Analysis of transient uncoupled thermoelasticity using the singular boundary method

Numerical analysis of uncoupled thermoelastic problems plays an important role in many engineering fields. To achieve this goal, it is crucial to develop efficient and accurate numerical methods. The singular boundary method (SBM), due to its semi analytical property, has been proven to be a powerful numerical technique for solving homogeneous problems. In view of this, the SBM is applied for the 2D and 3D transient uncoupled thermoelastic problems in this work. To avoid the occurrence of inhomogeneous terms, the considered transient problems are transformed into the Laplace domain first. Then, the SBM formulations are established with the Laplace domain fundamental solutions (FSs) as kernel functions. To isolate the singularity of the kernel function, the simple origin intensity factor empirical formulas are derived. Due to the fact that the FSs satisfy the governing equations, the present method avoids discretizing the domain. To obtain the transient responses from the SBM results in the Laplace space, the numerical inversion of Laplace transform is employed. Finally, the validity and accuracy of the proposed method are demonstrated by comparing the numerical results with the exact solution and FEM results for thermoelasticity problems in different domains.