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A solution method for the sub-surface stresses and local deflection of a semi-infinite inhomogeneous elastic medium

Chidlow, SJ and Teodorescu, M and Vaughan, ND (2012) A solution method for the sub-surface stresses and local deflection of a semi-infinite inhomogeneous elastic medium. Applied Mathmatical Modelling, 36 (8). pp. 3486-3501. ISSN 0307-904X

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Abstract

This paper proposes analytical Fourier series solutions (based on the Airy stress function) for the local deflection and subsurface stress field of a two-dimensional graded elastic solid loaded by a pre-determined pressure distribution. We present a selection of numerical results for a simple sinusoidal pressure which indicates how the inhomogeneity of the solid affects its behaviour. The model is then adapted and used to derive an iterative algorithm which may be used to solve for the contact half width and pressure induced from contact with a rigid punch. Finally, the contact of a rigid cylindrical stamp is studied and our results compared to those predicted by Hertzian theory. It is found that solids with a slowly varying elastic modulus produce results in good agreement with those of Hertz whilst more quickly varying elastic moduli which correspond to solids that become stiffer below the surface give rise to larger maximum pressures and stresses whilst the contact pressure is found to act over a smaller area.

Item Type: Article
Uncontrolled Keywords: 0102 Applied Mathematics
Subjects: Q Science > QA Mathematics
T Technology > TA Engineering (General). Civil engineering (General)
Divisions: Applied Mathematics
Publisher: Elsevier
Related URLs:
Date Deposited: 07 Sep 2017 09:06
Last Modified: 07 Sep 2017 09:12
DOI or Identification number: 10.1016/j.apm.2011.10.006
URI: http://researchonline.ljmu.ac.uk/id/eprint/7050

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