NUMERICAL SOLUTION OF ELASTODYNAMIC PROBLEMS IN FRACTURE MECHANICS (SINGULAR INTEGRAL EQUATIONS, APPLIED MECHANICS)

Three separate elastodynamic problems in Linear Elastic Fracture Machanics are formulated as mixed boundary-value problems of classical elasticity. Each problem is reduced to a singular integral equation with a Cauchy principal value kernel which is then solved numerically using Gauss-Chebyshev quadrature for some physical quantities of interest.;The first problem deals with a stationary cruciform crack embedded in an infinite isotropic elastic medium. Using a combined Fourier-Laplace transform analysis, the corresponding mixed boundary-value problem is reduced to a system of dual integral equations which is then reduced to a one-parameter family of singular integral equation of Cauchy type. The approximate numerical solution of these integral equations furnishes estimates for the stress intensity factor and the crack energy. The results for the case of "dynamic equilibrium" are in excellent agreement with well-known static results.;For the case of non-stationary cracks, a variant of the first problem formulated as a Yoffe type crack is considered. Under the assumption of plane strain conditions, the propagation of a system of four preexisting cracks in an infinite isotropic medium arranged in a cruciform pattern is investigated. Using Fourier transform analysis, the corresponding wave equations are reduced to a system of triple integral equations which is, in turn, reduced to a Cauchy type sngular integral equation. The dynamic stress intensity factors at the leading and trailing ends of the cracks and the crack energy are computed from the numerical solution of the singular integral equation.;Finally, the problem of the dynamic interaction of a crack embedded in a semi-infinite isotropic elastic strip with suddenly displaced boundaries is considered. The corresponding wave equations are reduced to a system of dual integral equations utilizing the Fourier-Laplace transform pair. The problem is further reduced to a one-parameter family of singular integral equations of Cauchy type whose numerical solution is utilized in obtaining the dynamic stress intensity factor and the crack profile for different times.