Unit Galerkin Method In Plane Thermal Stress Analysis

Element Free Method is a new numerical method developed recently. In EFM, the smooth function can be obtained by Moving Least Squares method (MLS) , which is used to approach approximately, and the shape function can be constructed. It is of the charters of FEM. But it gets rid of restricts during meshing and simplifying preceding disposal. It is adaptive to numerical simulation. It is very flexible especially for the complex boundary problems, and it is very easy to realize computer and adaptive calculation. Thus, the method has been used widely. In this dissertation, on the basis of the theories of EFGM, it is applied to solve plane stable state heat conduction problems and plane thermal stress problems. The main contributions of the dissertation are as follows:(1) On the basis of reading a lot of literatures, the developing actuality, advantages and disadvantages of EFGM. The physical meaning of MLS, reversibility of matrix A, selection of weight function, making the radius of support domain certain and the charter of interpolation function are investigated in detail.(2) During the course of solving the plane stable state heat conduction problems and plane thermal stress problems, the theories are obtained by element free Galerkin method on the basis of moving least squares. And numerical analytical methods are founded on it. At the same time, the way to key problems, such as the integration of stiffness matrix, is brought forward etc.(3) On the basis of the theories of EFGM, the corresponding computer programs are developed and large numbers of numerical examples are given. And typical examples are calculated. The influences that the node density and radius of support domain have bought on to the thermal stress problems are discussed. Meanwhile, in the multilayer, the influences that different thermal conductivity has bought on to structural temperature field and different temperature contraction coefficient has bought on to structural temperature stress are discussed.All above conclusions may be used to investigate the two-dimension thermal stress with complicated boundary conditions and the three-dimension thermal stress problems furthermore.