Explicit expression of derivatives of elastic Green’s functions for general anisotropic materials |
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Authors: | Ven-Gen Lee |
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Affiliation: | Department of Civil Engineering, National Chi Nan University, Nantou 545, Taiwan, ROC |
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Abstract: | The analytical expressions of Green’s function and their derivatives for three-dimensional anisotropic materials are presented here. By following the Fourier integral solutions developed by Barnett [Phys. Stat. Sol. (b) 49 (1972) 741], we characterize the contour integral formulations for the derivatives into three types of integrals H, M, and N. With Cauchy’s residues theorem and the roots of a sextic equation from Stroh eigenrelation, these integrals can be solved explicitly in terms of the Stroh eigenvalues Pi (i=1,2,3) on the oblique plane whose normal is the position vector. The results of Green’s functions and stress distributions for a transversely isotropic material are discussed in this paper. |
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Keywords: | Green’ s functions Anisotropic materials Derivatives Stroh eigenrelation |
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