Topology optimization of dynamic problems based on finite deformation theory
Shun Ogawa, Takayuki Yamada
Abstract
Abstract This study proposes a topology optimization method for dynamic problems based on the finite deformation theory to derive a structure that can reduce deformations for arbitrary dynamic loads that have large deformations. To obtain a structure that can minimize deformations due to dynamic loading for the isotropic hyperelastic model, the square norm of dynamic compliance is set as the objective function. A sensitivity analysis method of the equation of motion, based on Newmark's method for unknown displacements, is presented in the current study. The analysis is carried out by developing a general design sensitivity equation that can accurately account for the response of the structure to dynamic loading and simultaneously display a high affinity for the general constitutive law by using the adjoint variable method. The accuracy of the obtained sensitivity is verified by using the finite difference method as a benchmark. Numerical examples are then used to demonstrate the validity of the proposed method. The results show that the proposed method is able to derive optimization results according to the magnitude of the applied load.