A hybrid finite element formulation for a beam-plate system

Abstract

A new development in the area of the hybrid finite element analysis (hybrid FEA) is presented. The hybrid FEA method combines the conventional FEA method with energy FEA (EFEA) for analysis of systems that contain both flexible and stiff members. A formulation for analyzing flexible plates spot-welded to stiff beams when the excitation is applied on the stiff members is developed. Conventional FEA models are employed for modeling the behavior of the stiff members in a system. Appropriate damping elements are introduced in the connections between stiff and flexible members in order to capture the presence of the flexible members during the analyses of the stiff ones. The component mode synthesis method is combined with analytical solutions for determining the driving point conductance at joints between stiff and flexible members and for defining the properties of the damping elements which represent the flexible members when analyzing the stiff components. Once the vibration of the stiff members and the amount of power dissipated at the damping elements has been identified, an EFEA analysis is performed in order to determine the amount of vibrational energy in the flexible members. The new developments are validated by comparing results of the hybrid FEA with results from very dense conventional finite element analyses for structures of increasing complexity.