Concurrent topology optimization design of material and structure within FE2 nonlinear multiscale analysis framework

This paper revisits concurrent design of material and structure within FE2 nonlinear multiscale analysis framework. For structural stiffness maximization at macroscopic scale, design variables are defined at the both scales. Cellular material models are defined at microscopic scale in a pointwise manner for the considered macroscopic structure. They are optimized to adapt the macroscopic structural physical response. Though linear models are assumed at both scales, the macroscopic structural equilibrium is in general nonlinear due to the adaptation of cellular material microstructures. For this reason, an iterative resolution based on FE2 scheme is developed to address this nonlinearity. Discrete topology optimization algorithm, bi-directional evolutionary structural optimization (BESO) is used at the both scales. It is shown by means of numerical tests that FE2 scheme can well bridge the two scales and address the nonlinearity. Reasonable design solutions of the macroscopic structure and its corresponding cellular materials have been obtained by the developed concurrent design framework.