The lightweight topology optimization of multi-material structures with displacement constraints

Abstract

Multi-material Topology Optimization is a simulation technique based on the principle of the finite element method which is able to determine the optimal distribution of two or more different materials in combination under thermal and mechanical loads. This paper develops a lightweight topology optimization formulation of multi-material structures considering displacement constraints based on independent, continuous and mapping (ICM) method. Furthermore, explicit expression of optimised formulation is derived, approximations of displacement and weight are given by the first and second order Taylor expansion. And the optimization problem is solved by sequential quadratic programming approach. The feasibility and effectiveness of proposed method are demonstrated by numerical examples. It is found that the best transfer path of load is provided using multi-material topology optimization. The results show that a clear topological structure is obtained and the best transfer path of load is provided after multi-material topology optimization. In addition, under the precondition of satisfying the displacement constraint condition, the weight of the optimized structure based on various materials is lighter. The weight of multi-material topology optimization structure decreases with the increase of displacement constraint. And the optimal topological structure of the multi-material is different with the component materials. Besides, the optimization model established by using the structural performance parameters as a constraint is more reliable and more suitable for practical engineering applications.