中文摘要：

用无网格局部径向点插值法分析了非均质中厚板的弯曲问题．利用虚位移原理推导了中厚板的离散系统方程．采用径向基函数耦合多项式基函数来近似试函数，用四次样条函数作为加权残值公式中的权函数．所构造成的形函数具有Kronecker delta性质，可以很方便地施加本质边界条件．此方法不需要任何形式的网格划分，所有的积分都在规则形状的子域及其边界上进行，是一种真正的无网格方法．在计算过程中，取积分中的高斯点的材料参数来模拟问题域材料特性的变化．算例结果表明这种无网格方法具有效率高、精度高和易于实现等优点．

英文摘要：

A meshless local radial point interpolation method （LRPIM） for the bending analysis of a nonhomogeneous moderately thick plate is presented in this paper. The discretized system equation of the plate is obtained using the principle of virtual work. It uses a radial basis function coupled with a polynomial basis function as a trail function and a quartic spline function as a test function of the weighted residual formula. The shape functions obtained in the trail function have the Kronecker delta function property,and the essential boundary conditions can be easily imposed. The present method is a true meshless method as it does not need any grids and all integrals can be easily evaluated over regularly shaped domains and their boundaries. In computational procedures, variations of material properties in the considered domain are modelled by adopting proper material parameters at Gauss points in integrations. The results show that the presented method has a number of advantages, such as high efficiency, good accuracy and easy to implement.