Radial basis functions and level set method for structural topology optimization

By Shengyin Wang, Michael Y. Wang. 2006

388 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/8279611a540d284e3b608fd755a995eff85868b8

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Evolutionary level set method for structural topology optimization (2011, methodology): “Wang and his coauthors [29,30] proposed level set method for structural topology optimization and many other variants of this algorithm to improve its solving ability.”
A multi-material level set-based topology and shape optimization method (2015, methodology): “Parametric level set method A parametric level set method [30,31] is employed to evolve the topology of the multi-material structures.”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “…been explored that convert the Hamilton-Jacobi PDE into a simpler set of ordinary differential equations (ODEs) using radial basis functions (RBFs) (Wang and Wang 2006a, b, Wang et al. 2007b) or system of algebraic equations using compactly supported RBFs (CSRBFs) (Luo et al. 2007, 2008c, 2009a).”
Topology optimization approaches (2013, methodology): “…element schemes, such as the extended finite element method (xFEM) (Van Miegroet and Duysinx 2007; Kreissl and Maute 2012; Wei et al. 2010), the super-imposed finite element method (Wang and Wang 2006a; Wang et al. 2007), and local remeshing schemes (Yamasaki et al. 2011), within level set methods.”
Multiscale isogeometric topology optimization for lattice materials (2017, methodology): “As a benchmark problem, we examine a simply supported beam under mid-span point load (Figure 6), commonly used to evaluate the merit of a given TO method [20, 59-61].”
Isogeometric analysis for parameterized LSM-based structural topology optimization (2016, methodology): “For theminimumcompliance design problem, themathematical model [63] may be defined as”
Structural Shape and Topology Optimization Using an Implicit Free Boundary Parametrization Method (2006, methodology): “The positive features of RBFs such as the unique solvability of the interpolation problem and their excellent smoothness and convergence make them very attractive in the level set methods [Wang and Wang (2005d)].”