Simply Supported On Elastic Foundation, Multilateral Sheet Issues Green Quasifunction Method

Compared with the method of numerical analysis such as finite element method, boundary element method and meshless method, etc, Green quasifunction method has its own advantages. In recent years, some domestic and international scholars have reap many important fruits in study of Green quasifunction method. Green quasifunction method is first proposed by Rvachev, and applied to solve the problem of boundary value of Poisson equation. Yuan Hong, etc. popularize this method in various kinds of arithmetic operators, and applies to solve the problem of polygonal elastic plate under different edge conditions. On the basis of their work, application of Green quasifunction method to the simple-support polygonal thin plate on elastic foundation are presented in this dissertation, which enriches theory of Green quasifunction and extends applications of Green quasifunction method.At the beginning of the dissertation, finite element method, boundary element method, etc and their advantages and disadvantages are briefly introduced. The dissertation summarizes characteristic and superiority of Green quasifunction method and explains the essence of Green quasifunction method. Several kinds of elastic foundation model, various kinds of analytical and numerical methods of the plate on elastic foundation at present are briefly reviewed, and recent research and development of Green quasifunction method are introduced.Chapter 1 surveys the application of Green quasifunction method to all kinds of arithmetic operators such as Laplace operator, Helmholtz operator and biharmonic operator, etc. These arithmetic operators are widely used in the Mechanics and Physics problems.Chapter 2 deals Green quasifunction method of the bending problem of the simple-support polygonal thin plate on Winkler foundation. Utilizing intermediate variable, the governing differential equation of the bending problem of simple-support polygonal thin plate on Winkler foundation is divided into two simultaneous differential equations of lower order which couple each other. Through the change of variables, inhomogeneous boundary condition of the original problem is reduced to the boundary value problem of homogeneous boundary condition. In order to be convenience for comparison of result, dimensionless...