A new boundary integral equation method for cracked 2-D anisotropic bodies

Yin-bang, Wang; Sun, Yuzhou

doi:10.1016/j.engfracmech.2005.01.007

Cited by 19 publications

(12 citation statements)

References 30 publications

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“…Sun [10] where they used integration by parts to the traditional boundary integral formulation for the analysis of the cracked 2D anisotropic bodies. Fig.…”

Section: Results and Discussuionmentioning

confidence: 99%

“…Cracked structures on an aircraft could lead to a catastrophic failure because the tensile strengths of composite laminates are significantly reduced when stress concentrations such as cracks and cutouts are present. Solutions to these problems in anisotropic elasticity are therefore of great interest in the design and strength analysis of composite structures [1][2][3][4][5][6][7][8][9][10][11]. The Finite Element(FE) and Boundary Element(BE) are the most extensively used methods for the analysis of engineering structures.…”

Section: Introductionmentioning

confidence: 99%

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Fracture Mechanics Analysis of Composite Structures Using the Boundary Element Shape Sensitivities

Tafreshi

2009

AIAA Journal

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“…Sun [10] where they used integration by parts to the traditional boundary integral formulation for the analysis of the cracked 2D anisotropic bodies. Fig.…”

Section: Results and Discussuionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fracture Mechanics Analysis of Composite Structures Using the Boundary Element Shape Sensitivities

Tafreshi

2009

AIAA Journal

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“…Later, Wang [14] and Wang and Chau [15,16] applied integration by parts to derive a more universal boundary integral formulation for isotropic bodies containing cracks and holes; the derived BIE incorporates all crack boundary INTERACTION BETWEEN COPLANAR SQUARE CRACKS 1185 conditions (both upper and lower) and can be applied directly to the cracked body (no displacement BIE is necessary). This technique has also been applied to anisotropic medium by Wang and Sun [17] and cracked bimaterials by Belytschko et al [18]. In the present work, the authors apply this technique to a three-dimensional cracked body to derive a new general traction BIE using integration by parts.…”

Section: Introductionmentioning

confidence: 91%

Analyzing interaction between coplanar square cracks using an efficient boundary element‐free method

Sun

Liew

2012

Numerical Meth Engineering

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This paper examines the interaction between coplanar square cracks by combining the moving least-squares (MLS) approximation and the derived boundary integral equation (BIE). A new traction BIE involving only the Cauchy singular kernels is derived by applying integration by parts to the traditional boundary integral formulation. The new traction BIE can be directly applied to a crack surface and no displacement BIE is necessary because all crack boundary conditions (both upper and lower ones) are incorporated. A boundary element-free method is then developed by combining the derived BIE and MLS approximation, in which the crack opening displacement is first expressed as the product of weight functions and the characteristic terms, and the unknown weight is approximated with the MLS approximation. The efficiency of the developed method is tested for isotropic and transversely isotropic media. The interaction between two and three coplanar square cracks in isotropic elastic body is numerically studied and the case of any number of coplanar square cracks is deduced and discussed.

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“…Pertinent works in this regard for anisotropic materials still remain very scarce indeed. Very recently, Wang and Sun [16] derived a non-singular boundary integral equation with the technique of integration by parts to analyze cracked anisotropic bodies. In this article, the nearly singular integrals associated with the inertial effects [17] are integrated analytically for quadratic elements that are commonly adopted in the BEM analysis.…”

Section: Introductionmentioning

confidence: 99%

BEM Stress Analysis for Thin Multilayered Composites Subjected to Inertial Loads

Shiah

Hwang

Shiah

2009

Journal of Composite Materials

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For the stress analysis of ultra-thin structures, the modeling of conventional domain solution techniques will require a tremendous amount of domain elements, whose aspect ratios must have orders close to unity. Due to this reason, past research work by the finite element method seldom investigated ultra-thin layers of composites. This article proposes a boundary element approach that may yield accurate stress analysis by coarse mesh-modeling for ultra-thin layers of multilayered composites subjected to inertial loads. In this article, the nearly singular integrals in the boundary integral equations for displacements and strains are analytically integrated. The algorithm has been successfully implemented in an existing computer program based on quadratic elements.

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A new boundary integral equation method for cracked 2-D anisotropic bodies

Cited by 19 publications

References 30 publications

Fracture Mechanics Analysis of Composite Structures Using the Boundary Element Shape Sensitivities

Fracture Mechanics Analysis of Composite Structures Using the Boundary Element Shape Sensitivities

Analyzing interaction between coplanar square cracks using an efficient boundary element‐free method

BEM Stress Analysis for Thin Multilayered Composites Subjected to Inertial Loads

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