A Heuristic Approach to Solve Stiffness Design of Continuum Structures with Tension/Compression-Only Materials

A new heuristic approach is presented to find the optimal topologies of structures with tension/compression-only materials. In civil engineering, the structures, such as brick walls have only compressive stiffness, or as the cable-membrane structures can only against tension loadings. To find their optimal topologies with traditional continuum topology optimization methods are very hard. Two reasons are as follows. Firstly, the material in structure should be considered as nonlinear in a finite element analysis (FEA) process. Secondly, many times of structural FEA are required to find the proper displacement, strain and stress fields in each iteration for updating the design variables. To avoid such difficulties, a structural optimization is considered as the remodelling process of a piece of bone. In bone-mechanics, the function of mechanical stimulation means that the distribution of local material in a bone tissue varies when the deformation of tissue goes beyond an interval, which is called as dead zone. Based on the concept, the update rule of local material called as growth law is proposed and the original material in design domain is taken the place of isotropic porous material whose growing law is determined by two floating intervals of reference strain according to the local stress/strain states in optimization. The update of the reference intervals are determined by the active constraint of optimization problem. Numerical examples are given to demonstrate the validity of the present approach.