无网格局部边界积分方程方法

Elasticity plane problems are firstly solved using the meshless local boundary integral equation(LBIE) method and the meshless local Petrov-Galerkin method(MLPG) in our country. The companion of the bending problem for thin plates is firstly found, in the world. Behaviors of the moving least square approximation, especially the weighted function in meshless methods are investigated. Among various functions satisfying basic conditions of the weighted function, exponential, Gaussian functions and spline functions satisfying some continuity conditions are best weighted functions with high accuracy and rapid convergence as well as good stability in the meshless analysis. Influences of the shape and size of a support domain for the .weighted function and a local integral domain on accuracy, convergence and stability are investigated. Sphere (for 3-D) or circle (for 2-D) is a optimal shape. Optimal size ranges for support and local domains are quantitatively given. Nonlinear problems such as elasto-plasticity and large deformation are analyzed using the element free Galerkin method.

针对把计算模型转换成有限元或边界元的数据太费机时和人力物力以及可能引起数据歧义的缺陷，提出无网格局部边界积分方程方法。这种方法不需要在求解问题的域内和边界上划分任何网格或单元，且具有精度高，收敛快，易于实现数值计算等优点，而且在工程计算中非常容易实现智能化的自适应技术。