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.
- Infinite plate
- Pasternak foundation
- Integral operator
- Analytical solution
Khazanovich, L., & Levenberg, E. (2020). Analytical solution for a viscoelastic plate on a Pasternak foundation. Road Materials and Pavement Design, 21(3), 800–820. https://doi.org/10.1080/14680629.2018.1530693