Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 323, Issue -, Pages 389-415Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2017.05.029
Keywords
Discontinuous Galerkin; Polygonal finite elements; Plane stress state; Very high-order method
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Discontinuous Galerkin with finite difference rules (DGFD) is applied to mechanical plane stress state problem. The considered domain is discretized by polygonal mesh. The polygonal elements can be for example a hexagon, pentagon or just quadrangle or triangle. They do not have to be convex and a fish mesh, where the elements have fish shapes, is used. When the elements are rectangular then the orthogonality of Chebyshev basis functions can be utilized. In such a case very high-order approximate solution can be obtained. In this work the approximation order exceeds 10 and reaches 60, which in the latter case means 3600 numbers of degrees of freedom in a single element. The paper is illustrated by a benchmark example in which the exact solution is recovered by DGFD method for various meshes. In the other example the stress concentration is easily recovered by very high-order version of DGFD method. (C) 2017 Elsevier B.V. All rights reserved.
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