Analysis of a Thin Membrane Coated Half-Space under Arbitrary Buried Loads

Document Type : Article

Authors

Department of Civil Engineering, Sharif University of Technology, P.O. Box: 11155-9313, Tehran, Iran

10.24200/sci.2024.62163.7684

Abstract

In this paper, the traditional elasticity problem in which a homogenous isotropic half-space covered by an extensible thin membrane on the surface is subjected to an arbitrary load is treated. The strongly thin membrane with negligible flexural stiffness is attached perfectly to half-space such that bonding between surrounding media and continuity in elastic fields are strictly maintained. A newfound idea is developed to deal with thin film effects, the manner by which the thickness of film tends to zero but simultaneously its shear modulus tends to infinity and as a result, the value of those multiplications remains constant. Based on this idea, equivalent boundary conditions instead of coated thin film are proposed. By utilizing Hankel integral transform and Fourier expansion, Muki's potential functions are obtained in the transformed domain. Closed-form expressions in Hankel transformed domain are derived with general asymmetry. Derivation of thin film equation in the case of axial symmetry is presented along with limiting states of well-known Kelvin’s, Cerruti’s, and Mindlin’s problems, which are examined as specific cases. In addition, a numerical study has been carried out to present the proposed equations' results and explain the method’s efficacy.

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Scientia Iranica

Articles in Press, Accepted Manuscript
Available Online from 21 April 2024

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