A Beam Theory for Laminated Composites and Application to Torsion Problems

A theory for laminated composite beams is derived from the shear deformable laminated plate theory. The displacement field in the beam is derived by retaining the first-order terms in the Taylor series expansion for the plate midplane deformations in the width coordinate. The displacements in the beam are expressed in terms of three deflections, three rotations, and one warping term. The equilibrium equations are assumed to be satisfied in an average sense over the width of the beam. This introduces a new set of force and moment resultants for the beam. The principle of minimum potential energy is applied to derive the equilibrium equations and boundary conditions. A closed-form solution is derived for the problem of torsion of a specially orthotropic laminated beam.