A BDEM FOR TRANSIENT THERMOELASTIC CRACK PROBLEMS IN FUNCTIONALLY GRADED MATERIALS UNDER THERMAL SHOCK

摘要

A boundary-domain element method (BDEM) for solving transient crack problems of linear coupled thermoelasticity in two-dimensional, finite, isotropic, continuously non-homogeneous and linear elastic functionally graded materials (FGMs) subjected to thermal shock is developed. The governing equations of the linear coupled thermoelasticity are given by the equations of motion and the energy balance equation. To eliminate the time-dependence in these equations the Laplace-transform technique is utilized. Fundamental solutions for isotropic, homogeneous and linear elastic solids are applied to derive a boundary-domain integral formulation. Boundary-domain integral equations (BDIEs) are obtained from the integral representations, which include strongly and weakly singular kernels. A collocation method is implemented for the spatial discretization of the BDIEs by using quadratic boundary and quadrilateral domain elements. To obtain the time-dependent solutions the sophisticated Stehfest's algorithm is applied. Stress intensity factors are obtained by using the extrapolation technique following directly from the asymptotic expansion of the stresses or displacements in the vicinity of the crack-tip. Numerical examples for an exponential gradation of the material parameters are presented and discussed.