A Quasi-3D Polynomial Shear and Normal Deformation Theory for Laminated Composite, Sandwich, and Functionally Graded Beams

Bending analyses of isotropic, functionally graded, laminated composite, and sandwich beams are carried out using a quasi-3D polynomial shear and normal deformation theory. The most important feature of the proposed theory is that it considers the effects of transverse shear and transverse normal deformations. It accounts for parabolic variations in the strain/stress produced by transverse shear and satisfies the transverse shear stress-free conditions on the top and bottom surfaces of a beam without the use of a shear correction factor. Variationally consistent governing differential equations and associated boundary conditions are obtained by using the principle of virtual work. Navier closed-form solutions are employed to obtain displacements and stresses for the simply supported beams, which are subjected to sinusoidal and uniformly distributed loads. Results are compared with those derived using other higher-order shear deformation theories. The comparison validates the accuracy and efficiency of the theory put forward in this work.