Mode III fracture analysis by Trefftz boundary element method

Yuhong Cui; Juan Wang; Manicka Dhanasekar; Qinghua Qin

doi:10.1007/s10409-007-0056-7

Mode III fracture analysis by Trefftz boundary element method

Yuhong Cui^*, Juan Wang, Manicka Dhanasekar, Qinghua Qin

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

This paper presents a hybrid Trefftz (HT) boundary element method (BEM) by using two indirect techniques for mode III fracture problems. Two Trefftz complete functions of Laplace equation for normal elements and a special purpose Trefftz function for crack elements are proposed in deriving the Galerkin and the collocation techniques of HT BEM. Then two auxiliary functions are introduced to improve the accuracy of the displacement field near the crack tips, and stress intensity factor (SIF) is evaluated by local crack elements as well. Furthermore, numerical examples are given, including comparisons of the present results with the analytical solution and the other numerical methods, to demonstrate the efficiency for different boundary conditions and to illustrate the convergence influenced by several parameters. It shows that HT BEM by using the Galerkin and the collocation techniques is effective for mode III fracture problems.

Original language	English
Pages (from-to)	173-181
Number of pages	9
Journal	Acta Mechanica Sinica/Lixue Xuebao
Volume	23
Issue number	2
DOIs	https://doi.org/10.1007/s10409-007-0056-7
Publication status	Published - Jul 2007

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title = "Mode III fracture analysis by Trefftz boundary element method",

abstract = "This paper presents a hybrid Trefftz (HT) boundary element method (BEM) by using two indirect techniques for mode III fracture problems. Two Trefftz complete functions of Laplace equation for normal elements and a special purpose Trefftz function for crack elements are proposed in deriving the Galerkin and the collocation techniques of HT BEM. Then two auxiliary functions are introduced to improve the accuracy of the displacement field near the crack tips, and stress intensity factor (SIF) is evaluated by local crack elements as well. Furthermore, numerical examples are given, including comparisons of the present results with the analytical solution and the other numerical methods, to demonstrate the efficiency for different boundary conditions and to illustrate the convergence influenced by several parameters. It shows that HT BEM by using the Galerkin and the collocation techniques is effective for mode III fracture problems.",

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author = "Yuhong Cui and Juan Wang and Manicka Dhanasekar and Qinghua Qin",

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T1 - Mode III fracture analysis by Trefftz boundary element method

AU - Cui, Yuhong

AU - Wang, Juan

AU - Dhanasekar, Manicka

AU - Qin, Qinghua

PY - 2007/7

Y1 - 2007/7

N2 - This paper presents a hybrid Trefftz (HT) boundary element method (BEM) by using two indirect techniques for mode III fracture problems. Two Trefftz complete functions of Laplace equation for normal elements and a special purpose Trefftz function for crack elements are proposed in deriving the Galerkin and the collocation techniques of HT BEM. Then two auxiliary functions are introduced to improve the accuracy of the displacement field near the crack tips, and stress intensity factor (SIF) is evaluated by local crack elements as well. Furthermore, numerical examples are given, including comparisons of the present results with the analytical solution and the other numerical methods, to demonstrate the efficiency for different boundary conditions and to illustrate the convergence influenced by several parameters. It shows that HT BEM by using the Galerkin and the collocation techniques is effective for mode III fracture problems.

AB - This paper presents a hybrid Trefftz (HT) boundary element method (BEM) by using two indirect techniques for mode III fracture problems. Two Trefftz complete functions of Laplace equation for normal elements and a special purpose Trefftz function for crack elements are proposed in deriving the Galerkin and the collocation techniques of HT BEM. Then two auxiliary functions are introduced to improve the accuracy of the displacement field near the crack tips, and stress intensity factor (SIF) is evaluated by local crack elements as well. Furthermore, numerical examples are given, including comparisons of the present results with the analytical solution and the other numerical methods, to demonstrate the efficiency for different boundary conditions and to illustrate the convergence influenced by several parameters. It shows that HT BEM by using the Galerkin and the collocation techniques is effective for mode III fracture problems.

KW - Galerkin technique

KW - Hybrid Trefftz method

KW - Mode III fracture

KW - Point-collocation technique

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DO - 10.1007/s10409-007-0056-7

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JO - Acta Mechanica Sinica/Lixue Xuebao

JF - Acta Mechanica Sinica/Lixue Xuebao

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Mode III fracture analysis by Trefftz boundary element method

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