scholarly journals Reduced-Order Modelling and Homogenisation in Magneto-Mechanics: A Numerical Comparison of Established Hyper-Reduction Methods

2019 ◽  
Vol 24 (1) ◽  
pp. 20 ◽  
Author(s):  
Benjamin Brands ◽  
Denis Davydov ◽  
Julia Mergheim ◽  
Paul Steinmann
Keyword(s):  
Interpolation Method ◽  
Computational Effort ◽  
Numerical Comparison ◽  
Engineering Structures ◽  
Reduced Models ◽  
Micro Scale ◽  
Reduction Methods ◽  
Computational Homogenisation ◽  
Reduced Integration Domain ◽  
Gappy Pod

The simulation of complex engineering structures built from magneto-rheological elastomers is a computationally challenging task. Using the FE 2 method, which is based on computational homogenisation, leads to the repetitive solution of micro-scale FE problems, causing excessive computational effort. In this paper, the micro-scale FE problems are replaced by POD reduced models of comparable accuracy. As these models do not deliver the required reductions in computational effort, they are combined with hyper-reduction methods like the Discrete Empirical Interpolation Method (DEIM), Gappy POD, Gauss–Newton Approximated Tensors (GNAT), Empirical Cubature (EC) and Reduced Integration Domain (RID). The goal of this work is the comparison of the aforementioned hyper-reduction techniques focusing on accuracy and robustness. For the application in the FE 2 framework, EC and RID are favourable due to their robustness, whereas Gappy POD rendered both the most accurate and efficient reduced models. The well-known DEIM is discarded for this application as it suffers from serious robustness deficiencies.

Comparison between maintenance policies based on q-Weibull and Weibull models

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Edilson Machado de Assis ◽  
Celso Luiz Santiago Figueirôa Filho ◽  
Gabriel Costa Lima ◽  
Gisele Maria de Oliveira Salles ◽  
Ailton Pinto
Keyword(s):  
Weibull Distribution ◽  
Preventive Maintenance ◽  
Weibull Model ◽  
Computational Effort ◽  
Numerical Comparison ◽  
Content Type ◽  
Optimal Interval ◽  
Maintenance Cycle ◽  
Weibull Models ◽  
Maintenance Policies

PurposeThe purpose of this article is to compare maintenance policies based on Weibull and q-Weibull models.Design/methodology/approachThis paper uses analytical developments, several figures and tables for graphical and numerical comparison. Previously published hydropower equipment data are used as examples.FindingsModels for optimal maintenance interval determination based on q-Weibull distribution were defined. Closed-form expressions were found, and this allows the application of the method with small computational effort.Practical implicationsThe use of the q-Weibull model to guide the definition of maintenance strategy allows decision-making to be more consistent with sample data. The flexibility of the q-Weibull model is able to produce failure rate modeling with five different formats: decreasing, constant, increasing, unimodal and U-shaped. In this way, the maintenance strategies resulting from this model should be more assertive.Originality/valueExpressions for determining the optimal interval of preventive maintenance were deduced from q-Weibull distribution. Expected costs per maintenance cycle of Brazilian hydropower equipment were calculated with q-Weibull and Weibull distributions. These results were compared in terms of absolute values and trends. Although a large number of works on corrective and preventive maintenance have been proposed, no applications of the q-Weibull distribution were found in literature.

Numerical comparison of robustness of some reduction methods in rough grids

2014 ◽  
Vol 30 (5) ◽  
pp. 1484-1506 ◽  
Author(s):  
Jiangyong Hou ◽  
Shuyu Sun ◽  
Zhangxin Chen
Keyword(s):  
Numerical Comparison ◽  
Reduction Methods

scholarly journals Comparison of structural model reduction methods applied to a large-deformation wing box

2021 ◽  
pp. 1-23
Author(s):  
R.R. Medeiros ◽  
C.E.S. Cesnik ◽  
O. Stodieck ◽  
D.E. Calderon ◽  
J.E. Cooper ◽  
...  
Keyword(s):  
Finite Element ◽  
Structural Model ◽  
Structural Response ◽  
Order Reduction ◽  
Element Model ◽  
Computational Effort ◽  
Beam Model ◽  
Wing Structures ◽  
Reduction Methods ◽  
Geometrical Effects

Abstract In this paper, the accuracy and practical capabilities of three different reduced-order models (ROMs) are explored: an enhanced implicit condensation and expansion (EnICE) model, a finite element beam model, and a finite volume beam model are compared for their capability to accurately predict the nonlinear structural response of geometrically nonlinear built-up wing structures. This work briefly outlines the different order reduction methods, highlighting the associated assumptions and computational effort. The ROMs are then used to calculate the wing deflection for different representative load cases and these results are compared with the global finite element model (GFEM) predictions when possible. Overall, the ROMs are found to be able to capture the nonlinear GFEM behaviour accurately, but differences are noticed at very large displacements and rotations due to local geometrical effects.

scholarly journals MODEL REDUCTION METHODS APPLIED TO A NONLINEAR MECHANICAL SYSTEM

2019 ◽  
Vol 7 (7) ◽  
pp. 281-300
Author(s):  
Romes Antonio Borges ◽  
Daniel Gonçalves ◽  
Antônio Marcos De lima ◽  
Lázaro Fonseca Júnior
Keyword(s):  
Model Reduction ◽  
Point Of View ◽  
Time Saving ◽  
Computational Point ◽  
Reduced Models ◽  
Nonlinear Mechanical ◽  
Nonlinear Mechanical System ◽  
Reduction Methods ◽  
The Stability ◽  
High Flexibility

Modern structures of high flexibility are subject to physical or geometricnonlinearities, and reliable numerical modeling to predict their behavior is essential.The modeling of these systems can be given by the discretization of the problem usingthe Finite Element Method (FEM), however by using this methodology, it is a veryrobust model from the computational point of view, making the simulation processdifficult. Using reduced models has been an excellent alternative to minimizing thisproblem. Most model reduction methods are restricted to linear problems, whichmotivated us to maximize the efficiency of these methods considering nonlinearproblems. For better accuracy, in this study, adaptations and improvements aresuggested in reduction methods such as the Enriched Modal Base (EMB), the SystemEquivalent Reduction Expansion Process (SEREP), QUASI-SEREP and the IteratedImproved Reduced System (IIRS). The stability of a system is discussed according tothe calculation of the Lyapunov exponents and phase space. Numerical simulationsshowed that the reduced models presented a good performance, according to thecommitment of quality and speed of responses (or time saving).

scholarly journals Vibration of carbon nanotubes with defects: order reduction methods

2018 ◽  
Vol 474 (2211) ◽  
pp. 20170555 ◽  
Author(s):  
Robert B. Hudson ◽  
Alok Sinha
Keyword(s):  
Carbon Nanotubes ◽  
Periodic Structures ◽  
Order Reduction ◽  
Domain Analysis ◽  
Computational Effort ◽  
Mode Shapes ◽  
Mode Localization ◽  
Reduction Techniques ◽  
Reduction Methods ◽  
The Impact

Order reduction methods are widely used to reduce computational effort when calculating the impact of defects on the vibrational properties of nearly periodic structures in engineering applications, such as a gas-turbine bladed disc. However, despite obvious similarities these techniques have not yet been adapted for use in analysing atomic structures with inevitable defects. Two order reduction techniques, modal domain analysis and modified modal domain analysis, are successfully used in this paper to examine the changes in vibrational frequencies, mode shapes and mode localization caused by defects in carbon nanotubes. The defects considered are isotope defects and Stone–Wales defects, though the methods described can be extended to other defects.

scholarly journals Performance Evaluation of Wave Input Reduction Techniques for Modeling Inter-Annual Sandbar Dynamics

2019 ◽  
Vol 7 (5) ◽  
pp. 148
Author(s):  
Bruna de Queiroz ◽  
Freek Scheel ◽  
Sofia Caires ◽  
Dirk-Jan Walstra ◽  
Derrick Olij ◽  
...  
Keyword(s):  
Performance Evaluation ◽  
Numerical Models ◽  
Wave Climate ◽  
Computational Effort ◽  
Brute Force ◽  
Reduction Techniques ◽  
Simulation Based ◽  
Comprehensive Performance ◽  
Reduction Methods

In process-based numerical models, reducing the amount of input parameters, known as input reduction (IR), is often required to reduce the computational effort of these models and to enable long-term, ensemble predictions. Currently, a comprehensive performance assessment of IR-methods is lacking, which hampers guidance on selecting suitable methods and settings in practice. In this study, we investigated the performance of 10 IR-methods and 36 subvariants for wave climate reduction to model the inter-annual evolution of nearshore bars. The performance of reduced wave climates is evaluated by means of a brute force simulation based on the full climate. Additionally, we tested how the performance is affected by the number of wave conditions, sequencing, and duration of the reduced wave climate. We found that the Sediment Transport Bins method is the most promising method. Furthermore, we found that the resolution in directional space is more important for the performance than the resolution in wave height. The results show that a reduced wave climate with fewer conditions applied on a smaller timescale performs better in terms of morphology than a climate with more conditions applied on a longer timescale. The findings of this study can be applied as initial guidelines for selecting input reduction methods at other locations, in other models, or for other domains.

Quantification of Vibration Localization in Periodic Structures

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
A. Chandrashaker ◽  
S. Adhikari ◽  
M. I. Friswell
Keyword(s):  
Complex Geometry ◽  
Periodic Structures ◽  
Random Noise ◽  
Computational Effort ◽  
Mode Shapes ◽  
Engineering Structures ◽  
Modal Assurance Criterion ◽  
Mode Localization ◽  
Modal Data ◽  
Wide Range

The phenomenon of vibration mode localization in periodic and near periodic structures has been well documented over the past four decades. In spite of its long history, and presence in a wide range of engineering structures, the approach to detect mode localization remains rather rudimentary in nature. The primary way is via a visual inspection of the mode shapes. For systems with complex geometry, the judgment of mode localization can become subjective as it would depend on visual ability and interpretation of the analyst. This paper suggests a numerical approach using the modal data to quantify mode localization by utilizing the modal assurance criterion (MAC) across all the modes due to changes in some system parameters. The proposed MAC localization factor (MACLF) gives a value between 0 and 1 and therefore gives an explicit value for the degree of mode localization. First-order sensitivity based approaches are proposed to reduce the computational effort. A two-degree-of-freedom system is first used to demonstrate the applicability of the proposed approach. The finite element method (FEM) was used to study two progressively complex systems, namely, a coupled two-cantilever beam system and an idealized turbine blade. Modal data is corrupted by random noise to simulate robustness when applying the MACLF to experimental data to quantify the degree of localization. Extensive numerical results have been given to illustrate the applicability of the proposed approach.

A Comparison of Data-Reduction Methods for a Seven-Hole Probe

2002 ◽  
Vol 124 (2) ◽  
pp. 523-527 ◽  
Author(s):  
David Sumner
Keyword(s):  
Data Reduction ◽  
Reduction Method ◽  
Interpolation Method ◽  
Low Flow ◽  
Leeward Side ◽  
Pressure Probe ◽  
Calibration Data ◽  
Grid Spacing ◽  
Reduction Methods ◽  
Data Reduction Method

Two data-reduction methods were compared for the calibration of a seven-hole conical pressure probe in incompressible flow. The polynomial curve-fit method of Gallington and the direct-interpolation method of Zilliac were applied to the same set of calibration data, for a range of calibration grid spacings. The results showed that the choice of data-reduction method and the choice of calibration grid spacing each have an influence on the measurement uncertainty. At high flow angles, greater than 30 deg, where flow may separate from the leeward side of the probe, the direct-interpolation method was preferable. At low flow angles, less than 30 deg, where flow remains attached about the probe, neither data-reduction method had any advantage. For both methods, a calibration grid with a maximum interval of 10 deg was recommended. The Reynolds-number sensitivity of the probe began at Re=5000, based on probe diameter, and was independent of the data-reduction method or calibration grid spacing.

Ab initio band theory approach to electron energy loss near edge structures

1988 ◽  
Vol 46 ◽  
pp. 506-507
Author(s):  
Xudong Weng ◽  
O.F. Sankey ◽  
Peter Rez
Keyword(s):  
Ab Initio ◽  
Local Density ◽  
Interpolation Method ◽  
Atomic Orbital ◽  
Plane Waves ◽  
Large Set ◽  
Theory Approach ◽  
Band Theory ◽  
Atomic Orbitals ◽  
Pseudopotential Calculations

Single electron band structure techniques have been applied successfully to the interpretation of the near edge structures of metals and other materials. Among various band theories, the linear combination of atomic orbital (LCAO) method is especially simple and interpretable. The commonly used empirical LCAO method is mainly an interpolation method, where the energies and wave functions of atomic orbitals are adjusted in order to fit experimental or more accurately determined electron states. To achieve better accuracy, the size of calculation has to be expanded, for example, to include excited states and more-distant-neighboring atoms. This tends to sacrifice the simplicity and interpretability of the method.In this paper. we adopt an ab initio scheme which incorporates the conceptual advantage of the LCAO method with the accuracy of ab initio pseudopotential calculations. The so called pscudo-atomic-orbitals (PAO's), computed from a free atom within the local-density approximation and the pseudopotential approximation, are used as the basis of expansion, replacing the usually very large set of plane waves in the conventional pseudopotential method. These PAO's however, do not consist of a rigorously complete set of orthonormal states.

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