A one point integration rule over star convex polytopes
Author
dc.contributor.author
Francis, Amrita
Author
dc.contributor.author
Natarajan, Sundararajan
Author
dc.contributor.author
Atroshchenko, Elena
Author
dc.contributor.author
Lévy, Bruno
Author
dc.contributor.author
Bordas, Stéphane P. A.
Admission date
dc.date.accessioned
2019-10-15T12:23:53Z
Available date
dc.date.available
2019-10-15T12:23:53Z
Publication date
dc.date.issued
2019
Cita de ítem
dc.identifier.citation
Computers and Structures, Volumen 215,
Identifier
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00457949
Identifier
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10.1016/j.compstruc.2019.01.001
Identifier
dc.identifier.uri
https://repositorio.uchile.cl/handle/2250/171639
Abstract
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In this paper, the recently proposed linearly consistent one point integration rule for the meshfree methods is extended to arbitrary polytopes. The salient feature of the proposed technique is that it requires only one integration point within each n-sided polytope as opposed to 3n in Francis et al. (2017) and 13n integration points in the conventional approach for numerically integrating the weak form in two dimensions. The essence of the proposed technique is to approximate the compatible strain by a linear smoothing function and evaluate the smoothed nodal derivatives by the discrete form of the divergence theorem at the geometric center. This is done by Taylor's expansion of the weak form which facilitates the use of the smoothed nodal derivatives acting as the stabilization term. This translates to 50% and 30% reduction in the overall computational time in the two and three dimensions, respectively, whilst preserving the accuracy and the convergence rates. The