Three-Dimensional Fundamental Solutions of Displacements and Stresses in an Inclined Transversely Isotropic Materials Subjected to three-Dimensional Point Loads
| Autor: | Hu, Tin-Bin, 胡廷秉 |
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| Rok vydání: | 2009 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 97 Three-dimensional fundamental solutions of displacements and stresses due to three-dimensional point loads in a transversely isotropic material, where the planes of transverse isotropy are inclined with respect to the horizontal loading surface, are presented in this thesis. Generally, the governing equations for infinite or semi-infinite solids are partial differential equations. The Fourier and Laplace integral transforms are commonly two efficient methods for solving the corresponding boundary value problems of full or half space. Employing the Fourier transform, the partial differential equations can be simplified as ordinary differential equations (ODE). Then, three distinct approaches were used to solve the ODE and the solutions were presented for both infinite and semi-infinite solids in this thesis. Firstly, we solve traditionally the nonhomogeneous ordinary differential equations by the methods of undetermined coefficients and separate variables Secondly, the method of an imaginary space was proposed for deriving the solutions of the problems. Thirdly, the method of algebraic is adopted for deriving the solutions for both full space and half space problems. Finally, the present fundamental solutions are derived by performing the required triple inverse Fourier transforms, or double inverse Fourier and Laplace transforms. These transformations are powerful to generate the displacements and stresses resulting from the three-dimensional point loads, acting in an inclined transversely isotropic material. The yielded solutions demonstrate that the displacements and stresses are profoundly influenced by: (1) the rotation of the transversely isotropic planes (??, (2) the type and degree of material anisotropy (E/E?S, ????S, G/G?S), (3) the geometric position (r, ?? ??, and (4). the types of three-dimensional loading (Px, Py, Pz). The proposed solutions are exactly the same as those of Wang and Liao (1999) if the full-space is homogeneous, linearly elastic, and the planes of transversely isotropy are parallel to the horizontal loading surface. Additionally, a parametric study is conducted to elucidate the influence of the above-mentioned factors on the displacements and stresses. Computed results reveal that the induced displacements and stresses in the planes of transversely isotropic are parallel to the horizontal loading surface of isotropic/transversely isotropic rocks by a vertical point load are quite different from those from Wang and Liao (1999). Therefore, in the fields of practical engineering, the dip at an angle of inclination should be taken into account in estimating the displacements and stresses in a transversely isotropic rock subjected to applied loads. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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