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

Abstract

The new improved discrete Kirchhoff quadrilateral element based on the third-order zigzag theory developed earlier by the present authors for the static analysis of composite and sandwich plates is extended for dynamics and assessed for its performance for the free vibration response. The element is free from the shear locking. The finite element formulation is validated by comparing the results for simply supported plates with the analytical Navier solution of the zigzag theory. Comparison of the present results for the natural frequencies with those of a recently developed triangular element based on the zigzag theory, 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 for composite and sandwich plates with various boundary conditions and aspect ratio by comparing the finite element results with the 3D elasticity analytical and finite element solutions.

Refined Zigzag Theory for laminated composite and sandwich plates derived from Reissner’s Mixed Variational Theorem

“…These functions satisfy the clamped boundary conditions at 1 0 = x , that is where the same Gram-Schmidt approximation scheme is used as in the previous example (Problem 2.) In addition, a high-fidelity FEA is performed [43] and its results are used as reference solutions.…”

A C0 zig-zag model for the analysis of angle-ply composite thick plates

“…The six-node plate element developed is a nonconforming element as the element does not satisfy the normal slope continuity requirement. Thus, Kulkarni and Kapuria [34] indicated that the six-node triangular element [33] underestimated the natural frequencies of the sandwich plates. Therefore, three-node triangular element based on the C 1 -type zig-zag model [18] has been developed for comparison in this paper.…”

Assessment of the Refined Zigzag Theory for bending, vibration, and buckling of sandwich plates: a comparative study of different theories

“…In Table 8, the first ten circular frequencies, computed with different approaches, are compared with the RZT results. Solution cited as 3D FE [58] is obtained by means of three-dimensional finite element analysis and it can be considered as a reference result. For comparison purposes, solutions are also obtained with FSDT (shear correction factors as in [55]).…”