Craig-Bampton Substructuring for Geometrically Nonlinear Subcomponents

Abstract

The efficiency of a modal substructuring method depends on the component modes used to reduce the subcomponent models. Methods such as Craig-Bampton (CB) and Craig-Chang have been used extensively to reduce linear finite element models with thousands or even millions of degrees-of-freedom down to a few tens or hundreds. The greatest advantage to these approaches is that they can obtain acceptable accuracy with a small number of component modes. Currently, these modal substructuring methods only apply to linear substructures. A new reduction method is proposed for geometrically nonlinear finite element models using the fixed-interface and constraint modes (collectively termed CB modes) of the linearized system. The reduced model for this system is written in terms of cubic and quadratic polynomials of the modal coordinates, and the coefficients of the polynomials are determined using a series of static loads/responses. This reduction is a nonlinear extension to the Craig-Bampton model for linear systems, and is readily applied to systems built directly in a commercial FEA package. The nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. The efficiency of this new substructuring approach is demonstrated on an example problem that couples two geometrically nonlinear beams at a shared rotational degree-of-freedom. The nonlinear normal modes of the assembled models are compared with those of a truth model to validate the accuracy of the approach.KeywordsSubstructuringReduced order modelingGeometric nonlinearityComponent mode synthesisInternal resonance