Finite element formulations for 3d convex polyhedra in nonlinear continuum mechanics - Kraus, Markus; Steinmann, Paul (International Journal of Computational Methods in Engineering Science and Mechanics, 2012)
In this paper, we present finite element formulations for general three-dimensional convex polyhedra for use in a common finite element framework that are well suited, e.g., for modeling complex granular materials and for mesh refinements. Based on an universally applicable interpolant for any convex polyhedron, different interpolation schemes are investigated in the context of nonlinear elastostatics. The modeling benefits and the numerical performance regarding the mechanical response and the computational cost are analyzed by several examples.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.finite

Investigations on the polygonal finite element method: Constrained adaptive Delaunay tessellation and conformal interpolants - Kraus, Markus; Rajagopal, Amirtham; Steinmann, Paul (Computers & Structures, 2013)
We present a polygonal finite element method based on constrained adaptive Delaunay tessellation and conformal interpolants on arbitrary polygons. For mesh generation we use the adaptive Delaunay tessellation, an unstructured hybrid tessellation of a scattered point set that minimally covers the proximal space around each point, which is here extended to non-convex domains. Various types of polygonal interpolants are implemented. For the numerical integration of the Galerkin weak form we resort to classical Gaussian quadrature applied on triangular subdomains. The performance and efficiency of the interpolation and implementation are investigated for two dimensional elasticity in a stochastical analysis on random and regular meshes. © 2013 Elsevier Ltd. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.invest
Keywords: Constrained adaptive Delaunay tessellation; Patch test; Polygonal finite element; Polygonal interpolation