This paper describes a fully analytic solution method for the displacements and sub-surface stresses within a graded elastic layered solid. This method can be utilised to predict the local deformation of nano or micro-scale depositions under contacting conditions. The solid consists of two distinct layers which are considered to be perfectly bonded and comprise of a graded elastic coating whose shear modulus varies exponentially with the depth coordinate and an infinitely deep homogeneously elastic substrate. The solution given in this paper is generic and easily utilised to solve real problems as it requires only known physical characteristics of the solid under study and an applied surface pressure. As a result, this model is very cheap to use and can be easily integrated into tribological codes to predict local deflections.
- Design Engineering Division and Computers and Information in Engineering Division
Determining the Sub-Surface Stresses in a Graded-Elastic Solid Using Fourier Series Decomposition
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Chidlow, S, Teodorescu, M, & Vaughan, N. "Determining the Sub-Surface Stresses in a Graded-Elastic Solid Using Fourier Series Decomposition." Proceedings of the ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 7: 5th International Conference on Micro- and Nanosystems; 8th International Conference on Design and Design Education; 21st Reliability, Stress Analysis, and Failure Prevention Conference. Washington, DC, USA. August 28–31, 2011. pp. 405-412. ASME. https://doi.org/10.1115/DETC2011-47883
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