Spectral BEM for the Analysis of Wave Propagation and Fracture Mechanics

Abstract

This paper presents a spectral boundary element formulation for analysis of structures subjected to dynamic loading. Two types of spectral elements based on Lobatto polynomials and Legendre polynomials are used. Two-dimensional analyses of elastic wave propagation in solids with and without cracks are carried out in the Laplace frequency domain with both conventional BEM and the spectral BEM. By imposing the requirement of the same level of accuracy, it was found that the use of spectral elements, compared with conventional quadratic elements, reduced the total number of nodes required for modeling high-frequency wave propagation. Benchmark examples included a simple one-dimensional bar for which analytical solution is available and a more complex crack problem where stress intensity factors were evaluated. Special crack tip elements are developed for the first time for the spectral elements to accurately model the crack tip fields. Although more integration points were used for the integrals associated with spectral elements than the conventional quadratic elements, shorter computation times were achieved through the application of the spectral BEM. This indicates that the spectral BEM is a more efficient method for the numerical modeling of structural health monitoring (SHM) processes, in which high-frequency waves are commonly used to detect damage, such as cracks, in structures.