A moving superimposed finite element method for structural topology optimization

By Shengyin Wang, Michael Y. Wang. 2006

92 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/8071e98ba809f68e177c9e0874f3c08175238cbd

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

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.”
A level set‐based parameterization method for structural shape and topology optimization (2008, methodology): “For the discrete level set methods, on the one hand, the mesh should be fine enough to remove the numerical truncation errors caused by the polynomial snaking phenomena [16] if low-order shape functions are used [22, 29, 36].”
Radial basis functions and level set method for structural topology optimization (2006, background): “Further study on this relatively more complicated case has been included in another work of the authors [47] and is out of the interest of the present study.”
Design of three dimensional isotropic microstructures for maximized stiffness and conductivity (2007, methodology): “This type of technique has been used with the level–set method for topology optimization previously (Wang and Wang, 2006).”
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)].”
A topology optimization method based on the level set method incorporating a fictitious interface energy (2010, methodology): “Recently, numerous extensions of the level set-based method have been presented, such as the use of different expressions [63], the use of a specific numerical method such as meshless methods [64], the use of mathematical approaches in the optimization scheme [65], and other applications [66–70].”
Investigation and improvement of sensitivity computation using the area-fraction weighted fixed grid FEM and structural optimization (2011, methodology): “Methods that achieve this include filling the void part with a fictitious weak material [1,12], or smoothing the velocity field over the discontinuity at the boundary edge [6].”
Stress-based topology optimization using an isoparametric level set method (2012, methodology): “The parameter t is a fictitious time parameter that represents the optimization iteration number, and the time step dt is chosen in such a way that the CFL condition is satisfied [15].”
Level set topology optimization of fluids in Stokes flow (2009, methodology): “Research has also been focussed on parameterization schemes for the level set function [32–36], different velocity extensions [37, 38], alternative approaches for solving the evolution equation [39, 40], and ways to improve the accuracy of the level set representation and finite element solution nea”
Introducing the sequential linear programming level-set method for topology optimization (2015, methodology): “This constraint can be added to the objective using a fixed Lagrange multiplier (Allaire et al. 2004; Wang and Wang 2006a).”