轴对称动力学问题的无网格自然邻接点Petrov-Galerkin法

Meshless natural neighbour Petrov-Galerkin method for axisymmetric dynamic problems

基于无网格自然邻接点Petrov-Galerkin法,提出了复杂轴对称动力学问题求解的一条新途径。几何形状和边界条件的轴对称特点,将原来的空间问题转化为平面问题求解。计算时仅仅需要横截面上离散节点的信息,无论积分还是插值都不需要网格。自然邻接点插值构造的试函数具有Kronecker delta函数性质,因此能够直接准确地施加本质边界条件。有限元三节点三角形单元的形函数作为权函数,可以减少域积分中被积函数的阶次,提高计算效率。数值算例结果表明,所提出的方法对求解轴对称动力学问题是行之有效的。

A novel algorithm for solving complex axisymmetric dynamic problems was put forward on the basis of the meshless natural neighbour Petrov-Galerkin method.Due to axial symmetry of geometry and boundary conditions,an original three-dimensional （3D）problem was reduced into a two-dimensional （2D）problem.Only a set of discrete nodes on a cross section were needed and no meshes were required for either interpolation or integration.The natural neighbour interpolation shape functions had a Kronecker delta property and therefore the essential boundary conditions could be directly imposed.The three-node triangular finite element shape functions were taken as test functions,they reduced the orders of integrands involved in domain integrals and improved the computational efficiency.Numerical examples showed that the proposed method for solving axisymmetric dynamic problems is effective.