中文摘要：

利用局部加权残值法推导出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构造无网格点插值法的形函数,用四次样条函数作为权函数。插值函数具有Kroneckerdelta函数性质,可以很方便地施加本质边界条件。利用无网格局部径向点插值法对几种边界条件下中厚板的自由振动进行了分析。该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。对于求解中厚板的问题,可以克服剪切自锁问题。算例表明,用无网格局部径向点插值法分析中厚板的自由振动问题所得结果与已有文献解以及有限元解都十分地吻合。并且具有高效率、高精度和收敛性好等优点。

英文摘要：

The meshless local radial point interpolation method （LRPIM） for the free vibration analysis of a plate of moderate thickness under several boundary conditions is presented. The discretized system equations are obtained using a locally weighted residual method. It uses a radial basis function coupled with a polynomial basis function as a trail function, and uses the quartic spline function as a test function of the weighted residual method. 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 does not need any grids, and all integrals can be easily evaluated over regularly shaped domains and its boundary. The present method can also avoid the shear locking when it is used to solve the problem for the plate of moderate thickness. Examples show that results obtained by the presented method are found to agree well with the exiting solutions in the literature and with the results obtained by the finite element method, and the presented method has a number of advantages, such as the high efficiency and the quite good accuracy and high rate of convergence.