Analysis of Transversely Isotropic Half-Spaces Under The Effect of Bending of a Rigid Circular Plate

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Abstract

The main goal for this research is to make an in depth analysis for a transversely isotropic half-space under the effect of a circular rigid disc attached on the surface of the domain affected by a bending moment. To do so, the potential method is used to uncouple the Navier’s equilibrium equations. Utilizing both Fourier series and Hankel transforms, the potential function is determined. To find the unknown coefficients of the solution of differential equations involved in this paper, the boundary conditions are transforms into a dual integral equations. The dual integral equations is analytically solved from which the displacements and stresses are determined based on displacement- and stresses-potential relations. The contact pressure is presented in a closed form format and illustrated to be discussed deeply. By numerical evaluation of the results and comparing the results for the simpler case of isotropic half-space both the validity and accuracy are shown.

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