A combined boundary element/Laplace transform solution of time-dependent thermo-elasticity is extended to solve problems in multi-layered media in 2D. The method requires only boundary discretisation and no time stepping. An efficient Laplace inversion scheme is implemented which significantly improves the performance of the method. A library of constant, linear and quadratic elements is created. Equations of thermal conductivity are solved in the Laplace domain and the solution is inverted back to time domain. The effect of transient thermal loads on the boundary integral formulation of elastostatics is represented by an additional boundary integral. The scope of the method is illustrated by analysing a heated repository buried in a three-layer semi-infinite medium. Three factors combine to make the method an attractive option for the solution of transient thermoelasticity:

  1. the Laplace transform removes the need for time stepping,

  2. predictions are highly accurate as a result of the use of Green's functions,

  3. only boundary meshing is needed.

It is found that, with the newly implemented Laplace inversion scheme, forty to eighty linear analyses are required to derive the entire stress history of a typical problem at any number of time stations. The application of the method to nonhomogeneous media extends its applicability and improves its ability to solve realistic problems.


Differential thermal temperatures in layered media may occur in problems of mining excavations, road subgrade construction, extraction of geothermal energy, furnace foundation structures, or deep burial of heatgenerating waste. When temperature changes are moderate, the strata remain in the elastic range. When inertia loads and hydraulic effects are negligible, the problem may be represented by the coupled equations of transient thermo-elasticity. In many cases, the dependence of temperature on volume strain may be neglected and the equations uncoupled (Boley and Weiner, 1960).

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