Equivalent Single Layer Models in Free Vibration Analysis of Laminated Multi-Layered Plates

The performance of selected equivalent single-layer (ESL) models is evaluated within several classical benchmark tests for small amplitude free vibration analysis of multi-layered plates. The authors elaborated their own Finite Element software based on the first-order shear deformation (FOSD) theory with some modifications incorporated including a correction of the transverse shear stiffness and an application of zigzag type functions. Seven different ESL models were considered in the study; beside the classical FOSD model, there were three FOSD models with various transverse shear corrections and three ESL models enhanced by the application of zigzag functions and based on Reissner’s Mixed Variational Theorem.

Reissner’s Mixed Variational Theorem for Layer-Wise Refined Beam Models Based on the Unified Formulation

The present paper proposes the application of the Reissners Mixed Variational Theorem (RMVT) for the accurate stress analysis of general multi-layered beam problems. Laminated materials usually differ from homogeneous materials in that they exhibit much higher transverse shear and transverse normal deformabilities. These characteristics, and others such as the Transverse Anisotropy (TA) and the Interlaminar Continuity of transverse stresses (IC), make Classical Laminated Theories (CLT) inappropriate for the analysis of multi-layered structures. The Carrera Unified Formulation (CUF) sets a framework in which classical-to-refined beam models can be generated by expanding the unknown variables over the cross-sectional domain by means of arbitrary functions. A LW expansion is adopted for both displacements and transverse stresses over the cross-section section domain. In this manner, the ZZ condition is automatically satisfied through the use of independent kinematics for each layer in a LW sense, with no need of introducing ad-hoc ZZ functions.