A novel coupled thermo‐mechanical solution for layered isotropic media under various time‐dependent loadings

Abstract

This study proposes a novel coupled thermo‐mechanical solution for the response of layered isotropic media subjected to time‐varying loads by applying the transformed differential quadrature method (TDQM). Different from the methods of dealing with time partial derivatives with the Laplace transform, this solution discretizes the temporal domain according to the differential quadrature rule, resulting in a more convergent solution under various time‐varying loads. Then, the governing equations are transformed into the Hankel transformed domain that can be solved by the proposed TDQM. Examples are examined to verify the proposed solution and to discuss the convergence of the method. Meanwhile, the coupled thermo‐mechanical responses of the media subjected to time‐harmonic loads are obtained by the TDQM and the method using the Laplace transform, respectively. Comparisons are made to show the better convergence and efficiency of the TDQM. Furthermore, key parameters including the linear expansion coefficients, the thermal diffusivity and the stratification are investigated. Compared with the traditional differential quadrature method (DQM), the TDQM introduces the integral transform theorem to simplify the derivation process and reduce the number of algebraic equations. Consequently, it avoids the difficulty of large‐scale matrix inversion when solving multi‐dimensional problems, and divides the solution process into small‐scale matrix inversion and numerical transform inversion, which has advantages in solution accuracy and efficiency.

Transversely isotropic effects on the coupled thermo‐hydro‐mechanical performance for layered saturated media

“…The equations of internal layers are replaced to introduce the loadings. 37 For example, if there is a uniform circular mechanical load between the 𝐿 𝑝 th and the (𝐿 𝑝 + 1)th layers, we have…”

“…The equations of internal layers are replaced to introduce the loadings 37 . For example, if there is a uniform circular mechanical load between the $${L}_p$$ th and the $$( {{L}_p + 1} ){\mathrm{th}}$$ layers, we have …”