No abstract

No abstract

No abstract

Abstract:Extension-Bending coupling behaviour is believed to arise uniquely in anti-symmetric Cross-ply laminates. The results in this article serve to dispel this misconception by presenting solutions for both Cross-ply laminates and Standard laminates, defined as containing combinations of angle plies and cross plies, for a range of different sub-sequence symmetries. Details of the algorithm used to develop the definitive list of laminate stacking sequences with up to 21 plies are presented. Finally, natural frequency factor envelopes are developed, which identify significant differences in the bounds, across a range of aspect-ratios, between Standard laminate configurations and the previously assumed Cross-ply designs.

Three-point bending of a beam is studied based on the Timoshenko beam theory. Large deflection and large rotation of a beam resting on simple supports with friction are calculated for a concentrated force acting at the midspan. Using the Lagrangian kinematic relations, a system of non-linear differential equations are obtained for a prismatic sheardeformable Timoshenko beam. Exact solutions for the deflection, horizontal displacement, and rotation of cross-section are derived analytically. Two deflections of small and large scale exist under three-point bending. The solutions corresponding to linearized model coincide with the well-known solutions to the classical Timoshenko beams. Numerical calculations are carried out to show the effect of the important parameters such as shear rigidity of the beam and the coefficient of friction at the contact position between the beam and supports on the deflection. The load-deflection curves are graphically presented. A comparison of large deflections and large rotations with their classical counterparts and with experimental data is made. The obtained results are useful in safety design of linear and non-linear beams subject to three-point bending.