节点应力连续的四边形单元

A Novel Four-Node Quadrilateral Element With Continuous Nodal Stress

节点应力连续的四边形单元Q4-CNS是一种基于单位分解理论的混合的有限元无网格法.Q4-CNS可以视作FE-LSPIM QUAD4的发展.Q4-CNS形函数的导数在节点处是连续的,因此可以自然的得到节点应力,而不需要使用节点应力磨平算法.数值实验表明,与传统四边形单元(QUAD4)相比,Q4-CNS具有更好的计算精度和更高的收敛速度.在扭曲网格下,Q4-CNS也能取得满意的数值精度.然而,QUAD4的数值精度则会随着网格的扭曲明显的变差.基于Kirchhoff-Love假设的非协调板单元计算中,不仅要求形函数在单元的交界面上要保持C0连续性,而且要求形函数在节点处具有C1连续性,所以在任意的四边形单元上构造满足插值条件的非协调板单元形函数较为困难.Q4-CNS形函数的导数在节点处是连续的,所以Q4-CNS在求解基于Kirchhoff-Love假设的板单元问题中具有潜在的应用价值.

Formulation and numerical evaluation of a novel QUAD4 with continuous nodal stress （Q4- CNS ） were presented. And Q4-CNS can be regarded as an improved FE-LSPIM QUAD4, which is a hybrid FE-Meshless method. The derivatives of Q4-CNS are continuous at nodes, so continuous nodal stress can be obtained without any smoothing operation. It is found that, compared with standard 4- node quadrilateral element （QUAD4）, Q4-CNS can achieve significantly better accuracy and higher convergence rate. It is also found that Q4-CNS exhibits high tolerance to mesh distortion. Moreover, since the derivatives of Q4-CNS shape functions are continuous at nodes, Q4-CNS is potentially useful for the problem of bending plate and shell models.