Application of the quadrilateral area coordinate method: a new element for laminated composite plate bending problems

Recently, some new quadrilateral finite elements were successfully developed by the Quadrilateral Area Coordinate (QAC) method. Compared with those traditional models using isoparametric coordinates, these new models are less sensitive to mesh distortion. In this paper, a new displacement-based, 4-node 20-DOF (5-DOF per node) quadrilateral bending element based on the first-order shear deformation theory for analysis of arbitrary laminated composite plates is presented. Its bending part is based on the element AC-MQ4, a recent-developed high-performance Mindlin-Reissner plate element formulated by QAC method and the generalized conforming condition method; and its in-plane displacement fields are interpolated by bilinear shape functions in isoparametric coordinates. Furthermore, the hybrid post-processing procedure, which was firstly proposed by the authors, is employed again to improve the stress solutions, especially for the transverse shear stresses. The resulting element, denoted as AC-MQ4-LC, exhibits excellent performance in all linear static and dynamic numerical examples. It demonstrates again that the QAC method, the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple, effective and reliable finite element models.

[1]  Song Cen,et al.  Method of Area Coordinate — From Triangular to Quadrilateral Elements , 2001 .

[2]  Song Cen,et al.  Development of triangular flat-shell element using a new thin-thick plate bending element based on semiLoof constrains , 2003 .

[3]  Song-Ping Zhu,et al.  A new numerical approach for solving high-order non-linear ordinary differential equations , 2003 .

[4]  Song Cen,et al.  Application of the quadrilateral area co‐ordinate method: a new element for Mindlin–Reissner plate , 2006 .

[5]  Edward A. Sadek.  Some serendipity finite elements for the analysis of laminated plates , 1998 .

[6]  Song Cen,et al.  Some basic formulae for area co-ordinates in quadrilateral elements , 1999 .

[7]  K. S. Kim,et al.  A simple displacement-based 3-node triangular element for linear and geometrically nonlinear analysis of laminated composite plates , 2005 .

[8]  Song Cen,et al.  A new hybrid-enhanced displacement-based element for the analysis of laminated composite plates , 2002 .

[9]  J. Reddy.  Mechanics of laminated composite plates : theory and analysis , 1997 .

[10]  Cen Song,et al.  Development of eight-node quadrilateral membrane elements using the area coordinates method , 2000 .

[11]  Ki-Du Kim,et al.  Linear static and dynamic analysis of laminated composite plates and shells using a 4-node quasi-conforming shell element , 2005 .

[12]  Ai Kah Soh,et al.  A new 4-node quadrilateral FE model with variable electrical degrees of freedom for the analysis of piezoelectric laminated composite plates , 2002 .

[13]  K. S. Kim,et al.  Two simple and efficient displacement‐based quadrilateral elements for the analysis of composite laminated plates , 2004 .

[14]  Ai Kah Soh,et al.  Development of a new quadrilateral thin plate element using area coordinates , 2000 .

[15]  N. J. Pagano,et al.  Elastic Behavior of Multilayered Bidirectional Composites , 1972 .

[16]  Song Cen,et al.  A new quadrilateral area coordinate method (QACM‐II) for developing quadrilateral finite element models , 2008 .

[17]  Jeong Whan Yoon,et al.  A new approach to reduce membrane and transverse shear locking for one‐point quadrature shell elements: linear formulation , 2006 .

[18]  K. Bathe,et al.  Effects of element distortions on the performance of isoparametric elements , 1993 .

[19]  E. Sacco,et al.  MITC finite elements for laminated composite plates , 2001 .

[20]  Antonio Tralli,et al.  A four-node hybrid assumed-strain finite element for laminated composite plates , 2005 .

[21]  P. Lardeur,et al.  Composite plate analysis using a new discrete shear triangular finite element , 1989 .

[22]  Raimund Rolfes,et al.  A three-layered sandwich element with improved transverse shear stiffness and stresses based on FSDT , 2006 .

[23]  N. Pagano,et al.  Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates , 1970 .

[24]  Xiangqiao Yan.  Finite element modeling of consolidation of composite laminates , 2006 .

[25]  Gajbir Singh,et al.  A new lock-free, material finite element for flexure of moderately thick rectangular composite plates , 1998 .

[26]  Michel Brunet,et al.  Analysis of a rotation‐free 4‐node shell element , 2006 .

[27]  Song Cen,et al.  Area co-ordinates used in quadrilateral elements , 1999 .

[28]  Yabo Zhu,et al.  AN IMPROVED AREA-COORDINATE BASED QUADRILATERAL SHELL ELEMENT IN DYNAMIC EXPLICIT FEA , 2005 .

[29]  Song Cen,et al.  Membrane elements insensitive to distortion using the quadrilateral area coordinate method , 2004 .

[30]  Lin Zhongqin,et al.  A quadrilateral thin shell element based on area co-ordinate for explicit dynamic analysis , 2002 .

[31]  Ferdinando Auricchio,et al.  A mixed‐enhanced finite‐element for the analysis of laminated composite plates , 1999 .