the proposed optimization algorithm. The load-carry capacity and the stiffness of the optimal solutions by the elastic design and the limit analysis design are investigated. Considering the plastic deformation of the structures leads to different optimal layouts from those based on the elastic design. Results show that the optimization algorithm proposed can obtain the optimal structures which have much higher load-carrying capacity than those by the elastic analysis with comparatively less computing time.