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.
Highlights
The finite element method has experienced the development and evolution from a single mechanical variable to a number of mechanical variables
Based upon the weak formulation of mixed state equations including boundary conditions, mixed variational formulation is established in sectorial domain
The stress singularity at singular point is investigated by means of the fractal finite element method
Summary
The finite element method has experienced the development and evolution from a single mechanical variable to a number of mechanical variables. The multi-variable finite element method can solve the problem of first-order continuous differentiable smoothness at the junction of function curves, and obtain the elements with good precision. The quasi-conforming finite element method proposed creatively by [3] does not require the stress variable to satisfy the equilibrium equation in advance, and the process of calculating the inverse matrix is omitted to obtain the higher discrete precision of the strain. There are few studies on applying the symplectic algorithm to obtain numerical solution of elastic mechanics. Considering the special properties of Hamiltonian matrix, author proposed an effective symplectic algorithm based on weak formulation of equations to solve such problems. The stress singularity at singular point is investigated by means of the fractal finite element method
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