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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Abstract

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
ISSN1468-0629
DOIs
Publication statusAccepted/In press - 2020

Keywords

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

Cite this

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title = "Analytical solution for a viscoelastic plate on a Pasternak foundation",
abstract = "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.",
keywords = "Infinite plate, Pasternak foundation, Viscoelasticity, Integral operator, Analytical solution",
author = "Lev Khazanovich and Eyal Levenberg",
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language = "English",
pages = "1--21",
journal = "Road Materials and Pavement Design",
issn = "1468-0629",
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}

Analytical solution for a viscoelastic plate on a Pasternak foundation. / Khazanovich, Lev; Levenberg, Eyal.

In: Road Materials and Pavement Design, 2020, p. 1-21.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Analytical solution for a viscoelastic plate on a Pasternak foundation

AU - Khazanovich, Lev

AU - Levenberg, Eyal

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Infinite plate

KW - Pasternak foundation

KW - Viscoelasticity

KW - Integral operator

KW - Analytical solution

U2 - 10.1080/14680629.2018.1530693

DO - 10.1080/14680629.2018.1530693

M3 - Journal article

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EP - 21

JO - Road Materials and Pavement Design

JF - Road Materials and Pavement Design

SN - 1468-0629

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