Optimization of 2-D structures subjected to nonlinear deformations using the homogenization method

The generalized layout optimization method is applied to nonlinear problems. The algorithm was originally invented by Bendsoe and Kikuchi (1988), where an admissible design domain is assumed to be composed of periodic microstructures with tiny cavities; the sizes and the rotational angle of the cavities are defined as design variables which are optimized to minimize the applied work. The macroscopic material tensor of the porous material is calculated by the homogenization method for the sensitivity analysis. In order to apply it to nonlinear problems, we present a 2-D database of the material tensor calculated by the elasto-plastic homogenization method and an interpolation technique of the database for the practical computation. Several numerical examples of 2-D structures and a thin shell are shown to demonstrate the effectiveness of our algorithms. The algorithm is also extended to the finite deformation problems, and a practical optimized design is exhibited.