An improved discrete Kirchhoff quadrilateral element based on third‐order zigzag theory for static analysis of composite and sandwich plates

Abstract

SUMMARYA new improved discrete Kirchhoff quadrilateral element based on the third-order zigzag theory is developed for the static analysis of composite and sandwich 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 usual requirement of C 1 continuity of interpolation functions of the deflection in the third-order zigzag theory is circumvented by employing the improved discrete Kirchhoff constraint technique. The element is free from the shear locking. The finite element formulation and the computer program are validated by comparing the results for simply supported plate with the analytical Navier solution of the zigzag theory. Comparison of the present results with those using other available elements based on zigzag theories for composite and sandwich plates establishes the superiority of the present element in respect of simplicity, accuracy and computational efficiency. The accuracy of the zigzag theory is assessed by comparing the finite element results of the square all-round clamped composite plates with the converged three-dimensional finite element solution obtained using ABAQUS. The comparisons also establish the superiority of the zigzag theory over the smeared third-order theory having the same number of degrees of freedom.

Free vibration analysis of composite and sandwich plates using an improved discrete Kirchhoff quadrilateral element based on third-order zigzag theory

“…Thus, for the kth layer, the displacement field is given by Shu and Sun [40] and Kapuria and Kulkarni [19].…”

“…R k 1 ,R k 2 ,R 3 andR 4 are 2×2 coefficient matrices which depend on the material properties and lay-ups, whose expressions are given in [19]. For the smeared third order theory (TOT) [34], u can be expressed in the form of Eq.…”

“…To explore the potential of the DKQ and the IDKQ concepts to the third order smeared and zigzag theories for laminated elastic plates, Kapuria and Kulkarni [19,22] have developed and evaluated quadrilateral elements for static analysis of multilayered plates, based on the TOT and the ZIGT using the DKQ interpolation functions of Batoz and Tahar [5] and the improved DKQ (IDKQ) interpolation functions of Jeychandrabose et al [17]. In the present work, these elements are extended for the dynamics and their performance evaluated for the free vibration response of inhomogeneous composite and sandwich plates with different shapes and boundary conditions.…”

A new zig-zag theory and C0 plate bending element for composite and sandwich plates

“…7 and 8. It can be observed that the present zig-zag theory can predict more accurate transverse shear stresses than the zig-zag theory proposed by Kapuria and Kulkarni [27] by integrating the three-dimensional equilibrium equations. In addition, transverse shear stress for five-layer plate is shown in Fig.…”

A New C0 2D Fe Model Based on Improved Higher Order Zigzag Theory for the Analysis of Soft Core Sandwich Plate

“…Akhras and Li (2007) developed a spline finite strip method based on Cho's higher order zigzag theory for the static analysis of the plate. Kapuria and Kulkarni (2007) presented a four node quadrilateral element based on the third order zigzag theory for the analysis of laminates. The need of C 1 continuity requirement is circumvented by using a discrete Kirchoff constraint approach, where the derivaties of transverse displacement are replaced by rotational variables.…”