Displacement and stress analysis of laminated and sandwich beams under various mechanical loads using a quasi-2D theory

This study presents a fifth-order shear deformation theory for analyzing the displacement and stress of laminated and sandwich beams subjected to sinusoidal, uniformly distributed, and linearly varying loads. The theory's displacement field takes normal deformations and transverse shear effects into account. On both the upper and lower surfaces of the beams, the requirement of zero transverse shear stresses is fulfilled. Hence present theory does not require a shear correction factor. Governing equations and boundary conditions of laminated and sandwich beams are derived using the principle of virtual work. From the stress-equilibrium equations of the theory of elasticity, transverse shear stresses are recovered. Both the stress-free boundary conditions at the external surfaces and the continuity condition at the layer interface are satisfied by the transverse stresses that arise from this approach. Closed-form solutions for simply supported beams are obtained using Navier's solution method. A MATLAB program is developed based on the present formulation to generate numerical results. A comparison result of present 5th OSDTs and those of the 3rd OSDTs, FSDT, and CBT are presented. The inclusion of transverse normal strain into the theory resulted in significant variation in the displacements and stresses of laminated and sandwich beams when compared to the results predicted from the lower-order theories discarding transverse normal strain.