Variable thermal singularity boundary elements in the study of neighbouring singularities

Two new boundary elements are presented for the simulation of variable order thermal singularities in two dimensions. The 7rst can model the variable order temperature derivative and heat 9ux singularities at one end of the element. The second element can simulate the temperature derivative and heat 9ux singularities at both the ends of the element simultaneously. These elements are useful for studying the interaction of variable order thermal neighbouring singularities. They are employed here for the computation of stress intensity factors in the crack–crack interaction problems under thermal load. To improve the accuracy of such computations a modi7ed crack closure integral based method is adapted. Examples of mode I and mode II centre crack, two collinear neighbouring cracks, kinked crack in a plate, and tee joint with a kinked edge crack under thermal or thermal and mechanical loading are studied to illustrate the usefulness of these elements in the study of neighbouring thermal singularities