Integral Equations with Hypersingular Kernels -- Theory and Applications to Fracture Mechanics
Professor Youn-Sha Chan (Dept. of Computer and Mathematical 下午 4:00–4:50 鴻經館 107 室Singular integral equation method is one of the most effective numerical methods solving a (plane) crack problem in fracture mechanics. In this talk we address how the integral equations with hypersingular kernels are applied in solving crack problems. In terms of materials, we consider the examples that include classical linear elastic fracture mechanics (LEFM), functionally graded materials (FGM), and strain-gradient elasticity theory. The corresponding governing partial differential equations are derived for each different type of material. Some semi-analytical results and numerical simulation (including crack displacement profiles and stress singularities in front of the crack-tip) will be presented.