Multiple objectives adaptive topology optimization for microstructures of composite materials

An adaptive weighted sum algorithm proposed for multiple objective problems is presented to optimize the topology of the microstructure with periodic two-phase materials. The microstructure of porous composite with a certain volume fraction of solid materials and structural symmetry is studied. By means of the homogenization method and method of moving approximating (MMA), the equivalent elastic module of cell is calculated and maximized, based on the finite element method. The relative density of each element of the cell is defined as the design variable based on the finite element method, with SIMP density-stiffness scheme which has the effect of penalizing to elements with intermediate density. During the process of iteration, the weighing coefficient is adaptively adjusted according to the variety of the objective function. Several microstructure topologies are obtained by the adaptive weighting algorithm with different combinations of equivalent elastic module and weighing coefficients. Numerical results verify the validity of the proposed adaptive weighted sum algorithm in the multiple objective topology design of microstructures.