用无网格局部Petrov-Galerkin法分析非线性地基梁

利用无网格局部Petrov-Galerkin法求解了非线性地基梁。在Petrov-Galerkin方法中，采用移动最小二乘（MLS）近似函数作为场主量挠度的试函数并取移动最小二乘近似函数中的体验函数作为近似场函数的加权函数，采用罚因子法施加本质边界条件。文末给出了两个计算实例，算例的结果表明，Petrov-galerkin法不仅能成功地分析线性地基梁，而且也适用于解非线性地基梁，在分析非线性地基梁时具有收敛快，稳定性好的优点。

An Analysis of Beam on Nonlinear Foundation by Meshless Local Petrov-Galerkin Method

The thin beam on a nonlinear foundation was analysed by meshless local Petrov-Galerkin method. In the Petrov-Galerkin method, the moving least squares (MLS) approximation was employed as the trial function of a field variable - deflection, and the weight function in MLS was taken as the weighted function of the approximate function. The penalty factor was used to impose the essential boundary condition. Two examples were given. The results show that the thin beam not only on elastic foundation, but also on nonlinear foundation can be successfully analysed by the Petrov-Galerkin method. In analyzing the thin beam on the nonlinear foundation, the present method possesses excellent rates of convergence and good stability.