无网格伽辽金法在悬臂梁中的应用

The application of element-free galerkin method in the problem of the cantilever beam

无网格伽辽金法(EFGM)是一种刚刚兴起的数值算法,它在数值领域中表现出了精度高、收敛快、数值稳定、能消除体积闭锁等一系列突出优点。采用移动最小二乘法构造形函数,引入拉格朗日乘子满足位移边界条件,并选用不同的权函数对悬臂梁问题进行了分析。计算结果表明,只要恰当的选取权函数,该方法的计算结果与理论解还是相当吻合的,表明了无网格伽辽金法的可行性和有效性。

Element -Free Galerkin Method （EFGM） is a new numerical method developed recently. In this paper, shape function is constructed by Moving Least Square （MLS） Lagrange multiplier is used to satisfy essential boundary conditions. The problem of the cantilever beam is analyzed by using different weight functions. The numerical example shows that the EFGM results are similar with the exact results if weight function selected properly, which shows that EFGM is feasible and effective.