Higher-order closed-form solution for the analysis of laminated composite and sandwich plates based on new shear deformation theories

Abstract

In the present study, new shear deformation theories (algebraic (ADT), exponential (EDT), hyperbolic (HDT), logarithmic (LDT) and trigonometric (TDT)) were developed to analyze the static, buckling and free vibration responses of laminated composite and sandwich plates using Navier closed form solution technique. The present theories assume parabolic variation of transverse shear stresses through the depth of the plate. Besides, the transverse shear stresses vanish at the top and bottom of the plate surfaces. Thus, the necessity of shear correction factor is evaded. The governing differential equations and boundary conditions are obtained from the virtual work principle. Like FSDT, the present models consist of 5 unknowns. The shear stress parameter “m” that involves in shear strain function is selected through inverse method. To verify the accuracy and applicability of the present models, numerical comparisons were made with 3D elasticity solutions and existing theories. From the obtained results, it is observed that the proposed shear strain functions have significant effects on structural responses. Also, it is observed that the present theories are more accurate than the renowned theory, for the static, buckling and free vibration analysis of laminated plates.