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Analytical solution for a viscoelastic plate on a Pasternak foundation

Lev Khazanovich, Eyal Levenberg
2018 International Journal on Road Materials and Pavement Design  
This work contributed an analytical solution to the problem of an infinite viscoelastic plate supported on a Pasternak foundation and subjected to axisymmetric normal loading. The derivation was based on defining a set of iterative functions, each containing information on the plate's relaxation modulus and on the time-variation of the loading. By writing the sought solution as a linear combination of these functions it was shown how to decompose the original viscoelastic problem into a set of
more » ... blem into a set of independent elastic plate problems for which analytical solutions exist. Thus, the plate's quasistatic deflection evolution at any point of interest was provided in closed-form, without resorting to integral transform techniques. The formulation was applied and subsequently validated for several test cases, demonstrating that a very small set of elastic solutions is needed for generating a highly accurate viscoelastic result. Overall, the proposed solution is deemed well suited for engineering calculations, as a computational kernel for backcalculation, and for benchmarking numerical solutions.
doi:10.1080/14680629.2018.1530693 fatcat:2qkbq23gs5gadpyanl2qqi6dky