点插值无网格方法在平板弯曲问题中的应用

点插值方法是近年来发展起来的一种新型无网格方法．运用该方法时，在问题域上离散一系列随机分布的节点，一点的位移值由该点影响域内的节点插值得到．由于插值函数具有Kronecher Delta函数特性，因此可以很方便地施加本质边界条件．根据变分原理得到平板弯曲的点插值无网格控制方程，将其应用于简支方板和地基板的计算中．算例表明该方法是有效的，适用于薄板和厚板的计算．

The Application of the Point Interpolation Meshless to the Problem of Thin Plate Bind

Point interpolation method developed in recent years is one of the new kinds of meshless method. In the PIM, the problem domain is represented by properly scattered points, and the interpolating point is selected at the displacements in the influence domain of this point. The interpolation function has the property of Delta function, so the essential boundary conditions can be simply imposed. The governing equation of point interpolation method is obtained on the basis of variational principle . The presented method is applied to compute the deflection and the moment of the square plate and the elastic foundation. Numerical results show that the accuracy of the method is satisfied. Therefore, it is reasonable and feasible for using the point interpolation meshless method in the plate bending problems.