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An Analytical Solution to the Three-Dimensional Problem on Elastic Equilibrium of an Exponentially-Inhomogeneous Layer

Published online by Cambridge University Press:  14 April 2015

Y. Tokovyy  and
C.-C. Ma
Y. Tokovyy*
Affiliation:
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine Lviv, Ukraine
C.-C. Ma
Affiliation:
Mechanical Engineering Department National Taiwan University Taipei, Taiwan
*
* Corresponding author (tokovyy@gmail.com)
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Abstract

In this paper, we present an analytical solution to the general three-dimensional elasticity problem in a layer, whose Young’s modulus varies exponentially within the thickness coordinate and the Poisson’s ratio is constant. By making use of the direct integration method, the complete set of the governing equations in terms of stresses has been formed. The latter equations were reduced to separate equations for each stress-tensor component and then solved by means of the Fourier double-integral transformation with respect to the planar coordinates.

Keywords

Three-dimensional problemExponentially-inhomogeneous layerExact solutionDirect integration method
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 5 , October 2015 , pp. 545 - 555
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2015 

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