Geometrically exact nonlinear modeling and non-classical effect influence of composite beams

The geometrically exact nonlinear modeling of composite beam with arbitrary cross sectional shape, generally anisotropic material behavior and large deflection had been presented, based on the generalized Timoshenko beam theory of Hodges. The concept of decomposition of rotation tensor was used to calculate the strains in the beam. The variational asymptotical method was used to determine the arbitrary warping of the beam cross section. The generalized Timoshenko strain energy was derived from the equilibrium equations and the second-order asymptotically correct strain energy. The geometrically exact nonlinear equations of motion were established by the Hamilton's generalized principle. The established modeling was used for the static and dynamic analysis of composite beams and was verified by the comparisons with experimental data. The influences of the non-classical effects such as the cross sectional warping and the transverse shear deformation on the composite beams were investigated. The results indicate that the cross sectional warping has significant influences on the static deformation and the natural frequencies of the composite beams, and the influences of the transverse shear deformation on the static deformation and the natural frequencies of the composite beams are related to the length to depth ratio of the beam.