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. Copyright (C) 2004 John Wiley Sons, Ltd

A matrix function solution for the scaled boundary finite-elementequation in statics

The scaled boundary finite-clement method is a fundamental-solution-less boundary element method based oil finite elements. It leads to semi-analytical solutions for displacement and stress fields, which permits problems with singularities or in infinite domains to be handled conveniently and accurately. However, the present eigenvalue method for solving the scaled boundary finite-element equation requires additional treatments for multiple eigenvalues with parallel eigenvectors, which results from logarithmic terms in the solutions. A matrix function solution for the scaled boundary finite-element equation in statics is presented in this paper. It is numerically stable for multiple or near-multiple eigen-values as it is based oil real Schur decomposition. Power functions, logarithmic functions and their transitions as occurring in fracture mechanics, composites and two-dimensional unbounded domains, are represented semi-analytically. No a priori knowledge on the types and orders of singularity are required when simulating stress singularities. (C) 2004 Elsevier B.V. All rights reserved

Dynamic analysis of unbounded domains by a reduced set of base functions

The scaled boundary finite-element method, a semi-analytical method based on finite element technology, is well suited to model unbounded domains. Only the boundary is discretized. No fundamental solution is necessary. General anisotropic material is analyzed without any increase in computational effort. The goal of this paper is to increase the computational efficiency of the scaled boundary finite-element analysis of large-scale problems. A reduced set of weighted block-orthogonal base functions is introduced. The scaled boundary finite-element equation is reformulated in generalized coordinates reducing the number of degrees of freedom on boundary. The solution procedure in frequency domain is presented. To enforce the radiation condition at infinity, an asymptotic expansion for displacement at high frequency is developed. Numerical examples have demonstrated that the computational time is reduced by more than an order of magnitude. © 2005 Elsevier B.V. All rights reserved