A local variational principle and its application to an infinite strip containing a central transverse crack

✍ Scribed by C. R. Chiang

• Publisher: Springer Netherlands
• Year: 1992
• Tongue: English
• Weight: 136 KB
• Volume: 57
• Category: Article
• ISSN: 1573-2673
• DOI: 10.1007/bf00035081

✦ Synopsis

A numerical procedure based on Williams' eigenfunctions [1] was developed for solving elastic fracture problems [2]. The results indicate that the method can easily handle traction, displacement, or mixed type boundary conditions with reasonable accuracy. However, there is a major inherent limitation. When the radial ratio (the largest distance from the crack tip to a boundary collocation point divided by the shortest one) is high, the resulting linear algebraic system becomes ill-conditioned. The present investigation is motivated by trying to develop some techniques to avoid such situations.

Consider an elastic body f/held in equilibrium. Let the body and the boundary conditions be separated into two parts: local and remote, respectively. It is assumed that Saint-Venant's principle holds so that the stress displacement fields of f/L do not depend on the details of the boundary condition on fl-, but instead depend on its statically equivalent resultant. It can easily be shown that of all admissible local solutions, the actual one would make I-I L a minimum, where rlL-f W d V -fs, T~ufls