A new formulation of boundary element method for cracked anisotropic bodies under anti-plane shear

Sun, Yuzhou; Yang, Shangwen; Yin-bang, Wang

doi:10.1016/s0045-7825(03)00297-4

Cited by 17 publications

(9 citation statements)

References 8 publications

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“…We can also cite here the work of Sun et al [20] He shows numerical results for a central crack (2 ) in a square, orthotropic, homogeneous sheet (2 × 2 ). He assumed that the sheet is subjected to an arbitrary antiplane shear stress.…”

Section: Homogeneous Anisotropic and Finite Casementioning

confidence: 99%

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Boundary element method analysis for mode III linear fracture mechanics in anisotropic and nonhomogeneous media

Simionato

Daros

2019

Z Angew Math Mech

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Funding informationCoordenação de Aperfeiçoamento de Pessoal de Nível Superior * BEM analysis for Mode III LFM in anisotropic, nonhomogeneous media.We present here a Boundary Element Method implementation for anti-plane fracture mechanics in nonhomogeneous and anisotropic media. The results are obtained using two different formulations based on displacement and traction Boundary Integral Equations (BIEs). The crack tips are discretized with special quarter-point boundary elements. The main crack configurations are studied to determine the stress intensity factors (SIFs). Results for homogeneous and isotropic/anisotropic cases are compared with available solutions in the literature, showing good results. For the case of exponential nonhomogeneity, numerical results are obtained for moderately stiffer media and for softer media. K E Y W O R D Sanisotropy, boundary element method, nonhomogeneous materials, SIF

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Section: Homogeneous Anisotropic and Finite Casementioning

confidence: 99%

“…The variables 44 , 45 and 55 are the rotated properties of an orthotropic material (with 0 45 = 0) and are represented by Equations (18), (19) and (20). Figure 15 shows the rotated reference system used here.…”

Section: Anisotropic Homogeneous and Infinite Mediummentioning

confidence: 99%

Boundary element method analysis for mode III linear fracture mechanics in anisotropic and nonhomogeneous media

Simionato

Daros

2019

Z Angew Math Mech

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“…Table 4 shows the results of normalized stress intensity factors K/q 0 √ π a versus the number of special It should be mentioned that, with the basic theorem of the Fourier transform and Fourier series, the general analytical solutions of SIF subjected to anti-plane shear load were obtained by many researchers, such as Refs. [28,29], but they are almost predetermined by the conditions of infinite edges or special boundaries. The numerical calculations in this paper are for certain finite edges or finite boundaries.…”

Section: A Rectangular Plate With Infinite Boundariesmentioning

confidence: 99%

Mode III fracture analysis by Trefftz boundary element method

2007

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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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“…The numerical framework of the BEM that is based on (33) can be established as in References [28,29] for anisotropic elastic fracture problems. In the following sections, we combine the MLS approximation with (33) to present a boundary element-free method.…”

Section: Boundary Integral Equationmentioning

confidence: 99%

Boundary element‐free method for fracture analysis of 2‐D anisotropic piezoelectric solids

Liew

Sun

Kitipornchai

2006

Numerical Meth Engineering

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SUMMARYThis paper considers a 2-D fracture analysis of anisotropic piezoelectric solids by a boundary elementfree method. A traction boundary integral equation (BIE) that only involves the singular terms of order 1/r is first derived using integration by parts. New variables, namely, the tangential derivative of the extended displacement (the extended displacement density) for the general boundary and the tangential derivative of the extended crack opening displacement (the extended displacement dislocation density), are introduced to the equation so that solution to curved crack problems is possible. This resulted equation can be directly applied to general boundary and crack surface, and no separate treatments are necessary for the upper and lower surfaces of the crack. The extended displacement dislocation densities on the crack surface are expressed as the product of the characteristic terms and unknown weight functions, and the unknown weight functions are modelled using the moving least-squares (MLS) approximation. The numerical scheme of the boundary element-free method is established, and an effective numerical procedure is adopted to evaluate the singular integrals. The extended 'stress intensity factors' (SIFs) are computed for some selected example problems that contain straight or curved cracks, and good numerical results are obtained.

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A new formulation of boundary element method for cracked anisotropic bodies under anti-plane shear

Cited by 17 publications

References 8 publications

Boundary element method analysis for mode III linear fracture mechanics in anisotropic and nonhomogeneous media

Boundary element method analysis for mode III linear fracture mechanics in anisotropic and nonhomogeneous media

Mode III fracture analysis by Trefftz boundary element method

Boundary element‐free method for fracture analysis of 2‐D anisotropic piezoelectric solids

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