Solution of nonstationary thermoelasticity problems with cracks using the boundary integral equations method

M. N. Perelmuter

Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russian Federation

Abstract: We applied the boundary integral equation (BIE) method in its direct formulation to solve two-dimensional unsteady problems of uncoupled thermoelasticity in the presence of cracks. First, we solved the unsteady heat conduction problem using the BIE formulation without integrating over the body volume. We employed a time-stepping scheme with piecewise-constant interpolation of temperature and heat flux along the boundary and over time. We used the results of the heat conduction analysis as input data for the thermoelasticity problem.
In the thermoelasticity analysis, we solved the BIE using quadratic isoparametric boundary elements and special elements near the crack tip to capture the asymptotic behavior of the field variables. We implemented these methods in a software package to solve unsteady thermoelasticity problems with cracks. Using this approach, we obtained solutions to previously unsolved thermoelasticity problems involving cracks.

Keywords: boundary integral equations method, nonstationary heat conduction, thermoelasticity, cracks.