Boundary integral equations and generalized solutions of transient problems of thermoelastodynamics

The transient boundary value problems of thermoelastodynamics in multi-connected regions are solved by boundary integral equations method. Two methods of the boundary integral equations construction are considered, both in Laplace time-transformation space. First method is based on the theory of distributions, which finally gives the BIE of indirect method of potential theory for solving boundary value problem. For the problem of uncoupled thermoelastodynamics the direct potential method is also used here. The determination of inverse transformations of the temperature, displacements and stresses are performed by use of numerical method. The computer implementation of Boundary Integral Equations Method is demonstrated on examples of external boundary value problems for arched holes in plane by the action of non-stationary impulsive heat flow. The shock thermo-elastic waves are considered as generalized solutions of thermo-elastic equations and the conditions at wave fronts on the gaps of stresses, velocities and gradient of temperature has also been obtained. (author)