Variational Principles and Explicit Finite-Element Formulations for the Dynamic Analysis of Partial-Interaction Composite Beams

Composite beams of steel and concrete have found extensive use in civil engineering structures. Technically, such composite structures take advantage of the high tensile strength of steel girders and the compressive strength of concrete slabs, leading to optimal strength to-weight ratios in real engineering practice. Overall, the integrated performance of composite structures is usually achieved through shear connectors and studs that are placed between the different constituents for the purpose of minimizing structural separation. Regardless, research has shown that a phenomenon of partial interaction consequently occurs between the components, leading to interlayer slips and more complicated situations relative to the monoclinic beams. In long-term services, several different types of dynamic loading conditions are usually applied to stimulate different responses of the composite beams. However, in existing literature, most of the dynamic analyses of partial-interaction composite beams are limited to free vibrations without considering more complex loading situations even if numerical techniques are involved. In comparison, the study on vibrations of composite beams under more general loading and boundary conditions is relatively scarce.

A thorough review of previously published research shows that majority of studies include the most sophisticated loading conditions for composite structures thus far, consequently making them unpopular for use in general situations. Therefore, to resolve this shortfall, researchers from the Zhejiang University in China: Professor Guannan Wang and Professor Rongqiao Xu, in collaboration with Associate Professor Jian-Ping Lin at the Huaqiao University, proposed to extend the recently developed one-dimensional (1D) static FE method, to enable study the dynamic behavior of partial-interaction composite beams. Their work is currently published in the Journal of Engineering Mechanics.

In their approach, the research team utilized the dynamic variational principles under the same framework of the (extended) Hamilton’s principle to develop finite-element (FE) formulations for the dynamic responses of composite beams with Timoshenko’s beam theory. Specifically, they focused on the forced vibrations of composite beams with a transverse point load, a moving mass, or a moving mass-spring-damper system, respectively, some of which remain critical in the consideration of the vehicle–bridge (structure) interaction. Overall, the developed dynamic FE theoretical framework was validated against numerical results in existing literature.

The authors reported that their work was unique in that it was the first to focus on several sophisticated loading conditions with their effects on the dynamic responses for the composite beams. Interestingly, a preliminary theoretical foundation was established for the vehicle–composite beam interaction, where the moving point load, mass, and mass-spring-damper system were applied on the composite structures for the first time.

In summary, the study carefully assessed the dynamic responses: mainly force vibrations, of partial interaction composite beams with sophisticated loading conditions. The developed theories and programs were validated by degenerating the simulated results for solid beams with the same loading conditions and always obtaining excellent agreement. In a statement to Advances in Engineering, the authors said their newly developed theories and programs provide solid foundations for further investigation of load/vehicle-composite-beam interactions, which have significant applications in bridge and transportation engineering.