A new discrete Kirchhoff quadrilateral element based on the third-order theory for composite plates

A new discrete Kirchhoff quadrilateral element based on the refined third-order theory is developed for the analysis of composite plates. The element has seven degrees of freedom per node, namely, the three displacements, two rotations and two transverse shear strain components at the mid-surface. The inplane displacements and the shear strains are interpolated using bilinear interpolation functions and the mid-surface rotations are interpolated using bi-quadratic functions based on the discrete Kirchhoff technique. The element stiffness matrix and the consistent load vector are developed using the principle of virtual work. The finite element formulation is validated by comparing the results for simply-supported plate with the analytical Navier solution. Comparison of the present results with those using other available elements based on the TOT establishes the superiority of the present element in respect of simplicity, accuracy and computational efficiency. The element is free from shear locking

[1]  E. Hinton,et al.  A family of quadrilateral Mindlin plate elements with substitute shear strain fields , 1986 .

[2]  O. C. Zienkiewicz,et al.  THE FINITE ELEMENT METHOD FOR ANALYSIS OF ELASTIC ISOTROPIC AND ORTHOTROPIC SLABS. , 1964 .

[3]  Jean-Louis Batoz,et al.  Evaluation of a new quadrilateral thin plate bending element , 1982 .

[4]  A. Ghosh,et al.  A simple finite element for the analysis of laminated plates , 1992 .

[5]  Perngjin F. Pai,et al.  A new look at shear correction factors and warping functions of anisotropic laminates , 1995 .

[6]  Abdul Hamid Sheikh,et al.  A new plate bending element based on higher-order shear deformation theory for the analysis of composite plates , 2003 .

[7]  J. Reddy.  A Simple Higher-Order Theory for Laminated Composite Plates , 1984 .

[8]  J. N. Reddy,et al.  On refined computational models of composite laminates , 1989 .

[9]  J. N. Reddy,et al.  A refined mixed shear flexible finite element for the nonlinear analysis of laminated plates , 1986 .

[10]  J. N. Reddy,et al.  Analysis of laminated composite plates using a higher‐order shear deformation theory , 1985 .

[11]  E. Hinton,et al.  The finite element analysis of homogeneous and laminated composite plates using a simple higher order theory , 1986 .

[12]  Medhat A. Haroun,et al.  Reduced and selective integration techniques in the finite element analysis of plates , 1978 .

[13]  J. Whitney,et al.  Shear Deformation in Heterogeneous Anisotropic Plates , 1970 .

[14]  Gangan Prathap,et al.  Field‐ and edge‐consistency synthesis of A 4‐noded quadrilateral plate bending element , 1988 .