Effect of thickness stretching on the static deformations, natural frequencies, and critical buckling loads of laminated composite and sandwich beams

The present study investigates the bending, buckling, and vibration responses of shear deformable laminated composite and sandwich beams using trigonometric shear and normal deformation theory. The most important feature of the present theory is that it includes the effects of transverse shear and normal deformations, i.e., the effect of thickness stretching. Therefore, the theory is also called as a quasi-2D theory. The axial displacement uses sine function in terms of the thickness coordinate to include the effect of transverse shear deformation, and the transverse displacement uses cosine function in terms of the thickness coordinate to include the effect of transverse normal deformation, i.e., the thickness stretching. The present theory satisfies the zero shear stress conditions at top and bottom surfaces of the beam without using shear correction factor. Governing differential equations and associated boundary conditions of the theory are derived by employing the dynamic version of principle of virtual work. Navier-type closed-form solutions are obtained for simply supported boundary conditions. The numerical results are obtained for deflections, stresses, natural frequencies, and critical buckling loads for isotropic, laminated composite, and sandwich beams. Since exact elasticity solutions for laminated composite and sandwich beams are not available in the literature, the results are compared with those obtained by using other higher-order shear deformation theories to demonstrate the accuracy of the proposed theory.