A Study on the Method of Structural Analysis with Uncertainty in Shape by Stochastic Finite Element Method

Chen, Xi; Kawamura, Yasumi; Okada, Tetsuo

doi:10.2534/jjasnaoe.22.187

Cited by 2 publications

(10 citation statements)

References 1 publication

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“…In general, the use of traditional SFEM to discuss uncertainty in shape is based on the FEA‐based point of view, ie, the SFEM is built from the analytical framework of the classic FEM . Thus, it inherits all the characteristics of FEA in terms of geometry and algebra.…”

Section: Formulation Of Siga For Uncertainty In Shapementioning

confidence: 99%

“…For instance, Honda proposed spectral stochastic boundary element method (SSBEM) based on the PCE and the K‐L expansion in order to analyze the problem of uncertainty in shape in the boundary. Chen et al presented a new method of structural analysis for the solution of response uncertainty problems in the cases involving uncertainty in shape. The proposed method includes a mathematical formulation, which is a natural extension of the deterministic finite element concept to the space of random functions by the Hermite PCE, in order to represent the uncertainty of shapes and the response surface.…”

Section: Introductionmentioning

confidence: 99%

“…The proposed method includes a mathematical formulation, which is a natural extension of the deterministic finite element concept to the space of random functions by the Hermite PCE, in order to represent the uncertainty of shapes and the response surface. Developments have been described in some key articles …”

Section: Introductionmentioning

confidence: 99%

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Development of stochastic isogeometric analysis (SIGA) method for uncertainty in shape

Zhang

Shibutani

2018

Numerical Meth Engineering

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In this paper, a new method is proposed that extend the classical deterministic isogeometric analysis (IGA) into a probabilistic analytical framework in order to evaluate the uncertainty in shape and aim to investigate a possible extension of IGA in the field of computational stochastic mechanics. Stochastic IGA (SIGA) method for uncertainty in shape is developed by employing the geometric characteristics of the non-uniform rational basis spline and the probability characteristics of polynomial chaos expansions (PCE). The proposed method can accurately and freely evaluate problems of uncertainty in shape caused by deformation of the structural model. Additionally, we use the intrusive formulation approach to incorporate PCE into the IGA framework, and the C++ programming language to implement this analysis procedure. To verify the validity and applicability of the proposed method, two numerical examples are presented. The validity and accuracy of the results are assessed by comparing them to the results obtained by Monte Carlo simulation based on the IGA algorithm. KEYWORDSisogeometric analysis, polynomial chaos expansions, stochastic isogeometric analysis, uncertainty in shape 18

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Section: Formulation Of Siga For Uncertainty In Shapementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Development of stochastic isogeometric analysis (SIGA) method for uncertainty in shape

Zhang

Shibutani

2018

Numerical Meth Engineering

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“…is following non-normal distribution, the n1 ( n2 ) can be derived by the approximation of the random variable using the method in [12,15]. Thus, ( )  A θ can be represented as follows.…”

Section: Statement Of the Stochastic Eigenvalue Problemmentioning

confidence: 99%

“…Recently, Honda [10] proposed stochastic boundary element method by using the PCE and a Karhunen-Loeve expansion method in which uncertainty of shape of boundary is assumed. Also, in recent years, the authors proposed SFEM based on response surface methodology considering uncertainty in shape of structures, where the validity and feasibility of the proposed method is demonstrated [11][12]. Thus SFEM are well developed for linear structured systems, but are less developed for the stochastic eigenvalue problem.…”

Section: Introductionmentioning

confidence: 99%

Solution of stochastic eigenvalue problem by improved stochastic inverse power method (I-SIPM)

2017

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Eigenvalue analysis is an important problem in a variety of fields. In structural mechanics in the field of naval architecture and ocean engineering, eigenvalue problems commonly appear in the context of, e.g. vibrations and buckling. In eigenvalue analysis, the physical characteristics are often considered as deterministic, such as mass, geometries, stiffness in the structures. However, in many practical cases, they are not deterministic. Such uncertainties may cause serious problems because the influence of the uncertainties is in general unknown. In order to solve the stochastic eigenvalue problem, in this article, we have proposed two methods. Firstly, the improved stochastic inverse power method (I-SIPM) based on response surface methodology is proposed. The method is different with previous stochastic inverse power method. The minimum eigenvalue and eigenvector of stochastic eigenvalue problems can be evaluated by using the proposed method. Secondly, the stochastic Wielandt deflation method (SWDM) is proposed which can realize to evaluate i th (i>1) eigenvalues and eigenvectors of stochastic eigenvalue problems. This is very important for solving natural mode and buckling mode analysis problem. Next, two example problems are investigated to show the validity of two new methods compared with a Monte-Carlo simulation, i.e. the vibration problem of a discrete 2-DOF system and the buckling problem of a continuous beam. Finally, the uncertainty estimation for the dynamic damper problem is discussed by using proposed method. The probability of the natural frequency falling into the range to be avoided is shown when the dynamic damper has a stochastic mass and stiffness. Keywords Improved stochastic inverse power method (I-SIPM)  Stochastic eigenvalue problem  Polynomial chaos expansion (PCE)  Stochastic Wielandt deflation method (SWDM)

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A Study on the Method of Structural Analysis with Uncertainty in Shape by Stochastic Finite Element Method

Cited by 2 publications

References 1 publication

Development of stochastic isogeometric analysis (SIGA) method for uncertainty in shape

Development of stochastic isogeometric analysis (SIGA) method for uncertainty in shape

Solution of stochastic eigenvalue problem by improved stochastic inverse power method (I-SIPM)

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