Abstract
AbstractThis paper proposes a new level set method for topological shape optimization of continuum structure using radial basis function (RBF) and discrete wavelet transform (DWT). The boundary of the structure is implicitly represented as the zero level set of a higher-dimensional level set function. The interpolation of the implicit surface using RBF is introduced to decouple the spatial and temporal dependence of the level set function. In doing so, the Hamilton-Jacobi partial differential equation (PDE) that defines the motion of the level set function is transformed into an explicit parametric form, without requiring the direct solution of the complicated PDE using the finite difference method. Therefore, many more efficient gradient-based optimization algorithms can be applied to solve the optimization problem, via updating the expansion coefficients of the interpolant and then evolving the level set function and the boundary. Furthermore, the DWT is employed to handle the full matrix arising from t...
Highlights
Topology optimization of continuum structures has been recognized as one of the most challengeable design problems in the field of structural optimization
In the work of Bendsøe and Kikuchi (1988), the microstructures with regularly shaped holes are positioned in the design space, and the topology optimization problem is transformed into a size optimization problem of the microstructures by using the optimality criteria (OC) method (Zhou & Rozvany, 1991)
The solid isotropic microstructure with penalization (SIMP) method has gained its popularity due to the conceptual simplicity and implementing easiness. Both the SIMP and homogenization methods are mainly based on the finite element method (FEM), to relax the original discrete topology optimization problem as the continuous problem, which allows the occurrence of the intermediate values of the design variables
Summary
Topology optimization of continuum structures has been recognized as one of the most challengeable design problems in the field of structural optimization. To overcome the shortcomings of GS-RBF interpolants, Luo et al (2008) incorporated the compactly supported RBF (CS-RBF) into the framework of parametric level set method, which is more efficient and effective for topology optimization problems, the numerical accuracy is lower than GS-RBF. Another parametric level set method (Ho, Wang, & Zhou, 2012) was developed by using a dynamic moving RBF knots scheme and the Partition of Unity (POU) method to alleviate the high computation cost due to the fully dense matrix in the parameterization using GS-RBF. Several numerical examples are used to demonstrate the effectiveness of the proposed level-set method
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