Model Order Reduction of Nonlinear Systems

Nonlinear mechanical systems are characterized by much richer and complex responses than their linearized counterparts. In several research and industrial applications, such responses can be obtained by computationally intensive numerical solutions of finely discretized models. The related memory and time requirements significantly hinder analysis, design, and optimization. In this context, model order reduction techniques enable the aforementioned activities by constructing low-order approximations of the underlying high-fidelity model. Then, the time required for the numerical solution of the reduced order model is typically orders of magnitudes smaller than the one associated to the solution of the corresponding high-fidelity model. If real-time simulations are possible, the obtained reduced models can even support structural health monitoring, and can model predictive control as well. 

Nonlinearities affecting mechanical systems are of different types, namely geometrical, material, contact/friction, interaction with other fields, and possibly combinations of all of these. Often, model order reduction techniques reflect the type of nonlinearity they are addressing, and dedicated, model-driven methods that do not require expensive high-fidelity solutions—and their statistical processing—can be developed. This is in contrast with data-triven techniques, which extensively rely on full order solutions to construct reduced-order models that span the parameter space of interest.

The goal of this Special Issue is to collect key contributions in the large area of reduced order models for nonlinear mechanical systems, with special emphasis on structural dynamics.

We welcome contributions in the following, as well as related, areas:

• Intrusive and non-intrusive model reduction;
• Reduction over nonlinear manifolds;
• Hyper-reduction;
• Substructuring methods;
• Model reduction of nonlinear mechanical systems interacting with other fields (e.g., aerodynamics, heat, and electro-magnetic forces).

Dr. Paolo Tiso
Guest Editor

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• reduced order models
• reduction basis
• hyper-reduction
• non-intrusive reduction
• nonlinear manifolds
• substructuring