轴对称几何非线性问题中的无网格算法

Algorithm of meshless method for geometrical nonlinearities of axi-symmetric structure

应用无网格伽辽金法对轴对称几何非线性问题进行了分析。在小变形假设的条件下,利用几何非线性的应变-位移关系,基于线性弹性本构关系,推导了无网格法的计算控制方程,并采用Newton-Raphson迭代法来求解非线性方程,初步计算了压力管道的几何非线性问题。由于无网格方法中的形函数不具备Kronecker delta性质,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轴对称几何非线性问题时,具有较高的计算精度,是一种有效的数值计算方法。

The element free Galerkin method is applied into analysis of axi-symmetric geometrical nonlinearities .The control equations by meshless method is presented by means of geometrically nonlinear strain-displacement relation under small deformation assumption and linear elastic constitutive law is also assumed in whole process, All nonlinear equations can be calculated through Newton-Raphson iterative method. The problems of geometrical nonlinearities on concrete pipe under pressure are calculated. Due to the lack of Kronecker delta properties in meshless method, the penalty method is used to realize the essential boundary conditions. Results of numerical examples in axi-symmetric geometrical nonlinearities have shown that element free Galerkin method, with its high accuracy, is much more efficient to solve these problems.