Journal article
Analytical solution for a viscoelastic plate on a Pasternak foundation
This work contributed an analytical quasistatic 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 independent elastic plate problems for which analytical solutions exist. Thus, the plate’s 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.
Language: | English |
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Publisher: | Taylor & Francis |
Year: | 2020 |
Pages: | 800-820 |
ISSN: | 21647402 and 14680629 |
Types: | Journal article |
DOI: | 10.1080/14680629.2018.1530693 |
ORCIDs: | Levenberg, Eyal |
analytical solution infinite plate integral operator viscoelasticity