2016
DOI: 10.1098/rspa.2015.0272
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Unified analytical expressions of the three-dimensional fundamental solutions and their derivatives for linear elastic anisotropic materials

Abstract: Novel unified analytical displacement and stress fundamental solutions as well as the higher order derivatives of the displacement fundamental solutions for three-dimensional, generally anisotropic and linear elastic materials are presented in this paper. Adequate integral expressions for the displacement and stress fundamental solutions as well as the higher order derivatives of the displacement fundamental solutions are evaluated analytically by using the Cauchy residue theorem. The resulting explicit displa… Show more

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Cited by 13 publications
(4 citation statements)
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“…where G(x − y) denotes the displacement-related Green's function tensor, satisfying the differential equation (Kneer, 1965;Ting and Lee, 1997;Tonon et al, 2001;Xie et al, 2016)…”
Section: Introduction-motivation and Scopementioning
confidence: 99%
“…where G(x − y) denotes the displacement-related Green's function tensor, satisfying the differential equation (Kneer, 1965;Ting and Lee, 1997;Tonon et al, 2001;Xie et al, 2016)…”
Section: Introduction-motivation and Scopementioning
confidence: 99%
“…The fundamental solutions, or Green's functions, of anisotropic elasticity corresponding to point loads applied to an infinite elastic space are key in solid mechanics: their integral and Fourier-based expressions [Mura and Kinoshita 1972;Barnett 1972] have found applications in inclusion, dislocation, and crack problems [Xie et al 2016]. In graphics, Green's functions have often been used to avoid the computational overhead involved in solving the elasticity equation when evaluating a static deformation under an imposed load, whether in animation Pai 1999, 2003], shape editing [Lipman et al 2008], or even water wave simulation [Schreck et al 2019] and acoustics [James et al 2006] to name a few applications.…”
Section: Introductionmentioning
confidence: 99%
“…Although boundary element method (BEM) is a very useful and powerful numerical method applied to various fields of engineering analysis, its application within anisotropic elasticity is somewhat difficult due to unavailability of closed-form analytical fundamental solutions for the both statics and dynamics of anisotropic solids [110]. Static anisotropic elastic (and with coupled fields) fundamental solutions are extensively investigated and many different approaches for their calculation have been proposed over the last years [11,12]. Most commonly used practical application form of regular part of the three-dimensional frequency-domain dynamic anisotropic elastic fundamental solution is derived using Radon transform.…”
Section: Introductionmentioning
confidence: 99%