A continuum structural topology optimization method considering frequency constraints and the effect of self-weight

Abstract This work proposes a method for optimizing the continuum structural topology under multiple load cases considering frequency constraints and the effect of self-weight. An improved Solid Isotropic Material with Penalization (SIMP) model is proposed to avoid the parasitic effect. At the same time, new matching smooth penalty functions on the element stiffness, volume and mass are constructed to greatly reduce the number of low-order pseudo-modes in the optimized structure. And low-order pseudo-mode identification and deletion measures are introduced to solve the pseudo-mode problem. The Heaviside three-field mapping scheme and two varied volume constraints are introduced to obtain a clear 0/1 distribution. Moreover, a volume change rate constraint measure of low-physical density elements is proposed to greatly improve optimization computation efficiency for the structural topology problem considering both frequency constraints and the effect of self-weight. It is concluded from examples that the proposed method is effective and robust for generating an optimal topology.