On Dynamic Substructuring of Systems with Localised Nonlinearities

TL;DR

This paper explores the use of dynamic substructuring methods, particularly the Craig-Bampton technique, to efficiently simulate systems with localized nonlinearities, demonstrating a hybrid simulation approach that reduces computational costs.

Contribution

It introduces a hybrid simulation framework combining linear substructuring with nonlinear elements, extending traditional methods to better handle nonlinearities in large systems.

Findings

Hybrid simulation reduces computational time compared to full system models.

The Craig-Bampton method, when combined with nonlinear isolators, maintains accuracy.

Coupling via Lagrange multipliers effectively integrates linear and nonlinear domains.

Abstract

Dynamic substructuring (DS) methods encompass a range of techniques to decompose large structural systems into multiple coupled subsystems. This decomposition has the principle benefit of reducing computational time for dynamic simulation of the system. In this context, DS methods may form an essential component of hybrid simulation, wherein they can be used to couple physical and numerical substructures at reduced computational cost. Since most engineered systems are inherently nonlinear, particular potential lies in incorporating nonlinear methods in existing substructuring schemes which are largely linear methods. The most widely used and studied DS methods are classical linear techniques such as the Craig-Bampton (CB) method. However, as linear methods they naturally break down in the presence of nonlinearities. Recent advancements in substructuring have involved the development of enrichments to linear methods, which allow for some degree of nonlinearity to be captured. The use of mode shape derivatives has been shown to be able to capture geometrically non-linear effects as an extension to the CBmethod. Other candidates include the method of Finite Element Tearing and Interconnecting. In this work, a virtual hybrid simulation is presented in which a linear elastic vehicle frame supported on four nonlinear spring damper isolators is decomposed into separate domains. One domain consisting of the finite element model of the vehicle frame, which is reduced using the CB method. The second domain consists of the nonlinear isolators whose restoring forces are characterised by nonlinear spring and damper forces. Coupling between the models is carried out using a Lagrange multiplier method and time series simulations of the system are conducted and compared to the full global system with regards to simulation time and accuracy.