抄録
Topology optimization is well-documented research topic, and the many methodologies have been proposed to obtain optimal configurations in various physical problems. In conventional topology optimization approaches, optimization problems are commonly formulated under the steady-state condition, which means that the derivative with respect to time in the governing equation is ignored. The steady-state governing equation is typically discretized using the finite element method, and is implicitly solved by matrix operations. The implicit approach is, however, unsuitable for parallel computations, because the numerical treatment of a large-scale matrix operation needs a massive computational cost and it is difficult to educe the high parallelism. In this study, we propose a topology optimization method in which an optimization problem is formulated using unsteady governing equations, which are discretized by an explicit scheme. The key idea of the proposed method is that the design sensitivities at each optimization step are calculated using the state and adjoint variables at the previous optimization step, so that the steady-state condition is rapidly satisfied by a few iterations of the explicit computations. We guess this is a promising methodology for solving large-scale topology optimization problems, and would like to discuss its validity.
