A Proposal of Multi-Dimensional Modal Reduction for Nonlinear Dynamic Simulations
Simulations of nonlinear mechanical systems have always been a challenge due to their computational cost: even though techniques able to reduce simulations cost have been deeply studied in the last decades, this is still an open field of research. Methods used to reduce model size are known as model order reduction methods.
The approach here proposed is a model order reduction method named Multi-Phi; it is addressed to nonlinear mechanical systems that vary their configuration depending on one or more parameters. This method describes the nonlinear system time evolution through a series of linear ODEs, projecting the nonlinear system in the configurations space. Linear modal analysis is used to reduce separately each linear system, allowing retaining of physical properties, as long as the elasticity hypothesis is respected.
In this paper the method is presented and details about its implementation are provided, specifying how interactions between linear systems are faced. Two simple examples of its application are provided, highlighting the potential of this method to deal with nonlinear systems in a simple and intuitive way and showing its perspectives in terms of computational time reduction. As conclusions, considerations about the capabilities of this method are discussed and future steps are proposed.
KeywordsMulti-Phi Modal analysis Model order reduction Nonlinear dynamics Computational mechanics
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