Analytical solution for a viscoelastic plate on a Pasternak foundation

Lev Khazanovich, Eyal Levenberg*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-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
Issue number3
Pages (from-to)800–820
Publication statusPublished - 2020


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

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