Quadratically consistent one-point (QC1) integration for three-dimensional element-free Galerkin method

Gao, Xin; Duan, Qinglin; Shao, Yulong; Li, Xikui; Chen, Biaosong; Zhang, Hongwu

doi:10.1016/j.finel.2016.01.003

Cited by 4 publications

(1 citation statement)

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“…In this section, a new numerical integration scheme is proposed to numerically integrate over the star convex arbitrary polygon and polyhedron inspired from the work of Duan et al, [20]. We restrict ourselves to cell-based smoothing technique, wherein the physical element is sub-divided into simplex elements.…”

Section: One Point Quadrature Schemementioning

confidence: 99%

A one point integration rule over star convex polytopes

Francis

Natarajan

Atroshchenko

et al. 2019

Computers & Structures

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2019. A one point integration rule over star convex polytopes. Computers and Structures 215 , pp. AbstractThe Linear Smoothing (LS) scheme [18] 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 [18] 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.keywords: Polygonal finite element method, Wachspress shape functions, numerical integration, linear consistency, one point integration.

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Section: One Point Quadrature Schemementioning

confidence: 99%