Dynamic behaviors of general composite beams using mixed finite elements

A novel mixed finite element method is developed and implemented for analyzing the vibration and buckling behavior of general composite beams which consists both transversely layered and axially jointed materials. The governing state-space equations are derived using the Hamilton's principle, where both displacements and stresses are treated as fundamental variables. This semi-analytical method uses transfer relations in the transverse direction and finite element meshing in the longitudinal direction, overcoming the difficulties for general composite beams analysis and providing computational efficiency and analyzing flexibilities. The developed mixed finite element model ensures continuity of both displacements and stresses across the material interface, thereby resolving interfacial stress singularity issues and offering more reliable simulations of boundary conditions at both ends. The proposed method is formulated and validated for the free vibration and buckling analysis of general composite beams. Additionally, it is observed that material properties such as Young's modulus and density, as well as the stiffness of the interface connecting layers, have significant effects on the free vibration and buckling responses of the composite beams. Analysis of periodically distributed and bi-directional composite beams demonstrates the versatility of this method in handling two types of combination forms. The proposed method serves as a valuable reference for obtaining accurate vibration and buckling results while ensuring stress-compatibility for composite beams in practical applications.