Analysis Of Two-dimensional Thermal Stress By Boundary Element Method

As an important supplement to the Finite Element Method(FEM), Boundary Element Method(BEM) is more efficient due to its inherent boundary-only discretization. By utilizing the fundamental solutions, the accuracy of BEM is improved. BEM is employed in this paper to analyze the two-dimensional thermal stress problems. The content of this paper is as follows:(1) Using the fundamental solutions and the Green theorem, the boundary integral equations for Laplace equation and two-dimensional elastostatics problems are established. The boundary integral equations are discretized, where the geometry is interpolated by continuous linear functions and the physical quantities are approximated by discontinuous interpolation functions. The exact expressions are given to evaluate the associated integral for BEM analysis.(2) Numerical examples are given to illustrate the efficiency of the proposed exact integral for BEM analysis. It is found from numerical implementation that the exact integral can both improve the accuracy and provide a uniform treatment for singular and nonsingular integral of BEM.(3) Boundary integral equation is derived by utilizing the weighted residual method. By virtue of the Galerkin tensor, the domain integrals are transformed into boundary integral in the analysis of thermal stress, which avoids the discretization of the interior domain. The thermal stress under the uniform and non-uniform temperature distribution is considered by the discontinuous boundary element with exact integration and desirable results with higher accuracy are obtained.