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Elastic Responses of a Transversely Isotropic Half-Space Reinforced by a Buried Extensible Membrane under Internal Loading

Shahsavarian, Ali | 2021

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 54257 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Eskandari, Morteza
  7. Abstract:
  8. In this research, a homogeneous elastic half-space with transversely isotropic behavior, reinforced by an isotropic thin membrane is investigated under static loading with an analytical approach. The membrane is considered as an infinite plane with a thickness of negligible and buried at the arbitrary depth from the surface of the half-space, also its flexural strength is neglected and only the in-plane stiffness is considered for it. The reinforced half-space is investigated under several concentrated and distributed static loads, which are applied to the surface of the half-space or buried at the depth of the membrane. The membrane is first modeled as a three-dimensional elastic layer and the problem is solved as a three-layer media. The thickness of the middle layer is then reduced to zero to become a membrane. Using the method of displacement potential functions, the governing differential equations of the problem are transformed from coupled to uncoupled form. Then by applying Hankel integral transform and Fourier series, the governing differential equations are transformed from partial to ordinary form and easily are solved. Using the governing boundary conditions of the problem, the elastic responses of the reinforced half-space are obtained under the static loads. To investigate the effects of the membrane on the reduction of displacements and stresses of the reinforced half-space, the obtained integral responses are solved numerically and several graphs are drawn. To verify the obtained results, the reinforced half-space responses, under in-plane loading and vertical loading, are obtained for the case that the stiffness of the membrane is equal to zero, and are compared with the available responses in the technical literature. Finally, according to the obtained results, in order to solve the problems dealing with thin membranes easier and faster, differential equations are presented as membrane equivalent boundary conditions that can replace the method used in this research for membrane modeling
  9. Keywords:
  10. Reinforced Half-space ; Mixed Boundary Value Problem ; Displacement Potentials Function ; Thin-film Composite Membrane ; Transversely Isotropic ; Static Loading

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