Weighted finite element method for elasticity problem with a crack

•Introduction of the novel definition of the Rν-generalized solution for suppressing of the singularity in the crack problem.•Weighted finite element method (WFEM) without loss of accuracy independently from the presence of reentrant corner of 2π on the boundary.•Presence of singular basis functions...

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Bibliographic Details
Published in:	Computers & structures Vol. 243; p. 106400
Main Authors:	Rukavishnikov, V.A., Mosolapov, A.O., Rukavishnikova, E.I.
Format:	Journal Article
Language:	English
Published:	New York Elsevier Ltd 15-01-2021 Elsevier BV
Subjects:	Accuracy Comparative numerical analysis Dimensional stability Elasticity problem with a crack Finite element method Grid refinement (mathematics) Mathematical models Model accuracy Norms Numerical analysis Weighted finite element method Weighted finite element method Elasticity problem with a crack Comparative numerical analysis
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Summary:	•Introduction of the novel definition of the Rν-generalized solution for suppressing of the singularity in the crack problem.•Weighted finite element method (WFEM) without loss of accuracy independently from the presence of reentrant corner of 2π on the boundary.•Presence of singular basis functions in the FEM space.•High accuracy computations of displacements and stresses both in a neighborhood of the crack tip and far from it. We consider the Lamé system posed in a domain with the reentrant corner of 2π as a mathematical model for the crack problem. We construct a version of the weighted finite-element method (FEM) on the base of a novel definition of the Rν-generalized solution. This allows us to suppress the influence of the singularity caused by the presence of the reentrant corner on the accuracy of computation of the approximate solution. Comparative numerical analysis of the presented approach with classical FEM and the method with mesh refinement has shown its advantages in the computational accuracy and stability as well as in the use of high-dimensional meshes. The results of investigation of the accuracy of solution to the model problem are presented in the Sobolev and energy norms. An absolute error in the mesh nodes is also analyzed.
ISSN:	0045-7949 1879-2243
DOI:	10.1016/j.compstruc.2020.106400