Honeycomb Wachspress finite elements for structural topology optimization

By Cameron Talischi, Glaucio H. Paulino, Chau H. Le. 2009

80 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/0fdac2cd105b6bd0e74f6c78f884bd18095e3ce5

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Topology optimization using B-spline finite elements (2011, methodology): “Topology optimization using honeycomb meshes whose elements use Wachspress shape functions were studied by Talischi et al. (2009) and shown to yield checkerboard-free designs.”
Addressing Integration Error for Polygonal Finite Elements Through Polynomial Projections: A Patch Test Connection (2013, background): “6,46 Similarly, polygonal elements can exclude checkerboard layouts and other numerical instabilities that plague finite element solutions of topology optimization problems.(42,43) In terms of accuracy, mixed polygonal finite elements can be more effective than some commonly used elements for analys”
PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab (2012, background): “…quads in topology optimization as they are not susceptible to numerical instabilities such as checkerboard patterns (Langelaar 2007; Saxena 2008; Talischi et al. 2009, 2010); (3) The isoparametric formulation for polygonal finite elements can be viewed as extension of the common linear…”
Topology design with negative masks using gradient search (2011, methodology): “The procedure for evaluation of the stiffness matrix is documented in (Saxena 2010; Talischi et al. 2009).”
Generalized Gaussian quadrature rules on arbitrary polygons (2010, background): “However, when elements with five vertices or more are used in polygonal finite element applications [13–16] one has to partition the element into triangular elements for the sake of numerical integration.”
Some basic formulations of the virtual element method (VEM) for finite deformations (2017, background): “For instance, polygonal and polyhedral finite elements have been shown to better capture crack propagation and branching in computational fracture simulations [1, 2, 3, 4], to produce numerically stable results in topology optimization [5, 6, 7] and fluid mechanics [8], and to better model contact [”
New perspectives on polygonal and polyhedral finite element methods (2014, unknown): “Along with the advances of barycentric coordinates in graphics, there has been a parallel development of barycentric finite element and boundary element methods on polygons and polyhedra [5, 39, 40, 41, 17, 42, 43, 44, 45, 46, 47, 48, 49, 50], with recent applications in fracture modeling [51, 52, 5”