Nonlinear static and transient analysis of generally laminated beams

Abstract

In this study two one-dimensional finite element formulations based on higher-order displacement models have been developed. Both theories account for geometric nonlinearities, a parabolic shear strain distribution through the thickness, and satisfy the shear stress free boundary conditions at the upper and lower surfaces of the beam. The theories also account for the bend-stretch, shear-stretch, and bend-twist couplings inherent to generally laminated composite beams. Further, a coupling between the shear deformation and the twisting is introduced. The lateral strains are assumed nonzero and retained in the formulation.

The first model termed SVHSDT also accounts for the continuity of the interlaminar shear stresses at the layer interfaces, while keeping the number of degrees of freedom independent of the number of layers. This theory though is restricted to the analysis of symmetrically laminated cross-ply beams. The formulation has been applied to the linear static and free vibration analysis.

The second model termed RHSDT is valid for generally laminated beams. This model has been applied to the nonlinear static and transient analysis of generally laminated beams, free vibration analysis, and impact analysis. The effect of axial stresses on the nonlinear transient response has also been investigated using this theory.

For generally laminated beams the lateral strains and the shear-twist coupling were found to have a significant effect on the vibrations frequencies. Also, as expected, initial stresses, boundary conditions and the lamination scheme were found to have a significant effect on the nonlinear responses.