How Adaptively Constructed Reduced Order Models Can Benefit Sampling-Based Methodsfor Reliability Analyses

2016 ◽  
Vol 23 (05) ◽  
pp. 1650019 ◽  
Author(s):  
Christian Gogu ◽  
Anirban Chaudhuri ◽  
Christian Bes
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Reliability Analysis ◽  
Computational Cost ◽  
Reduced Order Modeling ◽  
Finite Element Models ◽  
Reduced Order Models ◽  
Reduced Basis ◽  
Reduced Order ◽  
Separable Monte Carlo

Many sampling-based approaches are currently available for calculating the reliability of a design. The most efficient methods can achieve reductions in the computational cost by one to several orders of magnitude compared to the basic Monte Carlo method. This paper is specifically targeted at sampling-based approaches for reliability analysis, in which the samples represent calls to expensive finite element models. The aim of this paper is to illustrate how these methods can further benefit from reduced order modeling to achieve drastic additional computational cost reductions, in cases where the reliability analysis is carried out on finite element models. Standard Monte Carlo, importance sampling, separable Monte Carlo and a combined importance separable Monte Carlo approach are presented and coupled with reduced order modeling. An adaptive construction of the reduced basis models is proposed. The various approaches are compared on a thermal reliability design problem, where the coupling with the adaptively constructed reduced order models is shown to further increase the computational efficiency by up to a factor of six.

scholarly journals Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks—Part II: Application

2000 ◽  
Vol 123 (1) ◽  
pp. 100-108 ◽  
Author(s):  
R. Bladh ◽  
M. P. Castanier ◽  
C. Pierre
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Theoretical Models ◽  
Companion Paper ◽  
Reduced Order Modeling ◽  
Bladed Disks ◽  
Reduced Order ◽  
Component Interface ◽  
Forced Responses

In this paper, the component-mode-based methods formulated in the companion paper (Part I: Theoretical Models) are applied to the dynamic analysis of two example finite element models of bladed disks. Free and forced responses for both tuned and mistuned rotors are considered. Comprehensive comparisons are made among the techniques using full system finite element solutions as a benchmark. The accurate capture of eigenfrequency veering regions is of critical importance for obtaining high-fidelity predictions of the rotor’s sensitivity to mistuning. Therefore, particular attention is devoted to this subject. It is shown that the Craig–Bampton component mode synthesis (CMS) technique is robust and yields highly reliable results. However, this is achieved at considerable computational cost due to the retained component interface degrees of freedom. It is demonstrated that this problem is alleviated by a secondary modal analysis reduction technique (SMART). In addition, a non-CMS mistuning projection method is considered. Although this method is elegant and accurate, it is seen that it lacks the versatility and efficiency of the CMS-based SMART. Overall, this work shows that significant improvements on the accuracy and efficiency of current reduced order modeling methods are possible.

Reduced Order Models of Mistuned Cracked Bladed Disks

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Olguta Marinescu ◽  
Bogdan I. Epureanu ◽  
Mihaela Banu
Keyword(s):  
Finite Element ◽  
Effective Means ◽  
Structural Response ◽  
Element Model ◽  
Reduced Order Modeling ◽  
Reduced Order Models ◽  
Bladed Disks ◽  
Reduced Order ◽  
Modeling Methodology ◽  
Relative Coordinates

Predicting the influence of cracks on the dynamics of bladed disks is a very important challenge. Cracks change the structural response, which in turn changes the crack propagation characteristics. Hence, accurate and computationally effective means to model the dynamics of cracked bladed disks and blisks is particularly crucial in applications such as prognosis, guidance for repairs, characterization after repairs, design, and structural health monitoring. Most current models of bladed disks exploit cyclic symmetry to gain computational efficiency. However, the presence of cracks and mistuning destroys that symmetry and makes computational predictions much more expensive. In this work, we propose a new reduced order modeling methodology that can speed up computations by several orders of magnitude. There are two key components of the new methodology. First, the displacements and deformations of the crack surfaces are not modeled in absolute coordinates but relative coordinates, which allows for an effective model reduction based on (fixed-interface Craig–Bampton) component mode synthesis (CMS). The use of relative coordinates allows one to define one of the components in CMS as the pristine/uncracked structure (with mistuning). This approach is used in combination with a set of accurate approximations for the constraint modes used in CMS. Second, the effects of mistuning are captured by component mode mistuning, which allows the construction of extremely efficient reduced order models for the pristine/uncracked component with mistuning. The novel proposed method is applied to a finite element model of an industrial blisk. The combined presence of mistuning and cracks is shown to have important effects. Also, the proposed approach is shown to provide accurate predictions for the overall blisk while requiring computations using single-sector models only. The influence of various parameters on the accuracy of the reduced order models is investigated. Overall, the results show a very good agreement between full finite element analyses and the proposed reduced order modeling approach.

Reduced-Order Models of Mistuned Cracked Bladed Disks

2010 ◽  
Author(s):  
Olguta Marinescu ◽  
Bogdan I. Epureanu ◽  
Mihaela Banu
Keyword(s):  
Finite Element ◽  
Effective Means ◽  
Structural Response ◽  
Element Model ◽  
Reduced Order Modeling ◽  
Reduced Order Models ◽  
Bladed Disks ◽  
Reduced Order ◽  
Modeling Methodology ◽  
Relative Coordinates

Predicting the influence of cracks on the dynamics of bladed disks is a very important challenge. Cracks change the structural response, which in turn changes the crack propagation characteristics. Hence, accurate and computationally effective means to model the dynamics of cracked bladed disks and blisks is particularly crucial in applications such as prognosis, guidance for repairs, characterization after repairs, design, and structural health monitoring. Most current models of bladed disks exploit cyclic symmetry to gain computational efficiency. However, the presence of cracks and mistuning destroys that symmetry and makes computational predictions much more expensive. In this work, we propose a new reduced order modeling methodology which can speed up computations by several orders of magnitude. There are two key components of the new methodology. First, the displacements and deformations of the crack surfaces are not modeled in absolute coordinates but relative coordinates. That allows for an effective model reduction based on (fixed-interface Craig-Bampton) component mode synthesis (CMS). The use of relative coordinates allows one to define one of the components in CMS as the pristine/uncracked structure (with mistuning). This approach is used in combination with a set of accurate approximations for the constraint modes used in CMS. Second, the effects of mistuning are captured by component mode mistuning (CMM) which allows the construction of extremely efficient reduced order models for the pristine/uncracked component with mistuning. The novel proposed method is applied to a finite element model of an industrial blisk. The combined presence of mistuning and cracks is shown to have important effects. Also, the proposed approach is shown to provide accurate predictions for the overall blisk while requiring computations using single-sector models only. The influence of various parameters on the accuracy of the reduced order models is investigated. Overall, the results show a very good agreement between full finite element analyses and the proposed reduced order modeling approach.

scholarly journals A Computational Approach to Model Interfacial Effects on the Mechanical Behavior of Knitted Textiles

2018 ◽  
Vol 85 (4) ◽  
Author(s):  
Dani Liu ◽  
Bahareh Shakibajahromi ◽  
Genevieve Dion ◽  
David Breen ◽  
Antonios Kontsos
Keyword(s):  
Finite Element ◽  
Mechanical Behavior ◽  
Mechanical Performance ◽  
Computational Cost ◽  
Three Dimensional ◽  
Finite Element Models ◽  
Element Analysis ◽  
Reduced Order ◽  
Interfacial Effects ◽  
Relative Contribution

The mechanical behavior of knitted textiles is simulated using finite element analysis (FEA). Given the strong coupling between geometrical and physical aspects that affect the behavior of this type of engineering materials, there are several challenges associated with the development of computational tools capable of enabling physics-based predictions, while keeping the associated computational cost appropriate for use within design optimization processes. In this context, this paper investigates the relative contribution of a number of computational factors to both local and global mechanical behavior of knitted textiles. Specifically, different yarn-to-yarn interaction definitions in three-dimensional (3D) finite element models are compared to explore their relative influence on kinematic features of knitted textiles' mechanical behavior. The relative motion between yarns identified by direct numerical simulations (DNS) is then used to construct reduced order models (ROMs), which are shown to be computationally more efficient and providing comparable predictions of the mechanical performance of knitted textiles that include interfacial effects between yarns.

Evaluation of the Reduced Order Models for Thermoelastodynamic Response of Geometrically Nonlinear Finite Element Models

PAMM ◽  
2018 ◽  
Vol 18 (1) ◽  
Author(s):  
Morteza Karamooz Mahdiabadi ◽  
Francesco De Crescenzo ◽  
Christian H. Meyer ◽  
Daniel J. Rixen
Keyword(s):  
Finite Element ◽  
Nonlinear Finite Element ◽  
Finite Element Models ◽  
Geometrically Nonlinear ◽  
Reduced Order Models ◽  
Reduced Order

Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks: Part II — Application

2000 ◽  
Author(s):  
Ronnie Bladh ◽  
Matthew P. Castanier ◽  
Christophe Pierre
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Theoretical Models ◽  
Companion Paper ◽  
Reduced Order Modeling ◽  
Bladed Disks ◽  
Reduced Order ◽  
Component Interface ◽  
Forced Responses

In this paper, the component-mode-based methods formulated in the companion paper (Part I: Theoretical Models) are applied to the dynamic analysis of two example finite element models of bladed disks. Free and forced responses for both tuned and mistuned rotors are considered. Comprehensive comparisons are made among the techniques using full system finite element solutions as a benchmark. The accurate capture of eigenfrequency veering regions is of critical importance for obtaining high-fidelity predictions of the rotor’s sensitivity to mistuning. Therefore, particular attention is devoted to this subject. It is shown that the Craig-Bampton component mode synthesis (CMS) technique is robust and yields highly reliable results. However, this is achieved at considerable computational cost due to the retained component interface degrees of freedom (DOF). It is demonstrated that this problem is alleviated by a secondary modal analysis reduction technique (SMART). In addition, a non-CMS mistuning projection method is considered. Although this method is elegant and accurate, it is seen that it lacks the versatility and efficiency of the CMS-based SMART. Overall, this work shows that significant improvements on the accuracy and efficiency of current reduced order modeling methods are possible.

scholarly journals Shape Finding in Structural Optimization with Parametrically Reduced Finite Element Models

2018 ◽  
Author(s):  
Benjamin Fröhlich ◽  
Peter Eberhard
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Structural Optimization ◽  
Shape Optimization ◽  
Projection Methods ◽  
Design Parameters ◽  
Finite Element Models ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Parameterized Systems

In structural mechanics, shape optimization is one way to improve mechanical properties of the structure. Typical objectives are to minimize displacements or to minimize stresses. In this context, it is desirable to conduct optimizations with parameterized, reduced order models. However, commercial finite element codes do not provide parameterized system matrices for a geometrical parameterization making an application of PMOR challenging. Therefore, a geometrically parameterized solid finite element is derived which can be formulated with respect to global design parameters. This leads to an affine representation of the system matrices. This allows an efficient application of interpolatory projection methods for parameterized systems. The approach is demonstrated with a numerical example where the proposed approach shows a significant speedup.

scholarly journals Nonintrusive Nonlinear Reduced Order Models for Structures in Large Deformations: Validations to Atypical Structures and Basis Construction Aspects

Vibration ◽  
2022 ◽  
Vol 5 (1) ◽  
pp. 20-58
Author(s):  
Xiaoquan Wang ◽  
Ricardo A. Perez ◽  
Bret Wainwright ◽  
Yuting Wang ◽  
Marc P. Mignolet
Keyword(s):  
Finite Element ◽  
Large Deformations ◽  
Dynamic Responses ◽  
Finite Element Models ◽  
Vibration Modes ◽  
Reduced Order Models ◽  
Linear Vibration ◽  
Reduced Order ◽  
Basis Construction ◽  
Nonlinear Geometric

The focus of this investigation is on reduced order models (ROMs) of the nonlinear geometric response of structures that are built nonintrusively, i.e., from standard outputs of commercial finite element codes. Several structures with atypical loading, boundary conditions, or geometry are considered to not only support the broad applicability of these ROMs but also to exemplify the different steps involved in determining an appropriate basis for the response. This basis is formed here as a combination of linear vibration modes and dual modes, and some of the steps involved follow prior work; others are novel aspects, all of which are covered in significant detail to minimize the expertise needed to develop these ROMs. The comparisons of the static and dynamic responses of these structures predicted by the ROMs and by the underlying finite element models demonstrate the high accuracy that can be achieved with the ROMs, even in the presence of significant nonlinearity.

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