This paper proposes a highly efficient topology optimization using two accelerated methods, which can reduce the degrees of freedom (DOFs) of the finite element equations and accelerate the iteration convergence of the topology optimization. For the DOF reduction, a method based on the empty elements and the displacement change during the topology iterations is presented to remove the DOFs from the finite element equations. For the convergence acceleration, a gray-scale suppression method is proposed to accelerate the polarization of design variables which accelerates the iteration convergence of the topology optimization. Three numerical examples including 2D and 3D cases are tested, and the results show that the proposed method can significantly improve the efficiency of the topology optimization and obtain the optimization results with the same accuracy. The computational time is only about 7% - 29% compared to the conventional topology optimization method.

本文提出了一种使用两种加速方法的高效拓扑优化方法，可以降低有限元方程的自由度（DOF），并加快拓扑优化的迭代收敛速度。为了降低自由度，提出了一种基于空元素和拓扑迭代过程中位移变化的方法，以从有限元方程中去除自由度。为了加快收敛速度​​，提出了一种灰度抑制方法来加速设计变量的极化，从而加快拓扑优化的迭代收敛速度。测试了包括2D和3D情况在内的三个数值示例，结果表明，该方法可以显着提高拓扑优化的效率，并获得相同精度的优化结果。与常规拓扑优化方法相比，计算时间仅为大约7％-29％。