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.
Highlights
Structural topology optimization is capable of determining the best layout of material in the design domain, so as to optimize concerned structural performances under the given constraints
Several different methods have been established for topology optimization, such as the homogenization method [12], the solid isotropic material with penalization (SIMP) [13,14], the evolutionary structural optimization (ESO) method [15], as well as the level set method (LSM) [16,17,18,19,20], which are applied to a broad range of structure and material design problems [11,21]
The design sensitivity of is given by: Jd is obtained by finite element method (FEM), and we focus on the calculation of ∂Jd/∂αi
Summary
Structural topology optimization is capable of determining the best layout of material in the design domain, so as to optimize concerned structural performances under the given constraints. The main contribution of this study is to firstly propose an improved parametric level set method (iPLSM) based on incorporation of the DWT and GSRBF-based interpolation, so as to further improve the efficiency and effectiveness of topological shape optimization. This paper develops an efficient iPLSM for structural frequency response optimizations under the given excitation frequency ranges In this method, the Gaussian RBF with global support is used to parameterize the LSM. A matrix compression scheme, termed as DWT, is firstly integrated into the parameterization framework to reduce the nonzero elements in the Gaussian RBF-based interpolation matrix By this means, all the positive features of the LSM can be maintained, while the unfavorable numerical issues of the classic LSM can be avoided. To verify the efficiency and effectiveness of the proposed method, both the local frequency response optimization (non-self adjoint problem) and dynamic compliance optimization (self adjoint problem) within wide excitation frequency ranges are investigated
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