Numerical solution for degenerate scale problem for exterior multiply connected region

Chen, Y.Z.; Lin, X. Y.; Wang, Z.X.

doi:10.1016/j.enganabound.2009.05.005

Cited by 18 publications

(13 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is found that coordinate transform method for finding the degenerate scale is effective [7,9]. This method has now been used to the case of a doubly connected infinite region [16]. Using this method, a numerical examination is presented below.…”

Section: Numerical Illustrationmentioning

confidence: 96%

See 1 more Smart Citation

Degenerate scale problem for plane elasticity in a multiply connected region with outer elliptic boundary

2009

View full text Add to dashboard Cite

This paper investigates the degenerate scale problem for plane elasticity in a multiply connected region with an outer elliptic boundary. Inside the elliptic boundary, there are many voids with arbitrary configurations. The problem is studied on the relevant homogenous boundary integral equation. The suggested solution is derived from a solution of a relevant problem. It is found that the degenerate scale and the non-trivial solution along the elliptic boundary in the problem are same as in the case of a single elliptic contour without voids. The present study mainly depends on integrations of several integrals, which can be integrated in a closed form.

show abstract

Section: Numerical Illustrationmentioning

confidence: 96%

“…Using this method, a numerical examination is presented below. The merit of the coordinate transform method is as follows [7,9,16]. After using the coordinate transform, the original homogenous BIE in a degenerate scale can be reduced to a non-homogenous BIE in the normal scale.…”

Section: Numerical Illustrationmentioning

confidence: 99%

Degenerate scale problem for plane elasticity in a multiply connected region with outer elliptic boundary

2009

View full text Add to dashboard Cite

show abstract

“…It was early recognized [12] and the usual practical way to circumvent this problem is to add a constant to the Green's function which must be adjusted to the dimensions of the domain [13,9]. This method leads however to the obtaining of the potential up to an additional arbitrary constant value, this method being related to a convenient "scaling" of the distances introduced when using the fundamental solution [14]. Other methods are used to perform a "regularization" of the problem and to recover the uniqueness [15,16,17,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

On the solution of exterior plane problems by the boundary element method: A physical point of view

Bonnet

Corfdir

Nguyen

2014

Engineering Analysis with Boundary Elements

View full text Add to dashboard Cite

The paper is devoted to the solution of Laplace equation by the boundary element method. The coupling between a finite element solution inside a bounded domain and a boundary integral formulation for an exterior infinite domain can be performed by producing a "stiffness" or "impedance matrix" which is equivalent to the interaction coming from BEM, when coupled with FEM stiffness or impedance matrix. It is shown in a first step that the use of classical Green's functions for plane domains can lead to impedance matrices which have eigenvalues of different signs, which is physically and numerically unsatisfying and also to singular impedance matrices, corresponding to the classical degenerate scale problem. Avoiding the degenerate scale problem is classically overcome by adding to the Green's function a constant which is large compared to the size of the 2D domain. However, it is shown that this constant affects the solution of exterior problems in the case of non-null resultant of the normal gradient at the finite boundary. It becomes therefore important to precise the value of this constant related to a characteristic length introduced into the Green's function. Using a "slender body theory" allows to show that for long cylindrical domains with a given cross section, the characteristic length is asymptotically equal to the length of the cylindrical domain.Comparing numerical or analytical 3D and 2D solutions on circular cylindrical domains confirms this result for circular cylinders.

show abstract

“…In this paper, the method suggested in [Chen et al 2009] is used to solve the problems in the next two examples. Clearly, the degenerate scale must depend on the assumed constant s in (36).…”

Section: Introductionmentioning

confidence: 99%

“…In [Chen et al 2009], after using two fundamental solutions in the normal scale, the degenerate scale problem can be solved. In this paper, the method suggested in [Chen et al 2009] is used to solve the problems in the next two examples.…”

Section: Introductionmentioning

confidence: 99%

Influence of different integral kernels on the solutions of boundary integral equations in plane elasticity

Chen

Lin

Wang

2010

J. Mech. Mater. Struct.

View full text Add to dashboard Cite

A modified integral kernel is introduced for boundary integral equations (BIE). The formulation for the modified kernel is based on a representation in pure deformable form of the fundamental solution of concentrated forces. It is found that the modified kernel can be applied to any case, even if the loadings on the contour are not in equilibrium in an exterior boundary value problem. The influence of different integral kernels on solutions of BIE, particularly in the Neumann problem and Dirichlet problem, are addressed. Numerical examples are presented to prove the assertion proposed. Properties of solutions from the usage of the modified integral kernel are studied in detail. The influence of different integral kernels on the degenerate scale are discussed and numerical results are provided. It is found that the influence of the constants involved in the integral kernels is significant. For the cases of the elliptic and rectangular contour, the influence on the degenerate scale is studied with numerical results.

show abstract

Numerical solution for degenerate scale problem for exterior multiply connected region

Cited by 18 publications

References 15 publications

Degenerate scale problem for plane elasticity in a multiply connected region with outer elliptic boundary

Degenerate scale problem for plane elasticity in a multiply connected region with outer elliptic boundary

On the solution of exterior plane problems by the boundary element method: A physical point of view

Influence of different integral kernels on the solutions of boundary integral equations in plane elasticity

Contact Info

Product

Resources

About