Finite element approximation of dynamic problems for semi-infinite solids in elasticity

Donida, G.; Bernetti, R.

doi:10.1016/0045-7949(91)90192-o

Cited by 1 publication

(1 citation statement)

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“…The mathematical model of the motion of homogeneous anisotropic elastic media is presented by the dynamic system of equations of linear theory of elasticity [1][2][3][4][5]. This system consists of three partial differential equations of the second order with constant coefficients [1][2][3][6][7][8]. Fundamental solutions play an important role in solving problems for the system of anisotropic elastodynamics.…”

Section: Introductionmentioning

confidence: 99%

Equations of anisotropic elastodynamics as a symmetric hyperbolic system: Deriving the time-dependent fundamental solution

Yakhno¹,

Yaslan²

2011

Journal of Computational and Applied Mathematics

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a b s t r a c tThe dynamic system of anisotropic elasticity from three second order partial differential equations is written in the form of the time-dependent first order symmetric hyperbolic system with respect to displacement velocity and stress components. A new method of deriving the time-dependent fundamental solution of the obtained system is suggested in this paper. This method consists of the following. The Fourier transform image of the fundamental solution with respect to a space variable is presented as a power series expansion relative to the Fourier parameters. Then explicit formulae for the coefficients of these power series are derived successively. Using these formulae the computer calculation of fundamental solution components (displacement velocity and stress components arising from pulse point forces) has been made for general anisotropic media (orthorhombic and monoclinic) and the simulation of elastic waves has been obtained. These computational examples confirm the robustness of the suggested method.

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