Analysis of Complex Composite Beam by Using Timoshenko Beam Theory & Finite Element Method

Fiber-reinforced composites, due to their high specific strength, and stiffness, which can be tailored depending on the design requirement, are fast replacing the traditional metallic structures in the weight sensitive aerospace and aircraft industries. An analysis Timoshenko beam theory for complex composite beams is presented. Composite materials have considerable potential for wide use in aircraft structures in the future, especially because of their advantages of improved toughness, reduction in structural weight, reduction in fatigue and corrosion problems. The theory consists of a combination of three key components: average displacement and rotation variables that provide the kinematic description of the beam, stress and strain moments used to represent the average stress and strain state in the beam, and the use of exact axially-invariant plane stress solutions to calibrate the relationships between all these quantities. The Euler‐Bernoulli beam theory neglects Shear deformations by assuming that plane sections remain plane and perpendicular to the neutral axis during bending. As a result, shear strains and stresses are removed from the theory. Two essential aspects of Timoshenko’s beam theory are the treatment of shear deformation by the introduction of a mid-plane rotation variable, and the use of a shear correction factor [36].