A novel four-node quadrilateral element with continuous nodal stress

Formulation and numerical evaluation of a novel four-node quadrilateral element with continuous nodal stress (Q4-CNS) are presented. Q4-CNS can be regarded as an improved hybrid FE-meshless four-node quadrilateral element (FE-LSPIM QUAD4), which is a hybrid FE-meshless method. Derivatives of Q4-CNS are continuous at nodes, so the continuous nodal stress can be obtained without any smoothing operation. It is found that, compared with the standard four-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 derivatives of Q4-CNS shape functions are continuous at nodes, Q4-CNS is potentially useful for the problem of bending plate and shell models.