Dynamic analysis of generally laminated composite beam with a delamination based on a higher-order shear deformable theory

In this study, the dynamic response of the laminated composite beam with arbitrary lay-ups has been investigated within the framework of the third-order shear deformation theory using the finite element method. A new three-nodded finite element compliant with the theory is introduced next. To deal with the dynamic contact between the delaminated segments, unilateral contact constraints are employed in conjunction with Lagrange multiplier method. Furthermore, the Poisson's effect is incorporated in the formulation of the beam constitutive equation. Also, the higher-order inertia effects and material couplings (flexure-tensile, flexure-twist and tensile-twist couplings) are considered in the formulation. Results are extracted based on two methods namely the Eigen-value techniques for frequencies and the Newmark method to calculate the transient response. Then, the obtained results have been verified with the other results available in the literature and very good agreements have been observed. Furthermore, the new results have been obtained for the case where the excitation was due to a moving/non-moving force.