Multi-Objective Topology Optimization Of Microstructure Of Lightweight Materials

Light weight, function specialization, and integrated performance, which satisfy service environment, can be realized by topology optimization. The development of optimization theory and method plays an important role in replacing traditional design theories and methods, improving the design of products, abbreviating design time and reducing cost. Since macro properties exhibited by material results from microstructure's scale, topology, and concrete constituents, optimizing macro effective properties of material is necessary and feasible. By designing microstructure, composite exhibiting well expected properties can be obtained, and integrated design of materials and structures can be achieved, resulting in the integration of material and structure design as well as the best match of materials and structures. Then under the requirement of fulfilling macro structure's function, design potential of material and structure can maximally be exploited. Topology optimization for microstructure usually belongs to multi-objective optimization problem.In this paper, for topology optimization defined in the domain with periodic microstructure, applying homogenization method to obtain effective macro-coefficients, defining the values of topology description function as variables, a multi-objective nonlinear programming model was established to achieve material design with prescribed properties. Topology description function, describing the topology of the microstructure, was cited to restrain checkerboard phenomenon and obtain smooth boundary. For designing material with prescribed properties, microstructures were obtained in the following three cases: (1)designing microstructure composed of cavities and single-phase material with given macro effective elastic coefficients;(2)composite exhibits extreme thermal expansion coefficients with microstructure composed of two-phase materials;(3)composite composed of cavities and single-phase material exhibits extreme thermal conductivity. Optimization of microstructure is achieved when macro-structure's heat dissipation is defined as the objective function.