Linear smoothed polygonal and polyhedral finite elements

• Post by: alejandro
• June 1, 2016
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International Journal for Numerical Methods in Engineering
Vol. 109, No. 9, pp. 1263–1288, 2017                                                                                                                            

A. Francis, A. Ortiz-Bernardin, S.P.A. Bordas, S. Natarajan

Abstract

It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method. In this work, we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes. The main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain. This new strain is then used in the computation of the stiffness matrix. The convergence properties and accuracy of the proposed scheme are discussed by solving a few benchmark problems. Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes able to deliver the same optimal convergence rate as traditional quadrilateral and hexahedral approximations. The accuracy is also improved, and all the methods tested pass the patch test to machine precision.

Original Journal Article: http://dx.doi.org/10.1002/nme.5324

NOTICE: this is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document.