A Four-Variable Plate Theory for Thermoelastic Bending Analysis of Laminated Composite Plates

Abstract

In this article, the thermoelastic bending analysis of laminated composite plates subjected to thermal load linear across the thickness using the four variable refined plate theory is presented. The theory involves four unknown variables, as against five in case of other higher-order theories and first-order shear deformation theory. The theory gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free conditions at top and bottom surfaces of the plate. The theory does not require problem-dependent shear correction factors that are associated with the first-order shear deformation theory. The principle of virtual work is used to obtain variationally consistent governing equations and boundary conditions. The simply supported laminated composite plates are considered for the detail numerical study. A closed-form solution is obtained using the double trigonometric series technique suggested by Navier. The numerical results for thermal displacements and stresses of laminated composite plates are obtained and compared with those of other refined theories and exact solutions wherever applicable to assess the efficiency of the present theory. From the numerical results it is observed that since plate is subjected to pure thermal load and not subjected to transverse mechanical load, the present theory has strong similarity with classical plate theory in many aspects.

Keywords:

• Laminated plate
• Linear thermal load
• Navier solution
• Shear correction factor
• Transverse shear stress