用杂交边界点法分析简支薄板的热弯曲问题

THERMAL BENDING ANALYSIS OF SIMPLY SUPPORTED THIN PLATE BY THE HYBRID BOUNDARY NODE METHOD

该文利用杂交边界点法对简支薄板的热弹性弯曲进行了分析计算.采用薄板的热弹性理论,通过薄板的修正变分原理建立了各向同性薄板的边界局部积分方程,域内变量使用基本解插值,而边界上的变量则用移动最小二乘法近似.计算时仅需边界上离散点的信息,无论变量近似还是数值积分都不需要网格,因此该方法是一种纯边界类型无网格方法.数值算例表明,杂交边界点法在分析薄板的热弯曲问题时具有效率高、精度高和收敛性好等优点.

Thermal bending problem of thin plate is analyzed by the hybrid boundary node method in this contribution. The boundary local integral equation of isotropic thin plate is established based on ther- mal elastic theory and modified variational principle of thin plate. The domain variables are interpolated by fundamental solution, while the boundary variables are approximated by moving least squares. Only discrete nodes are constructed on the boundary, and no meshes are needed either for the purpose of interpolation of the solution variables, or for the numerical integration, so the present method is a true boundary type mesh- less method. The numerical examples show that this approach has such advantages as high efficiency,good accuracy and high convergence rate.