Accurate and efficient numerical integration of weight functions using Gauss-Chebyshev quadrature

✍ Scribed by Steven R. Daniewicz

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 302 KB
• Volume: 48
• Category: Article
• ISSN: 0013-7944
• DOI: 10.1016/0013-7944(94)90209-7

✦ Synopsis

Weight functions have been widely used to compute stress intensity factors and crack surface displacements in cracked bodies under arbitrary applied stress fields. For many geometries and applied stress fields of interest, these computations require the application of numerical integration or quadrature.

Weight functions exhibit a crack tip singularity. This singularity, if ignored, can lead to inaccurate or inefficient stress intensity factor and crack surface displacement computations. The numerical integration of weight functions using Gauss-Chebyshev quadrature is demonstrated. This type of quadrature is ideally suited for weight function integration as it allows removal of the integrable crack tip singularity, enabling accurate and efficient computation of stress intensity factors and crack surface displacements.

Stress intensity factors and crack surface displacements for the edge cracked half-plane under uniform tension have been computed applying both Gauss-Chebyshev and Gauss-Legendre quadrature. Gauss-Chebyshev quadrature is shown to be superior in terms of both accuracy and computational efficiency.