Analytical solution for a viscoelastic plate on a Pasternak foundation

Research output: Contribution to journalJournal article – Annual report year: 2019Researchpeer-review



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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.
Original languageEnglish
JournalRoad Materials and Pavement Design
Pages (from-to)1-21
Number of pages21
Publication statusAccepted/In press - 2019
CitationsWeb of Science® Times Cited: No match on DOI

    Research areas

  • Infinite plate, Pasternak foundation, Viscoelasticity, Integral operator, Analytical solution

ID: 163151217