An improved parametric level set method for structural frequency response optimization problems. (December 2018) - Li, Hao; Luo, Zhen; Gao, Liang; Wu, Jinglai
Highlights: An improved parametric level set method is proposed. The discrete wavelet transform is used to compress the Gaussian RBF-based interpolation matrix. Both self and non-self adjoint problems for global and local frequency responses are investigated. The efficiency and effectiveness of the proposed method are verified. Abstract: In conventional parametric level set methods, the compactly supported radial basis functions (CSRBF) are used to approximate the level set function due to their unique properties, such as the sparsity of the interpolation matrix. The CSRBFs only consider the contributions of knots within a narrow sub-region, which sacrifices accuracy for efficiency in the interpolation. However, the accuracy loss in the CSRBF-based method may prolong the iteration and gradually lead the topology optimization towards a worse local optimum or even an unfeasible design, especially when the allowable material usage in the design domain is relatively low. This will significantly affect the performance of the optimization method. This paper proposes an improved parametric level set method (iPLSM), which is more efficient and effective in topology optimization designs. In this method, the Gaussian radial basis function with global support is used to parameterize the level set surface, to ensure a high numerical accuracy due to the consideration of all interpolation knots in the global domain. Then, a discrete wavelet transform scheme is incorporated into the parametric form to compress the full interpolation matrix and save the computational cost. The proposed method is applied to both the global and local frequency response optimization problems under wide excitation frequency ranges, to validate its efficiency and effectiveness.