Enriched meshfree collocation method with diffuse derivatives for elastic fracture

Young Cheol Yoon; Sang Ho Lee; T. Belytschko

doi:10.1016/j.camwa.2006.04.010

Enriched meshfree collocation method with diffuse derivatives for elastic fracture

Young Cheol Yoon, Sang Ho Lee, T. Belytschko

Department of Civil and Environmental Engineering

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

A meshfree collocation method with intrinsic enrichment for solving elastic crack problems is presented. A diffuse derivative approximation is applied in conjunction with an intrinsic enrichment of the near-tip asymptotic fields and a polynomial basis. These consistent diffuse derivatives of the approximation do not require computing the derivative of the weight function or that of the moment matrix. The local behavior of the near-tip stresses is successfully captured so that the stress intensity factors can be accurately computed. Numerical experiments demonstrate the accuracy and robustness of the method for solving elastic fracture problems.

Original language	English
Pages (from-to)	1349-1366
Number of pages	18
Journal	Computers and Mathematics with Applications
Volume	51
Issue number	8 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.camwa.2006.04.010
Publication status	Published - 2006 Apr

Bibliographical note

Funding Information:
*Author to whom all correspondence should be addressed. The support of the Office of Naval Research (N00014-03-1-0097) and the Korean Research Foundation Grant (KRF-2004-042-D00189) are gratefully acknowledged.

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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title = "Enriched meshfree collocation method with diffuse derivatives for elastic fracture",

abstract = "A meshfree collocation method with intrinsic enrichment for solving elastic crack problems is presented. A diffuse derivative approximation is applied in conjunction with an intrinsic enrichment of the near-tip asymptotic fields and a polynomial basis. These consistent diffuse derivatives of the approximation do not require computing the derivative of the weight function or that of the moment matrix. The local behavior of the near-tip stresses is successfully captured so that the stress intensity factors can be accurately computed. Numerical experiments demonstrate the accuracy and robustness of the method for solving elastic fracture problems.",

author = "Yoon, {Young Cheol} and Lee, {Sang Ho} and T. Belytschko",

note = "Funding Information: *Author to whom all correspondence should be addressed. The support of the Office of Naval Research (N00014-03-1-0097) and the Korean Research Foundation Grant (KRF-2004-042-D00189) are gratefully acknowledged.",

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AU - Yoon, Young Cheol

AU - Lee, Sang Ho

AU - Belytschko, T.

N1 - Funding Information: *Author to whom all correspondence should be addressed. The support of the Office of Naval Research (N00014-03-1-0097) and the Korean Research Foundation Grant (KRF-2004-042-D00189) are gratefully acknowledged.

PY - 2006/4

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N2 - A meshfree collocation method with intrinsic enrichment for solving elastic crack problems is presented. A diffuse derivative approximation is applied in conjunction with an intrinsic enrichment of the near-tip asymptotic fields and a polynomial basis. These consistent diffuse derivatives of the approximation do not require computing the derivative of the weight function or that of the moment matrix. The local behavior of the near-tip stresses is successfully captured so that the stress intensity factors can be accurately computed. Numerical experiments demonstrate the accuracy and robustness of the method for solving elastic fracture problems.

AB - A meshfree collocation method with intrinsic enrichment for solving elastic crack problems is presented. A diffuse derivative approximation is applied in conjunction with an intrinsic enrichment of the near-tip asymptotic fields and a polynomial basis. These consistent diffuse derivatives of the approximation do not require computing the derivative of the weight function or that of the moment matrix. The local behavior of the near-tip stresses is successfully captured so that the stress intensity factors can be accurately computed. Numerical experiments demonstrate the accuracy and robustness of the method for solving elastic fracture problems.

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