A twenty DOF element for nonlinear analysis of unsymmetrically laminated beams

The purpose of this study was to develop a simple one- dimensional finite element for the nonlinear analysis of symmetrically and unsymmetrically laminated composite beams including shear deformation. There is a need for a simple and efficient method for analyzing unsymmetrically laminated beams since no other study on this topic is currently available. The beam element has ten degrees of p freedom at each of the two nodes: the axial displacement, the transverse deflection due to bending and shear, the twisting angle, the inplane shear rotation, and their derivatives along the axial direction. The formulation, solution procedure, and the computer program have been evaluated by solving a series of examples on the static response, free vibration, buckling, and nonlinear vibrations of isotropic and laminated beams. For unsymmetrically laminated beams, the nonlinear vibrations were found to have a soft spring behavior for certain boundary conditions as opposed to a hard spring behavior observed in isotropic and symmetrically laminated beams. The inplane boundary conditions were found to have a significant effect on nonlinear responses.