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A new one point quadrature rule over arbitrary star convex polygon/polyhedron
Natarajan, Sundararajan; Francis, Amrita; Atroshchenko, Elena et al.
n.d.
 

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Keywords :
smoothed finite element method; numerical integration; wachspress shape functions; polygonal finite element method; one point integration; numerical consistency; linear precision
Abstract :
[en] The Linear Smoothing (LS) scheme \cite{francisa.ortiz-bernardin2017} ameliorates linear and quadratic approximations over convex polytopes by employing a three-point integration scheme. In this work, we propose a linearly consistent one point integration scheme which possesses the properties of the LS scheme with three integration points but requires one third of the integration computational time. The essence of the proposed technique is to approximate the strain by the smoothed nodal derivatives that are determined by the discrete form of the divergence theorem. This is done by the Taylor's expansion of the weak form which facilitates the evaluation of the smoothed nodal derivatives acting as stabilization terms. The smoothed nodal derivatives are evaluated only at the centroid of each integration cell. These integration cells are the simplex subcells (triangle/tetrahedron in two and three dimensions) obtained by subdividing the polytope. The salient feature of the proposed technique is that it requires only $n$ integrations for an $n-$ sided polytope as opposed to $3n$ in~\cite{francisa.ortiz-bernardin2017} and $13n$ integration points in the conventional approach. The convergence properties, the accuracy, and the efficacy of the LS with one point integration scheme are discussed by solving few benchmark problems in elastostatics.
Disciplines :
Physical, chemical, mathematical & earth Sciences: Multidisciplinary, general & others
Author, co-author :
Natarajan, Sundararajan
Francis, Amrita
Atroshchenko, Elena
Bordas, Stéphane ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
Language :
English
Title :
A new one point quadrature rule over arbitrary star convex polygon/polyhedron
Publication date :
n.d.
Version :
1
Number of pages :
19
Focus Area :
Computational Sciences
Available on ORBilu :
since 02 July 2017

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