Investigations on the polygonal finite element method: Constrained adaptive Delaunay tessellation and conformal interpolants

Authors:
Markus Kraus;Amirtham Rajagopal;Paul Steinmann
Affiliations:
Chair of Applied Mechanics, University Erlangen-Nuremberg, Egerlandstrasse 5, 91058 Erlangen, Germany;Department of Civil Engineering, IIT Hyderabad, Yeddumailaram 502 205, India;Chair of Applied Mechanics, University Erlangen-Nuremberg, Egerlandstrasse 5, 91058 Erlangen, Germany
Venue:
Computers and Structures
Year:
2013

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Abstract

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.