Finite element-based model order reduction for nonlinear structural dynamics

Extensive computational resources are required to solve large-scale nonlinear problems having a finite element mesh with a large number of degrees of freedom (DOFs). Model order reduction (MOR) is a technique used to reduce these DOFs, facilitating a faster solution with reasonable accuracy. This work proposes a method for constructing a finite...

Modal derivatives based reduced-order modelling in parametrically driven structures and frequency dividers

The application of Modal Derivatives (MDs) in conventional reduction methods is an effective method to capture geometric nonlinearities in Finite Element Models (FEMs). Reduction methods, in general, are used to effectively reduce the number of unknowns in FEMs for the sake of computational efficiency. We investigated the applicability of three...

A modal derivatives enhanced Rubin substructuring method for geometrically nonlinear multibody systems

This paper presents a novel model order reduction technique for 3D flexible multibody systems featuring nonlinear elastic behavior. We adopt the mean-axis floating frame approach in combination with an enhanced Rubin substructuring technique for the construction of the reduction basis. The standard Rubin reduction basis is augmented with the...

Model order reduction and substructuring methods for nonlinear structural dynamics

Dynamic analysis of large-size finite element models has been commonly applied by mechanical engineers to simulate the dynamic behavior of complex structures. The ever-increasing demand for both detailed and accurate simulation of complex structures forces mechanical engineers to pursue a balance between two conflicting goals during the...

Nonlinear model order reduction for flexible multibody dynamics: A modal derivatives approach

An effective reduction technique is presented for flexible multibody systems, for which the elastic deflection could not be considered small. We consider here the planar beam systems undergoing large elastic rotations, in the floating frame description. The proposed method enriches the classical linear reduction basis with modal derivatives...

Bridging the Gap Between Nonlinear Normal Modes and Modal Derivatives

Nonlinear Normal Modes (NNMs) have a clear conceptual relation to the classical linear normal modes (LNMs), yet they offer a solid theoretical framework for interpreting a wide class of non-linear dynamical phenomena with no linear counterpart. The main difficulty associating with NNMs is that the computation for real-size models is expensive,...

Modal Derivatives based Reduction Method for Finite Deflections in Floating Frame

Model order reduction techniques are widely applied in the floating frame of reference. The use of linear vibration modes, however, is not applicable when the elastic deformations become finite. In this paper, the non-linear elastic formulation, where the higher-order terms will be included in the strain energy expression to consider the bending...

Component Mode Synthesis for geometrically nonlinear structures

In the field of computational physics and engineering, the introduction of computers opened a world of possibilities. The finite element method was developed in order to solve complex problems numerically. Over time, the method matured and structures in the field of engineering became more and more complex, resulting in large degree of freedom...