A novel four-node quadrilateral element with continuous nodal stress

Abstract

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.

On the accuracy and convergence of the hybrid FE-meshfree Q4-CNS element in surface fitting problems

“…Note that in the classical isoparametric fournode quadrilateral element (Q4), the weight functions are given as the shape functions and the nodal approximations are reduced to nodal values ui. Here the weight functions are defined as the non-conforming shape functions for the Kirchhoff's plate rectangular element [6,12], that is,…”

“…The nodal approximations ui(x,y) are constructed using the orthonormalized and constrained least-squares method (CO-LS) as presented by Tang et al [6] and Yang et al [9][10]. Here the CO-LS is briefly reviewed.…”

“…To synergize the strengths of the finite element and meshfree methods while avoiding their weaknesses, in the last decade several hybrid methods combining the two classes of methods based on the concept of partition-ofunity have been developed [4][5][6][7][8]. Among several hybrid methods available in literature, the authors are interested in the four-node quadrilateral element with continuous nodal stress (Q4-CNS) proposed by Tang el al.…”

“…Among several hybrid methods available in literature, the authors are interested in the four-node quadrilateral element with continuous nodal stress (Q4-CNS) proposed by Tang el al. [6] for the reason that this work is the pioneering hybrid method possessing the property of continuous nodal stress. The Q4-CNS can be regarded as an improved version of the FE-LSPIM Q4 [4][5].…”

“…In this novel method, the nonconforming shape functions for the Kirchhoff's plate rectangular element are combined with the shape functions obtained using an orthonormalized and constrained least-squares method. The benefits of the Q4-CNS are [6,9,10]: (1) the shape functions are C 1 continuous at nodes so that it naturally provides a globally smooth gradient fields. (2) The Q4-CNS can give higher accuracy and faster convergence rate than the standard quadrilateral element (Q4).…”