Use of expansion of highly reduced order models for the accurate prediction of full field dynamic characteristics in the forced response of linear and nonlinear systems and components

A comprehensive framework for the use of reduction and expansion methodologies of components and system models is proposed for the prediction of full field dynamic characteristics of models in both linear and nonlinear forced response for both displacement and strain. Commercial finite element models of high resolution are simplified to a reduced space in which different configuration of forces, boundary conditions and connecting/coupling elements can be tested efficiently and without loss in the fidelity of the model. With the calculated component or system model response at a reduced set of points, expansion can be employed to return to the full space of the model and predict the response at all degrees of freedom of the system. Furthermore, the system component response can be expanded to predict the dynamics of complete systems with complicated subcomponent or cascaded configurations as well as accurately calculate full field stress-strain.;The methodology proposed is developed for linear systems as well as more complex multi-component models in which nonlinear response occurs due to the presence of highly nonlinear coupling elements such as hard contacts, isolation mounts, gap springs, bilinear springs, etc. These cascaded systems require the embedding of dynamic information in the reduced order model as to accurately preserve the high level of resolution and detail of the full model. Common reduction methodologies and model improvement techniques such as SEREP, Guyan Condensation, and KM_AMI will be explored in the context of this type of nonlinear system modeling.;Using these new efficient methodologies, this work aims to show a complete set of analytical tools that allow for the simplification and accurate dynamic characterization of large complex finite element models as an alternative to current approaches involving nonlinear simulation of computationally expensive detailed models of structural systems.