Use of fundamental solutions in the collocation method in axisymmetric elastostatics

Redekop, D.; Thompson, J. C.

doi:10.1016/0045-7949(83)90043-3

Cited by 39 publications

(16 citation statements)

References 14 publications

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“…The MFS with fixed or moving singularities has been used for the solution of various second order axisymmetric problems [13][14][15]19]. In these applications, the MFS was applied to the axisymmetric version of the governing equations, for which the fundamental solutions involve complete elliptic integrals and are rather complicated.…”

Section: Introductionmentioning

confidence: 99%

A matrix decomposition MFS algorithm for axisymmetric biharmonic problems

2005

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We consider the approximate solution of axisymmetric biharmonic problems using a boundary-type meshless method, the Method of Fundamental Solutions (MFS) with fixed singularities and boundary collocation. For such problems, the coefficient matrix of the linear system defining the approximate solution has a block circulant structure. This structure is exploited to formulate a matrix decomposition method employing fast Fourier transforms for the efficient solution of the system. The results of several numerical examples are presented.

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Section: Introductionmentioning

confidence: 99%

A matrix decomposition MFS algorithm for axisymmetric biharmonic problems

2005

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“…The solution of anisotropic elasticity problems was considered in [4,22]. In [23], inverse problems in planar elasticity were considered whereas axisymmetric elastostatics problems are studied in [13,28]. Recently, the MFS has been applied to the computation of stress intensity factors in linear elastic fracture mechanics [5,14].…”

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confidence: 99%

“…Also, Matrix Decomposition Algorithms (MDAs) for the MFS have been developed for two-and three-dimensional boundary value problems in elastostatics and thermoelastostatics in domains with radial symmetry [15,16]. Further applications of the MFS to elasticity problems can be found in [8,11,[25][26][27]. For further details and comprehensive reference lists of applications of the MFS see [9,10,12,29,30] and references therein.…”

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confidence: 99%

Mathematical foundation of the MFS for certain elliptic systems in linear elasticity

Smyrlis

2009

Numer. Math.

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The method of fundamental solutions (MFS) is a Trefftz-type technique in which the solution of an elliptic boundary value problem is approximated by a linear combination of translates of fundamental solutions with singularities placed on a pseudo-boundary, i.e., a surface embracing the domain of the problem under consideration. In this work, we develop a mathematical framework for the numerical implementation of the MFS in elliptic systems. We obtain density results, with respect to the C -norms, which establish the applicability of the method in certain systems arising from the theory of elastostatics and thermo-elastostatics. The domains in our density results may possess holes and they satisfy the segment condition. Mathematics Subject Classification (2000)35A08 · 35A35 · 35J45 · 65N35 IntroductionLet Ω be an open domain in R n and L = |α|≤m a α D α be an elliptic partial differential operator with constant coefficients. In Trefftz methods, the solution of the boundary value problem Lu = 0 in Ω, Bu = f on ∂Ω, This work was supported by a grant

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“…For elasticity, previous work was reported by Patterson and Sheikh [16], Redekop [17] and Murashima et al [8] for planar problems and Karageorghis and Fairweather [18] and Redekop and Thompson [19] for axisymetric problems and by Patterson and Sheikh et al [9,12], Wearing and Sheikh [11], Redekop and Cheung [20] and Poullikas et al [21] for three-dimensional problems.…”

Section: Introductionmentioning

confidence: 87%

The Method of Fundamental Solutions applied to 3D structures with body forces using particular solutions

Fam

Rashed

2005

Comput Mech

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This paper presents the Method of Fundamental Solutions for three-dimensional elastostatics with body forces. The gravitational body loading is considered as an example for the treated body forces. A new set of particular solutions corresponding to such loading is derived using Ho¨rmander operator-decoupling technique, and the relevant particular solution expressions for displacements, tractions and stresses are derived and given explicitly. Several examples are tested and the results confirm the validity and efficiency of the presented method.

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Use of fundamental solutions in the collocation method in axisymmetric elastostatics

Cited by 39 publications

References 14 publications

A matrix decomposition MFS algorithm for axisymmetric biharmonic problems

A matrix decomposition MFS algorithm for axisymmetric biharmonic problems

Mathematical foundation of the MFS for certain elliptic systems in linear elasticity

The Method of Fundamental Solutions applied to 3D structures with body forces using particular solutions

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