Elastic solutions of displacements for a transversely isotropic full space with inclined planes of symmetry subjected to a point load |
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| Authors: | Ting‐Bin Hu Cheng‐Der Wang Jyh‐Jong Liao |
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| Institution: | 1. Department of Civil Engineering, National Chiao‐Tung University, Hsin‐Chu 300, Taiwan, Republic of China;2. Ph.D. Candidate.;3. Department of Civil and Disaster Prevention Engineering, National United University, Miao‐Li 360, Taiwan, Republic of China;4. Associate Professor.Department of Civil and Disaster Prevention Engineering, National United University, No. 1, Lien Da, Kung‐Ching Li, Miao‐Li 360, Taiwan, Republic of China;5. Professor. |
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| Abstract: | This work presents analytical solutions for displacements caused by three‐dimensional point loads in a transversely isotropic full space, in which transversely isotropic planes are inclined with respect to the horizontal loading surface. In the derivation, the triple Fourier transforms are employed toyield integral expressions of Green's displacement; then, the triple inverse Fourier transforms and residue calculus are performed to integrate the contours. The solutions herein indicate that the displacements are governed by (1) the rotation of the transversely isotropic planes (?), (2) the type and degree of material anisotropy (E/E′, ν/ν′, G/G′), (3) the geometric position (r, φ, ξ) and (4) the types of loading (Px, Py, Pz). The solutions are identical to those of Liao and Wang (Int. J. Numer. Anal. Methods Geomechanics 1998; 22 (6):425–447) if the full space is homogeneous and linearly elastic and the transversely isotropic planes are parallel to the horizontal surface. Additionally, a series of parametric study is conducted to demonstrate the presented solutions, and to elucidate the effect of the aforementioned factors on the displacements. The results demonstrate that the displacements in the infinite isotropic/transversely isotropic rocks, subjected to three‐dimensional point loads could be easily determined using the proposed solutions. Also, these solutions could realistically imitate the actual stratum of loading situations in numerous areas of engineering. Copyright © 2007 John Wiley & Sons, Ltd. |
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| Keywords: | displacements transversely isotropic full space inclined triple Fourier transforms residue calculus material anisotropy |
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