A general theory for the accurate stress analysis of homogeneous and laminated composite beams

Abstract

This paper has a twofold purpose. Initially, it presents a general four-degrees-of-freedom beam theory (G4DOFBT) which takes into consideration the effects of both transverse shear and normal deformation. On the basis of this new theory, it then proposes a method suitable for the accurate stress analysis of either homogeneous or laminated composite beams subjected to arbitrary edge boundary conditions. The new beam theory involves two general “shape” functions, each of which is associated with one of the two unknown displacement components. Upon assigning simple particular forms to these shape functions, most of the well-known classical and variationally consistent refined beam models may be obtained as particular cases. The new method for the accurate stress analysis of beam-type structures is based on the specification of a new pair of shape functions. These are obtained by introducing the stress distributions, caused by the assumed G4DOFBT displacement field, into the appropriate equations of three-dimensional elasticity which are subsequently solved for simply supported edges. This is considered to provide an excellent choice of both shape functions as the method then yields the exact elasticity solution presented by Pagano (Pagano, N. J. (1969). Exact solution for composite laminates in cylindrical bending. J. Comp. Mat.3, 398–411) for the cylindrical bending problem of simply supported infinite strips. Two particular examples are considered to show the potential of the present analysis. These are dealing with stress analysis of homogeneous or laminated composite beams having one edge rigidly clamped and the other edge either guided or free of external tractions.