A new laminated composite beam element based on eigenvalue problem

• We develop the shear deformable laminated composite beams.
• The element stiffness matrix is newly derived based on the eigenvalue problem.
• Some characteristics of flexural and torsional behavior are reported.

A new laminated composite beam element is developed based on the eigenvalue problem for the flexural and torsional analyses of beams with I- and channel-sections. Analytical technique is used to present the laminated composite beam theory considering the transverse shear and the restrained warping induced shear deformation based on an orthogonal Cartesian coordinate system. From the energy principle, the equilibrium equations are derived and the member stiffness matrix is determined using the force–displacement relations of the beam. In order to demonstrate the validity of this study, the deflections and the twist angles of composite beams with I- and channel-sections are presented and compared with the results from other researchers and the finite beam element using the Lagrange interpolation functions, and the detailed finite element analysis results using ABAQUS. Especially the flexural and torsional behavior and the effect of shear deformation are investigated with respect to the modulus ratio and the fiber angle change.