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
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Translated from Prikladnaya Mekhanika, Vol. 52, No. 6, pp. 3–25, November–December, 2016.
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Kubenko, V.D. Nonstationary Deformation of an Elastic Layer with Mixed Boundary Conditions. Int Appl Mech 52, 563–580 (2016). https://doi.org/10.1007/s10778-016-0777-z
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DOI: https://doi.org/10.1007/s10778-016-0777-z