非均质中厚板静力弯曲问题的无网格LRPIM分析

Static Bending Analysis for Nonhomogeneous Moderately Thick Plates by Meshless LRPIM

采用无网格局部径向点插值法来分析非均质中厚板的弯曲问题.这种无网格方法采用径向基函数耦合多项式基函数来近似试函数,采用四次样条函数作为加权残值法中的权函数.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.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.算例表明这是一种真正的无网格方法,具有效率高、精度高和易于实现等优点.

A meshless local radial point interpolation method for the analysis of nonhomogeneous moderately thick plate is presented in this paper. It uses a radial basis function （RBF） 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 function obtained in trail function has the Kronecker Delta property, and the essential boundary conditions can be easily imposed. In computational procedures, variations of material properties in the considered domain are simulated by adopting proper material parameters at Gauss points in integrations. The results show that the presented method is a truly meshless method and has a number o{ advantages, such as the high efficiency,the quite good accuracy and easy implement.