轴对称弹性体扭转问题的无网格自然邻接点Petrov-Galerkin法

本文将无网格自然邻接点Petrov-Galerkin法应用于轴对称弹性体扭转问题的求解.无网格自然邻接点Petrov-Galerkin法采用自然邻接点插值构造试函数,并且采用三角形线性单元的形函数作为加权残值法的加权函数.自然邻接点插值构造的试函数满足Kroneckerdelta函数性质,因此本质边界条件的施加十分方便.由于几何形状和边界条件的轴对称特点,原来的空间问题简化为二维问题求解,因此计算时只需要横截面上离散节点的信息.数值算例结果表明,所提出的方法对求解轴对称弹性体扭转问题是行之有效的.

Meshless Natural Neighbour Petrov-Galerkin Method for Torsion Problems of Axisymmetric Elastic Body

The meshless natural neighbour Petrov-Galerkin method has been developed to solve torsion problems of axisymmetric elastic body. In this method, the natural neighbour interpolation is adopted to construct the trial functions, and the linear triangular FEM shape functions are chosen as the test functions of the weighted residual method. The natural neighbour interpolation shape functions satisfy the Kronecker delta property and thus it is very convenient to impose the essential boundary conditions. Because of the axis-symmetry of geometry and boundary conditions, an original three-dimensional problem can be reduced into a two-dimensional problem and therefore it is only required to use a set of discrete nodes on the cross section. Several numerical examples are presented to show that the proposed method is effective for the torsion problems of axisymmetric elastic body.