A super-element for crack analysis in the time domain

A super-element for the dynamic analysis of two-dimensional crack problems is developed based on the scaled boundary finite-element method. The boundary of the super-element containing a crack tip is discretized with line elements. The governing partial differential equations formulated in the scaled boundary co-ordinates are transformed to ordinary differential equations in the frequency domain by applying the Galerkin’s weighted residual technique. The displacements in the radial direction from the crack tip to a point on the boundary are solved analytically without any a priori assumption. The scaled boundary finite-element formulation leads to symmetric static stiffness and mass matrices. The super-element can be coupled seamlessly with standard finite elements. The transient response is evaluated directly in the time domain using a standard time-integration scheme. The stress field, including the singularity around the crack tip, is expressed semi-analytically. The stress intensity factors are evaluated without directly addressing singular functions, as the limit in their definitions is performed analytically