Nonlinear Modal Substructuring of Geometrically Nonlinear Finite Element Models

In the past few decades reduced order modeling (ROM) strategies have been developed to create low order modal models of geometrically nonlinear structures from detailed finite element models built in commercial software packages. These models are capable of accurately predicting responses at a reduced computational cost, but it is often not straightforward to determine which modes must be included in the reduction basis, and which scaling amplitudes to apply to the static loads used to identify the nonlinear stiffness coefficients. Furthermore, the upfront cost grows in proportion to the number of modes needed to generate the static load cases. These ROM strategies have been successfully used in many applications, and this dissertation contributes to existing approaches in two ways. The first contribution is the use of the nonlinear normal mode (NNM) as a metric to gauge the convergence of candidate ROMs and to observe similarities and differences between them. If the NNMs of the ROMs converge or coincide with the true NNMs of the full order model over a range of frequency and energy, then the ROM is expected to correctly represent the full model. Since geometric nonlinearities depend only on displacements, the undamped NNM framework serves as an ideal metric for comparison since they are load independent properties of the system, and capture a wide range of response amplitudes experienced by the structure. The second contribution of this work is the development of a modal substructuring approach that utilizes these existing ROM strategies. The proposed approach creates a reduced order model of a large, complicated structure by first dividing it into smaller subcomponents, reducing these subcomponents with an appropriate set of basis vectors, and assembling them by satisfying force equilibrium and compatibility. Creating a reduced order model with substructuring allows one to build ROMs of simpler substructure models that may require fewer modes, and hence fewer static load cases. Nonlinear modal substructuring is readily applied to geometrically nonlinear finite element models built in commercial packages, and the NNMs of the assembled ROMs serve as a convergence metric to evaluate the sufficiency of the model.