Two-dimensional linear elasticity by the boundary node method

Kothnur, Vasanth S.; Mukherjee, Subrata; Mukherjee, Yu Xie

doi:10.1016/s0020-7683(97)00363-6

Cited by 86 publications

(45 citation statements)

References 19 publications

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“…To carry out the numerical integration, the general boundary and crack surface are firstly separated into a series of sub-domains that are being called 'integral cells' in References [37,38]. Some nodes are then selected on each cell.…”

Section: Boundary Element-free Methodsmentioning

confidence: 99%

“…For comparison purpose, the ratios of crack length to width and height to width are taken as a/w = 0.2 and h/w = 2, respectively [20,21]. The single-side MLS approximation [37,38] is used for the evaluation points that are close to the corner of the outside general boundary. Both electromechanical coupled and uncoupled (e i jk = 0) cases are computed.…”

Section: Inclined Crack In a Rectangular Platementioning

confidence: 99%

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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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Section: Boundary Element-free Methodsmentioning

confidence: 99%

Section: Inclined Crack In a Rectangular Platementioning

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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“…During the relatively short span of less than a decade, great progress has been made in solid mechanics applications of meshfree methods. Meshfree methods proposed to date include the element-free Galerkin (EFG) method [4], the reproducing kernel particle method (RKPM) [5], h-p clouds [6][7][8], the meshless local Petrov-Galerkin (MLPG) approach [9; 10], the local boundary integral equation (LBIE) method [11; 12], the natural element method (NEM) [13; 14], the generalized ÿnite element method (GFEM) [15], the extended ÿnite element method (X-FEM) [16][17][18], the ÿnite point method (FPM) [19; 20], the ÿnite cloud method (FCM) [21], the boundary cloud method (BCM) [22] and the boundary node method (BNM) [23][24][25][26][27][28].…”

Section: Meshfree Methodsmentioning

confidence: 99%

A ‘pure’ boundary node method for potential theory

Gowrishankar

Mukherjee

2002

Commun. Numer. Meth. Engng.

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SUMMARYThe standard boundary node method (BNM) uses a (meshless) di use interpolation (in terms of neighbouring scattered boundary points) for the primary variables. The method is not 'truly meshless', however, since cells on the boundary of a body are used for integration. This paper presents a 'pure' version of the BNM in which integration cells are dispensed with. Instead (overlapping), regions of in uence (ROIs) of boundary nodes are used for integration. Initial results for 2-D potential theory, presented here, are encouraging.

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“…Thus, the calculation of a geodesic is reduced to calculating the minimum distance between two points lying on a plane which is a straight line. It has been numerically observed (see [21]) that an arbitrary truncation of the range of in uence at the edges still yields overall acceptable results.…”

Section: Moving Least-squares (Mls) Approximationmentioning

confidence: 99%

“…This data structure considerably reduces the task of meshing and a solid model of a 3-D body can be directly used as input for stress analysis. This method has been successfully tried for 2-D problems in potential theory [20] and linear elasticity [21]. Very recently, the method has been extended to solve three-dimensional problems in potential theory by Chati and Mukherjee [22].…”

Section: Introductionmentioning

confidence: 99%

The boundary node method for three-dimensional linear elasticity

Chati

Mukherjee

1999

Int. J. Numer. Meth. Engng.

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SUMMARYThe Boundary Node Method (BNM) is developed in this paper for solving three-dimensional problems in linear elasticity. The BNM represents a coupling between Boundary Integral Equations (BIE) and Moving Least-Squares (MLS) interpolants. The main idea is to retain the dimensionality advantage of the former and the meshless attribute of the later. This results in decoupling of the 'mesh' and the interpolation procedure. For problems in linear elasticity, free rigid-body modes in traction prescribed problems are typically eliminated by suitably restraining the body. However, an alternative approach developed recently for the Boundary Element Method (BEM) is extended in this work to the BNM. This approach is based on ideas from linear algebra to complete the rank of the singular sti ness matrix. Also, the BNM has been extended in the present work to solve problems with material discontinuities and a new procedure has been developed for obtaining displacements and stresses accurately at internal points close to the boundary of a body.

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Two-dimensional linear elasticity by the boundary node method

Cited by 86 publications

References 19 publications

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

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

A ‘pure’ boundary node method for potential theory

The boundary node method for three-dimensional linear elasticity

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