Computation of dynamic stress intensity factors by the time domain boundary integral equation method-I. Analysis

Application of the direct time domain boundary integral equation method (BIEM)to the solution of a number of elastodynamic crack problems is presented. In this part I, we describe the analysis which includes the basic governing differential equations, their transformation to boundary integral equations and the numerical solution procedure of the discretized form of the BIE. In addition to the usual constant interpolation in space and time of tractions and displacements on the boundary, a new boundary element which incorporates quadratic variation in space and linear variation in time (of the traction and displacements)is developed. These two boundary elements are implemented in a computer code and are used in the examples described in part II. A consistent method of estimation of the dynamic stress intensity factors in conjunction with the two types of the elements mentioned is described. No special singular crack tip elements are used other than the quadratic isoparametric quarter-point boundary elements for modeling the crack tip singularities. Subsequent results show that the numerical solution is accurate and has good convergence properties with regard to mesh refinement and time step size.