scholarly journals Simulation-Free Hyper-Reduction for Geometrically Nonlinear Structural Dynamics: A Quadratic Manifold Lifting Approach

2018 ◽  
Vol 13 (7) ◽  
Author(s):  
Shobhit Jain ◽  
Paolo Tiso
Keyword(s):  
Structural Dynamics ◽  
Direct Methods ◽  
Cost Effective ◽  
Reduced Order Model ◽  
Geometrically Nonlinear ◽  
Order Model ◽  
Reduced Order ◽  
Manual Selection ◽  
Modal Derivatives ◽  
Dynamics Problems

We present an efficient method to significantly reduce the offline cost associated with the construction of training sets for hyper-reduction of geometrically nonlinear, finite element (FE)-discretized structural dynamics problems. The reduced-order model is obtained by projecting the governing equation onto a basis formed by vibration modes (VMs) and corresponding modal derivatives (MDs), thus avoiding cumbersome manual selection of high-frequency modes to represent nonlinear coupling effects. Cost-effective hyper-reduction is then achieved by lifting inexpensive linear modal transient analysis to a quadratic manifold (QM), constructed with dominant modes and related MDs. The training forces are then computed from the thus-obtained representative displacement sets. In this manner, the need of full simulations required by traditional, proper orthogonal decomposition (POD)-based projection and training is completely avoided. In addition to significantly reducing the offline cost, this technique selects a smaller hyper-reduced mesh as compared to POD-based training and therefore leads to larger online speedups, as well. The proposed method constitutes a solid alternative to direct methods for the construction of the reduced-order model, which suffer from either high intrusiveness into the FE code or expensive offline nonlinear evaluations for the determination of the nonlinear coefficients.

scholarly journals Stochastic Reduced-Order Model in Low-Frequency Dynamics in Presence of Numerous Local Elastic Modes

2011 ◽  
Vol 78 (6) ◽  
Author(s):  
C. Soize ◽  
A. Batou
Keyword(s):  
Structural Dynamics ◽  
Complex Structure ◽  
Probabilistic Approach ◽  
Low Frequency ◽  
Reduced Order Model ◽  
Frequency Range ◽  
Order Model ◽  
Reduced Order ◽  
Global Modes ◽  
Elastic Modes

This paper deals with the nonusual case in structural dynamics for which a complex structure exhibits both the usual global elastic modes and numerous local elastic modes in the low-frequency range. Despite the presence of these local elastic modes, we are interested in constructing a stochastic reduced-order model using only the global modes and in taking into account the local elastic modes with a probabilistic approach. In the first part, a formulation and an algorithm, which allow the “global elastic modes” and the “local elastic modes” to be calculated, are presented. The second part is devoted to the construction of the stochastic reduced-order model with the global elastic modes and in taking into account the uncertainties on the effects of the local elastic modes by the nonparametric probabilistic approach. Finally, an application, which validates the proposed theory is presented.

scholarly journals Geometrically nonlinear autonomous reduced order model for rotating structures

2018 ◽  
Author(s):  
Mikel Balmaseda ◽  
Georges Jacquet-Richardet ◽  
Antoine Placzek ◽  
Duc-Minh Tran
Keyword(s):  
Normal Modes ◽  
Harmonic Balance Method ◽  
Reduced Order Model ◽  
Static Equilibrium ◽  
Evaluation Procedure ◽  
Element Formulation ◽  
Geometrically Nonlinear ◽  
Reduced Basis ◽  
Order Model ◽  
Reduced Order

In the present work, as an extension to [2], an autonomous geometrically nonlinear reduced order model for the study of dynamic solutions of complex rotating structures is developed. In opposition to the classical finite element formulation for geometrically nonlinear rotating structures that considers small linear vibrations around the static equilibrium, nonlinear vibrations around the pre-stressed equilibrium are now considered. For that purpose, the linear normal modes are used as a reduced basis for the construction of the reduced order model. The stiffness evaluation procedure method (STEP) [4] is applied to compute the nonlinear forces induced by the displacements around the static equilibrium. This approach enhances the classical linearised small perturbations hypothesis to the cases of large displacements around the static pre-stressed equilibrium. Furthermore, a comparison between the steady solution given by HHT-α [1] and the Harmonic Balance Method (HBM) [3] is carried out. The proposed reduced order models are evaluated for a rotating beam case study.

Model Order Reduction of Transmission Line Model

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Transmission Line ◽  
Large Scale ◽  
Original System ◽  
Reduced Order Model ◽  
Benchmark Problems ◽  
Transmission Line Model ◽  
Order Model ◽  
Line Model ◽  
Reduced Order ◽  
Numerical Effort

Transmission Line model are an important role in the electrical power supply. Modeling of such system remains a challenge for simulations are necessary for designing and controlling modern power systems.In order to analyze the numerical approach for a benchmark collection Comprehensive of some needful real-world examples, which can be utilized to evaluate and compare mathematical approaches for model reduction. The approach is based on retaining the dominant modes of the system and truncation comparatively the less significant once.as the reduced order model has been derived from retaining the dominate modes of the large-scale stable system, the reduction preserves the stability. The strong demerit of the many MOR methods is that, the steady state values of the reduced order model does not match with the higher order systems. This drawback has been try to eliminated through the Different MOR method using sssMOR tools. This makes it possible for a new assessment of the error system Offered that the Observability Gramian of the original system has as soon as been thought about, an H∞ and H2 error bound can be calculated with minimal numerical effort for any minimized model attributable to The reduced order model (ROM) of a large-scale dynamical system is essential to effortlessness the study of the system utilizing approximation Algorithms. The response evaluation is considered in terms of response constraints and graphical assessments. the application of Approximation methods is offered for arising ROM of the large-scale LTI systems which consist of benchmark problems. The time response of approximated system, assessed by the proposed method, is also shown which is excellent matching of the response of original system when compared to the response of other existing approaches .

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