Refined hyperbolic shear deformation plate theory

Abstract

The paper presents a novel shear deformation plate theory involving only two variables. Taking a cue from exact three-dimensional theory of elasticity solutions for a plate, hyperbolic functions are used for describing displacement variation across plate thickness. The theory involves only two governing equations, which are uncoupled for statics and are only inertially coupled for dynamics. The shear stress free surface conditions are satisfied. No shear correction factor is required. The theory is variationally consistent, has a strong similarity with classical plate theory, and is simple, yet accurate. Illustrative examples for free vibration and for static flexure demonstrate the effectiveness of the theory.