A displacement‐based finite element formulation for general polyhedra using harmonic shape functions

By Joseph E. Bishop. 2014

129 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/bcd537e300cdd4c5a324d8cf9f6a23c0544e03ee

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

New perspectives on polygonal and polyhedral finite element methods (2014, methodology): “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”
The Hitchhiker's Guide to the Virtual Element Method (2014, background): “However in three dimensions we do not recover exactly the harmonic barycentric coordinates (see [9]), as our functions are not harmonic, in general, on the faces (see iii)’ in Remark 5.”
On the Virtual Element Method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes (2013, methodology): “We remark that the use of harmonic basis, explicitly computed, have been explored in practice (see, for example, [14, 32]).”
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].”
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.”
Some basic formulations of the virtual element method (VEM) for finite deformations (2017, background): “Additionally, any given face f ∈ ∂E is assumed to be star-convex [17] with respect to a point Xs given by Xs = m ∑”