用无网格局部径向点插值法分析非均质中厚板的弯曲问题

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.

A BENDING ANALYSIS OF THE NONHOMOGENEOUS MODERATELY THICK PLATE USING THE MESHLESS LOCAL RADIAL POINT INTERPOLATION METHOD

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 prope...