Abstract
We develop a method of topology optimization for structures at finite strains based on the mathematical homogenization theory. After formulating the geometrically nonlinear problems with hyperelastic material, we briefly review the conventional approach that employs orthotropic homogenized properties. We then propose to use finite number of sampling points for updating design variables in a finite element by introducing isotropic homogenized material properties, whereas the conventional approach uses one set of design variables in an element. The corresponding formulation approach is consistent with the mechanical problem modeled by the homogenization method. Several representative numerical examples are presented to show the validity and applicability of the proposed approach. In particular, we try to clarify the mechanism which generates the optimal structure prevented from revealing structural instabilities such as buckling.
