Nonstationary Deformation of an Elastic Layer with Mixed Boundary Conditions

The analytic solution to the plane problem for an elastic layer under a nonstationary surface load is found for mixed boundary conditions: normal stress and tangential displacement are specified on one side of the layer (fourth boundary-value problem of elasticity) and tangential stress and normal d...

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Bibliographic Details
Published in:International applied mechanics 2016-11, Vol.52 (6), p.563-580
Main Author: Kubenko, V. D.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Classical Mechanics
Integral transforms
Physics
Physics and Astronomy
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Summary:The analytic solution to the plane problem for an elastic layer under a nonstationary surface load is found for mixed boundary conditions: normal stress and tangential displacement are specified on one side of the layer (fourth boundary-value problem of elasticity) and tangential stress and normal displacement are specified on the other side of the layer (second boundary-value problem of elasticity). The Laplace and Fourier integral transforms are applied. The inverse Laplace and Fourier transforms are found exactly using tabulated formulas and convolution theorems for various nonstationary loads. Explicit analytical expressions for stresses and displacements are derived. Loads applied to a constant surface area and to a surface area varying in a prescribed manner are considered. Computations demonstrate the dependence of the normal stress on time and spatial coordinates. Features of wave processes are analyzed
ISSN:1063-7095
1573-8582
DOI:10.1007/s10778-016-0777-z