The method of fundamental solutions for three-dimensional elastostatic problems of transversely isotropic solids

This paper solves the penny-shaped crack configuration in transversely isotropic solids with coupled magneto-electro-elastic properties. The crack plane is coincident with the plane of symmetry such that the resulting elastic, electric and magnetic fields are axially symmetric. The mechanical, electrical and magnetical loads are considered separately. Closed-form expressions for the stresses, electric displacements, and magnetic inductions near the crack frontier are given.

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Yielding and Failure of Transversely Isotropic Solids

Applications of Tensor Functions in Solid Mechanics ◽

10.1007/978-3-7091-2810-7_5 ◽

1987 ◽

pp. 67-97 ◽

Cited By ~ 4

Author(s):

J. P. Boehler

Keyword(s):

Transversely Isotropic ◽

Transversely Isotropic Solids ◽

Isotropic Solids

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A Moving Pseudo-Boundary MFS for Three-Dimensional Void Detection

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.13-13s07 ◽

2013 ◽

Vol 5 (04) ◽

pp. 510-527 ◽

Cited By ~ 7

Author(s):

Andreas Karageorghis ◽

Daniel Lesnic ◽

Liviu Marin

Keyword(s):

Three Dimensional ◽

Nonlinear Least Squares ◽

Fundamental Solutions ◽

Cauchy Data ◽

Three Dimensions ◽

Method Of Fundamental Solutions ◽

Void Detection ◽

Spherical Parametrization ◽

Least Squares Minimization

AbstractWe propose a new moving pseudo-boundary method of fundamental solutions (MFS) for the determination of the boundary of a three-dimensional void (rigid inclusion or cavity) within a conducting homogeneous host medium from overdetermined Cauchy data on the accessible exterior boundary. The algorithm for imaging the interior of the medium also makes use of radial spherical parametrization of the unknown star-shaped void and its centre in three dimensions. We also include the contraction and dilation factors in selecting the fictitious surfaces where the MFS sources are to be positioned in the set of unknowns in the resulting regularized nonlinear least-squares minimization. The feasibility of this new method is illustrated in several numerical examples.

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The Method of Fundamental Solutions for Solving Exterior Axisymmetric Helmholtz Problems with High Wave-Number

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.13-13s04 ◽

2013 ◽

Vol 5 (04) ◽

pp. 477-493 ◽

Cited By ~ 9

Author(s):

Wen Chen ◽

Ji Lin ◽

C.S. Chen

Keyword(s):

Large Scale ◽

Three Dimensional ◽

Matrix Decomposition ◽

Coefficient Matrix ◽

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Wave Number ◽

High Wave Number ◽

Memory Space ◽

High Wave

AbstractIn this paper, we investigate the method of fundamental solutions (MFS) for solving exterior Helmholtz problems with high wave-number in axisymmetric domains. Since the coefficient matrix in the linear system resulting from the MFS approximation has a block circulant structure, it can be solved by the matrix decomposition algorithm and fast Fourier transform for the fast computation of large-scale problems and meanwhile saving computer memory space. Several numerical examples are provided to demonstrate its applicability and efficacy in two and three dimensional domains.

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