Weakly-singular symmetric Galerkin boundary element method in thermoelasticity for the fracture analysis of three-dimensional solids

The Symmetric Galerkin Boundary Element Method has demonstrated significant advantages for the fracture mechanics analysis of three-dimensional solid structures. However, when dealing with structures in thermal environments, strongly-singular domain integrals resulting from the temperature field require meshing of the interior of the domain. In this paper, formulation and implementation of the weakly-singular SGBEM of threedimensional thermoelastic intact and cracked solids are presented where temperature-induced domain integrals are transformed into boundary integrals. The strong singularity of these temperature-induced integrals is reduced to the weak singularity by exploring the feature of double-layer surface integrals in the SGBEM. Obtained temperature-induced boundary integrals affect only the right-hand-side vector of the SGBEM equation, and therefore the advantages of the SGBEM, such as the symmetry of the stiffness matrix, are retained. Several examples of three-dimensional solids with or without cracks subjected to thermal loadings are presented to validate the developed methods. Advantages and disadvantages of SGBEMs with different temperature-induced boundary integrals are also discussed.

Automated summary

This paper presents a weakly-singular SGBEM method for solving the fracture mechanics analysis problems of three-dimensional solid structures in thermal environments, transforming domain integrals induced by temperature fields into boundary integrals, retaining the advantages of SGBEM, and providing several examples for validation.