Singularity Study of Sectorial Domain by Weak Formulation and Fractal Finite Element in Hamilton System

Abstract

The weak formulation of mixed state equations including boundary conditions are presented in polar coordinate system, mixed variational formulation is established in sectorial domain. The fractal finite element method is used to analyse the sector domain problem. The present result is exactly analogous to the Hamiltonian mechanics for a dynamic system by simulating time variable t with coordinate variable r. The stress singularity at singular point is investigated by means of the fractal finite element method. The present study satisfies the continuity conditions of stresses and displacements at the interfaces. The principle and method suggested here have clear physical concepts. So this method would be easily popularized in dynamics analysis of elasticity.