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<p>In this work, an infinite-thick circular plate of finite thickness under thermomechanical loading, utilizing the modified couple stress thermoelastic diffusion (MCSTD) theory with the non-local and Moore–Gibson–Thompson (MGT) heat equations, has been investigated. The governing equations for two-dimensional problems are derived initially. Initially, the plate is considered unstrained and unstressed at uniform temperature. The governing equations are non-dimensionalized and simplified using potential functions. The combined Laplace and Hankel transforms are employed to simplify the problem into an ordinary differential equation. The arbitrary constants are determined by applying the loading conditions on the boundary surface. A particular type of uniformly distributed normal force and a uniformly distributed thermal source are taken to depict the utility of the approach. The physical quantities like displacements, stresses, temperature field, mass concentration, and chemical potential field are solved semi-analytically in the Laplace–Hankel transform domain. Numerical inversion techniques are employed to retrieve the resulting quantities for the original space–time domain.</p>

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Investigation of a thick circular plate due to thermomechanical sources in modified couple stress thermoelastic diffusion with non-local and Moore–Gibson–Thompson model

  • 期刊论文

  • 发表日期：

    2026年5月14日

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  • Pragati,
  • Rajneesh Kumar,
  • Sachin Kaushal,
  • Gamal M. Ismail,
  • Amr M. S. Mahdy,
  • Alaa A. El-bary,
  • Khaled Lotfy

摘要

In this work, an infinite-thick circular plate of finite thickness under thermomechanical loading, utilizing the modified couple stress thermoelastic diffusion (MCSTD) theory with the non-local and Moore–Gibson–Thompson (MGT) heat equations, has been investigated. The governing equations for two-dimensional problems are derived initially. Initially, the plate is considered unstrained and unstressed at uniform temperature. The governing equations are non-dimensionalized and simplified using potential functions. The combined Laplace and Hankel transforms are employed to simplify the problem into an ordinary differential equation. The arbitrary constants are determined by applying the loading conditions on the boundary surface. A particular type of uniformly distributed normal force and a uniformly distributed thermal source are taken to depict the utility of the approach. The physical quantities like displacements, stresses, temperature field, mass concentration, and chemical potential field are solved semi-analytically in the Laplace–Hankel transform domain. Numerical inversion techniques are employed to retrieve the resulting quantities for the original space–time domain.