Fundamental solutions for the collocation method in three-dimensional elastostatics

Redekop, D.; Cheung, Ronald

doi:10.1016/0045-7949(87)90017-4

Cited by 31 publications

(12 citation statements)

References 6 publications

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“…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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confidence: 99%

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

Smyrlis

2009

Numer. Math.

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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: 88%

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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“…The apphcation of the MFS to two-dimensional problems of steady-state heat conduction and elastostatics in isotropic and anisotropic bimaterials has been addressed by Berger and Karageorghls [12,13]. Karageorghis [14] has investigated the calculation of the eigenvalues of the Helmholtz equation subject to homogeneous Dirichlet boundary conditions for circular and rectangular geometries by employing the MFS, whilst Redekop and Cheung [15] and Poullikkas et al [16] have successfully applied the MFS for solving three-dimensional elastostatics problems. The MFS, in conjunction with singular value decomposition, has been employed by Ramachandran [17] in order to obtain numerical solutions of the Laplace and the Helmholtz equations.…”

Section: Introductionmentioning

confidence: 98%

A meshless method for solving the cauchy problem in three-dimensional elastostatics

Marin

2005

Computers & Mathematics with Applications

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An International Joumal Available online at www.sc,encedirect.com computers & .=,=.o= mathematics with applications Computers and Mathematics with Applications 50 (2005) 73-92 www elsevmr com/locate/camwaAbstract--The apphcatlon of the method of fundamental solutions to the Cauchy problem in three-dimensional lsotroplc linear elasticity is mvestlgated The resulting system of linear algebraic equations is ill-conditioned and therefore, its solution is regularized by employing the first-order Tlkhonov functional, while the choice of the regularizatlon parameter Is based on the L-curve method. Numerical results are presented for both under-and equally-determined Cauchy pioblems in a pmcewise smooth geometry. The convergence, accuracy, and stabihty of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solutmn domain, and decreasing the amount of noise added into the Input data, respectively, are analysed. ~)

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Fundamental solutions for the collocation method in three-dimensional elastostatics

Cited by 31 publications

References 6 publications

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

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

A meshless method for solving the cauchy problem in three-dimensional elastostatics

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