Header menu link for other important links
X
A one point integration rule over star convex polytopes
Amrita Francis, , Elena Atroshchenko, Bruno Lévy, Stéphane P.A. Bordas
Published in Elsevier Ltd
2019
Volume: 215
   
Pages: 43 - 64
Abstract
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 convergence properties, the accuracy and the efficacy of the one point integration scheme are discussed by solving few benchmark problems in elastostatics. © 2019 Elsevier Ltd
About the journal
JournalData powered by TypesetComputers and Structures
PublisherData powered by TypesetElsevier Ltd
ISSN00457949
Open AccessYes
Concepts (13)
  •  related image
    Computation theory
  •  related image
    Functions
  •  related image
    Numerical methods
  •  related image
    Topology
  •  related image
    Bench-mark problems
  •  related image
    Conventional approach
  •  related image
    Convergence properties
  •  related image
    LINEAR CONSISTENCIES
  •  related image
    Numerical integrations
  •  related image
    POLYGONAL FINITE ELEMENT
  •  related image
    Shape functions
  •  related image
    TAYLOR'S EXPANSION
  •  related image
    Integration