The dynamic response of complex structures using hybrid methods

Abstract

Within many complex structures, there are regions which easily lend themselves to closed-form analytic solutions. A hybrid analytic-numeric formulation for the time harmonic structural vibration response of such structures is presented. The seamless inclusion of analytic solutions into the Galerkin finite element method is accomplished by using transition elements which couple the tractions between analytic and numeric solution regions. The main advantage of this formulation is to increase the overall efficiency of a model by eliminating regions of the structure from the computational domain. In this way, the total number of degrees-of-freedom will be reduced, which in turn reduces memory requirements and computational time. This allows for the analysis of higher frequency or more complex problems. One application is the study of systems comprised of structural members which are coupled at nonidealized joints. Using a discretization of the equations of elasticity for a joint, its response may be represented to a desired level of accuracy. This elasticity model is coupled to the reduced beam or shell theory producing an efficient model of the complete structure. The effect of the joint and the level of modeling detail for prediction of the time harmonic response are studied.