A guide-weight criterion-based topology optimization method for maximizing the fundamental eigenfrequency of the continuum structure

This paper first introduces the guide-weight criterion into the topology optimization problems for maximization of the fundamental eigenfrequency of vibrating continuum structures. The traditional solid isotropic material with penalization model is modified to eliminate the artificial localized modes. Based on this modified model, the iteration formula of the design variables is derived using the guide-weight criterion. An iterative mass control strategy is adopted to satisfy the equality constraint on the final mass and to stabilize the iteration process. Additionally, a mass preserving density filter based on Heaviside function is used to solve the gray transition problem. Several typical examples are used to validate the proposed method. Numerical results show that the proposed method is capable of achieving iterative convergence and clear profiles of topologies; meanwhile, the optimal results obtained by the proposed method agree well with those obtained by the commonly used bi-directional evolutionary structural optimization (BESO) method. In particular, the proposed method has a faster convergence rate than the BESO method.