几何非线性分析的无网格伽辽金算法

Analysis for geometrical nonlinearity with Element-free Galerkin Method

利用几何非线性的应变-位移关系,在小应变假设的条件下,推导出二维几何非线性问题中的无网格伽辽金法的计算格式。由于无网格方法中的形函数不具备Kronecker delta性质,文中采用罚方法来实现本质边界条件。数值实例表明,无网格伽辽金法在处理几何非线性问题时,具有较高的计算精度,是一种有效的数值计算方法。

Element-free Galerkin Method for the analysis of 2D geometrical nonlinearities is presented by means of geometrically nonlinear strain-displacement relation under small strain assumption. Due to the lack of Kronecker delta properties in meshless method,the penalty method is explored to enforce the essential boundary conditions. Results of numerical examples in geometrical nonlinearities have shown that element-free Galerkin method, with its high accuracy, is much more efficient to deal with these problems.