Efficient stochastic structural analysis using Guyan reduction

Panayirci, H. Murat; Pradlwarter, H. J.; Schuëller, Gerhart I.

doi:10.1016/j.advengsoft.2011.02.004

Cited by 18 publications

(5 citation statements)

References 34 publications

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“…Ongoing research will focus on several axes of development. In particular, an implementation using the same framework suited for nonlinear problems, but with a Galerkin-type SFE approach, similar to the work described in [14] would be most interesting. In fact, as the proposed implementation uses stochastic collocation, it is mostly usable for problems with large number d of DOFs in the mechanical system and small number of r.v.s n. To build a p-order metamodel on such a system, the single stochastic collocation would require (in the linear case) (p+1) n solutions of linear systems of size d, for a total complexity in O (p + 1) n d 2 .…”

Section: Discussionmentioning

confidence: 99%

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Condensed SFEs for nonlinear mechanical problems

Llau

Baroth

Jason

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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International audienceThis paper introduces a coupled approach between stochastic finite element methods and an adaptive condensation technique for the analysis of nonlinear mechanical problems under uncertainties. This coupling reduces the size of each individual nonlinear problem solved in SFE by the use of an adaptive condensation method. The reduced stiffnesses and other quantities necessary for the condensation technique are approximated using a second, low-order, polynomial expansion, thus taking advantage of the coupling with SFE. This approach also features a semi-analytical technique to compute accurately distributions of structural quantities of interest. This method is applied on an elasto-plastic steel bar with a small defect, and on a damaged beam under 4-point bending. In both cases it predicts the random behavior of the structure quite accurately, and is able to provide higher-order models than a state-of-the-art stochastic collocation method, for a reduced computation time

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Section: Discussionmentioning

confidence: 99%

“…This work presents a coupled method to solve nonlinear SFE problems at a reduced cost. It includes a deterministic system reduction approach similar to those in [13] (using dynamic condensation) or in [14] (using static condensation). However, the presented method :…”

Section: Introductionmentioning

confidence: 99%

Condensed SFEs for nonlinear mechanical problems

Llau

Baroth

Jason

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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“…This has also given rise to the application of the P-C method on structures of engineering practice, which might contain a substantial number of random parameters (see e.g. [28] ).…”

Section: Efficient Implementations and Strategies For Stochastic Analmentioning

confidence: 99%

General purpose software for efficient uncertainty management of large finite element models

Patelli

Panayirci

Broggi

et al. 2012

Finite Elements in Analysis and Design

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The aim of this paper is to demonstrate that stochastic analyses can be performed on large and complex models within affordable costs. Stochastic analyses offer a much more realistic approach for analysis and design of components and systems although generally computationally demanding. Hence, resorting to efficient approaches and high performance computing is required in order to reduce the execution time.A general purpose software that provides an integration between deterministic solvers (i.e. finite element solvers), efficient algorithms for uncertainty management and high performance computing is presented. The software is intended for a wide range of applications, which includes optimization analysis, life-cycle management, reliability and risk analysis, fatigue and fractures simulation, robust design.The applicability of the proposed tools for practical applications is demonstrated by means of a number of case studies of industrial interest involving detailed models.

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“…Applying this technique to a substructure allows to replace its model by a linearized model and focuses the computational effort on other substructures [19]. Possible applications include fluid mechanics, shape optimization, nuclear structure dynamic analysis [20], and stochastic structural simulation with finite elements [21]. However, those methods require previous knowledge on the localization of nonlinearities (and specifically the cracks in concrete) and are unable to detect the appearance of new cracks out of the zoomed areas.…”

Section: Introductionmentioning

confidence: 98%

Adaptive zooming method for the analysis of large structures with localized nonlinearities

Llau

Jason

Dufour

et al. 2015

Finite Elements in Analysis and Design

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a b s t r a c tSimulating concrete cracking requires nonlinear modeling applied on a refined mesh if a correct evaluation of crack properties needs to be achieved. Therefore, it is rather costly and even sometimes impossible when large reinforced concrete structures are considered. Alternative solutions have therefore to be proposed. This contribution presents a structural zooming method for the simulation of large reinforced concrete structures with localized nonlinearities. Our method is based on static condensation (Guyan [1]) and provides an adaptive framework for performance-oriented use of this method in nonlinear simulations. In particular, it only simulates the behavior of nonlinear interesting zones (detected by adapted criteria). The areas where refined modeling is not required are replaced by their equivalent stiffnesses. The linearity criteria, depending on the chosen mechanical models, are also used to activate new interesting zones during the simulation. This method substantially decreases the computational cost on both presented test cases (a two-dimensional concrete beam and a threedimensional reinforced concrete building).

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Efficient stochastic structural analysis using Guyan reduction

Cited by 18 publications

References 34 publications

Condensed SFEs for nonlinear mechanical problems

Condensed SFEs for nonlinear mechanical problems

General purpose software for efficient uncertainty management of large finite element models

Adaptive zooming method for the analysis of large structures with localized nonlinearities

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