Physics

Finite element method

Plate theory

Shell (structure)

Mathematics

Structural engineering

Bending

Composite number

Engineering

Mathematical analysis

Virtual work

Boundary value problem

Composite material

Vibration

Acoustics

Materials science

Kinematics

Classical mechanics

Shear (geology)

Computers and Concrete, an International Journal

This research is devoted to investigate the bending and free vibration behaviour of laminated composite/sandwichplates and shells, by applying an analytical model based on a generalized and simple refined higher-order shear deformation theory (RHSDT) with four independent unknown variables. The kinematics of the proposed theoretical model is defined by an undetermined integral component and uses the hyperbolic shape function to include the effects of the transverse shear stresses through the plate/shell thickness; hence a shear correction factor is not required. The governing differential equations and associated boundary conditions are derived by employing the principle of virtual work and solved via Navier-type analyticalprocedure. To verify the validity and applicability of the present refined theory, some numerical results related to displacements, stresses and fundamental frequencies of simply supported laminated composite/sandwich plates and shells are presented and compared with those obtained by other shear deformation models considered in this paper. From the analysis, it can be concluded that the kinematics based on the undetermined integral component is very efficient, and its use leads to reach higher accuracy than conventional models in the study of laminated plates and shells.

A generalized 4-unknown refined theory for bending and free vibration analysis of laminated composite and sandwich plates and shells