Topology optimization of structures composed of more than two materials with different tensile and compressive properties

A novel method is proposed to optimize the topology of composite structures made of more than two materials with different mechanical properties in tension and compression. In this method, the design domain of the structure is divided into tensile and compressive regions according to the first invariant of the stress tensor. Then two groups of materials suitable for tension and compression are arranged in the tensile and compressive regions of the structure, respectively. Using a bridge-type beam with a concentrated force as an example, the study of the four-material topologically optimized structures reveals the effects of the volume fractions and material mechanical properties on the optimization results. Further, the three-material topology optimization method, which is derived from the four-material topology optimization method, is used to design a series of novel sandwich structures. Application examples demonstrate that the proposed method can achieve a balance between enhancing structural stiffness and saving material costs, providing solutions competitive in various aspects and exploiting the performance and potential of different materials better than previous single- or dual-material topology optimization methods.