The Hamiltonian And Finite Element Method To Bending Problems Of A Circular Sector Thin Plate With Simply Supported A Long Radial Edges

This paper is organized as follows. The first chapter is about the research status of ring fan-shaped plate under hamiltonian system and the research status of the finite element method and its superconvergence are introduced.The second chapter of this paper to use to knowledge and related conclusions were simply introduced. In the third chapter, author by using the methods of separation of variables and the dual transformation solves bending problems of a circular sector thin plate with both straight sides simply supported, and with one straight side simply supported and the other straight side clamped supported, and with one straight side simply supported and the other straight side free along radial edges.The basic ideas is:used variable transformation, basic equations of a circular sector thin plate with simply supported are imported into hamiltonian system, through the class Hellinger-Reissner variational principle,and its corresponding Hamiltonian dual equation is obtained. then,eigen solutions and eigen vectors of bending problems of a circular sector thin plate with both straight sides simply supported, and with one straight side simply supported and the other straight side clamped supported, and with one straight side simply supported and the other straight side free along radial edges can be obtained through using the methods of separation of variables and eigen vector and analytical solution of the corresponding problems are calculated. Then, Considering to get the analytical solution of the equation which we study is difficult in the general area,so the author will use finite element method to research institute for numerical solution of the problem. The fourth chapter focus on using extrapolation technology to research the superconvergence and eigenvalues of =D-uu l on a bounded domain with a curved smooth boundary. The basic ideas: first, we adopt quasiuniform rectangular subdivision in the area and the border curved quadrilateral is split into two triangles(a side of a triangle is curved edge),then we get the special subdivision hT with grid size h. On the basis of it, using bilinear element in the area and linear element on the border,we put forward a finite element method through nmerical simulation of the equation.By extrapolation technique, we investigate the superconvergence of the finite element method and obtain the)(3h O convergence rate. The advantages of the finite element method is versatile and it applys to get the numerical solution of the research problem in the general area.Finally,in the fifth chapter,the author summarizes the research of ring fan-shaped plate bending problem and superconvergence of the finite element and resume the subject of further research.