Polygonal finite elements for topology optimization: A unifying paradigm

By Cameron Talischi, Glaucio H. Paulino, Anderson Pereira, Ivan Fabio Mota de Menezes. 2010

198 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/88c5af5420383365ab1ff3ea5561bee152091c3a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

Addressing Integration Error for Polygonal Finite Elements Through Polynomial Projections: A Patch Test Connection (2013, unknown): “Similarly, polygonal elements can exclude checkerboard layouts and other numerical instabilities that plague the ﬁnite element solution of topology optimization problems [40, 41].”
Improving multiresolution topology optimization via multiple discretizations (2012, methodology): “We can also apply the iMTOP approach to polygonal finite elements [31] to improve the resolution design.”
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”
Virtual Element Methods for general second order elliptic problems on polygonal meshes (2014, unknown): “We recall for instance [4], [5], [6], [7], [8], [20], [21], [31], [34], [38], [41], [42], [43], [44] [47], [48], [51], [52], [58], [57], [60], [61], [62], [63], [65], [66], [67], [70].”
PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab (2012, methodology): “This is pertinent to the isoparametric formulation for polygonal finite elements which requires convexity of all the elements in the mesh (Sukumar and Tabarraei 2004; Sukumar and Malsch 2006; Talischi et al. 2010).”
Divergence free Virtual Elements for the Stokes problem on polygonal meshes (2015, methodology): “We refer to the recent papers and monographs [6,10,15,17,20,21,24,31,39,41–47, 50, The Virtual Element Method (in short, VEM) has been recently introduced in [7] as a generalization of the ﬁnite element method to arbitrary element-geometry.”
Generalized Gaussian quadrature rules on arbitrary polygons (2010, background): “Quadrature rules on regular polygons can be presented as software libraries and readily used in codes where integration over polygons is needed [13–16,26].”
Topology optimization using polytopes (2013, background): “Constraints in the geometrical features of spatial discretization can result in mesh dependent designs [2].”
The Hitchhiker's Guide to the Virtual Element Method (2014, methodology): “On the one hand, VEM can be viewed as an extension of Finite Element Methods to general polygonal and polyhedral elements [11, 21, 29–31, 33–39].”
Efficient generation of large-scale pareto-optimal topologies (2013, methodology): “These include: (1) use of polygonal finite elements [19], [20] that circumvent anomalies such as checkerboard patterns, and are more adept at capturing optimal geometries, (2) an iso-geometric approach [21] where the material density is modeled via Non-Uniform Rational B-Spline basis functions, (3) ”