Static and dynamic responses of simply supported sandwich plates using non-polynomial zigzag theory

Abstract

The static, free vibration and transient responses of simply-supported laminated composites and sandwich plates are analytically derived using a non-polynomial zigzag theory. This mathematical model is displacement-based with five field variables and uses a non-polynomial mathematical function to introduce the non-linearity of transverse shear stresses through-thickness, thus eliminating the use of a large number of higher-order terms in the kinematic field. The zigzag kinematics is implemented by the inclusion of auxiliary variables defined at the interfaces of the plates with a piecewise linear function of the thickness coordinate. The dynamic governing equations of equilibrium are derived with Hamilton's principle that generates five coupled partial differential equations. The Navier's solution technique with the Newmark's time integration scheme is adopted to find the solutions of the coupled equations. The responses in the form of displacements, stresses, natural frequencies, and displacement–time responses are obtained by solving several standard problems in the literature. The transverse shear stresses are accurately obtained by integrating the three-dimensional equilibrium equations of elasticity. The forced-vibration analysis of the laminated composites and sandwich plates are presented in detail by considering various forms of time-dependent loads that also includes the various forms of blast loads. The present results agree closely with the published results in the literature for both laminated composites and sandwich plates. © 2020 Institution of Structural Engineers