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30
Stochastic Reduced Basis Methods
, 2001
"... This paper introduces stochastic reduced basis methods for solving largescale linear random algebraic systems of equations, such as those obtained by discretizing linear stochastic partial dierential equations in space, time, and the random dimension. The fundamental idea employed here is to repr ..."
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Cited by 24 (2 self)
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This paper introduces stochastic reduced basis methods for solving largescale linear random algebraic systems of equations, such as those obtained by discretizing linear stochastic partial dierential equations in space, time, and the random dimension. The fundamental idea employed here is to represent the system response using a linear combination of stochastic basis vectors with undetermined deterministic coecients (or random functions). We present
PROGRESS IN STRUCTURAL DYNAMICS WITH STOCHASTIC PARAMETER VARIATIONS: 1987 to 1996
"... This paper is an update of an earlier paper by Ibrahim (1987) and is aimed at reviewing the papers published during the last decade in the area of vibration of structures with parameter uncertainties. Analytical, computational, and experimental studies conducted on probabilistic modeling of struct ..."
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Cited by 18 (3 self)
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This paper is an update of an earlier paper by Ibrahim (1987) and is aimed at reviewing the papers published during the last decade in the area of vibration of structures with parameter uncertainties. Analytical, computational, and experimental studies conducted on probabilistic modeling of structural uncertainties and free and forced vibration of stochastically defined systems are discussed. The review also covers developments in the areas of statistical modeling of high frequency vibrations and behavior of statistically disordered periodic systems. 1.
A suitable computational strategy for the parametric analysis of problems with multiple contact
"... with multiple contact ..."
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Hicroraechanics as a basis of continuum random fields
"... Many problems in solid and geomechanics require the concept of a mesocontinuum, which allows a resolution of stress and other dependent fields over scales not infinitely larger than the typical microscale. Passage from the microstructure to such a mesocontinuum is based on a scale dependent windo ..."
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Cited by 7 (5 self)
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Many problems in solid and geomechanics require the concept of a mesocontinuum, which allows a resolution of stress and other dependent fields over scales not infinitely larger than the typical microscale. Passage from the microstructure to such a mesocontinuum is based on a scale dependent window playing the role of a Representative Volume Element (RVE). It turns out that the material properties at the mesoscale cannot be uniquely approximated by a random field of stiffness with continuous realizations, but, rather, two random continuum fields, corresponding to essential and natural boundary conditions on RVE, need to be introduced to bound the material response from above and from below. In this paper Monte Carlo simulations are used to obtain the first and secondorder one and twopoint characteristics of these two random fields for random chessboards and matrixinclusion composites. Special focus is on the correlation functions describing the autocovariances and crosscovariances of effective random mesoscale conductivity tensor Q; and its dual Sjj. Following issues are investigated: i) scaledependence of noisetosignal ratios of various components of Cy and Sjj, ii) spatial structure of the correlation function, iii) uniform strain versus exact calculations in determination of the correlation function, iv) correlation structure of composites with inclusions without and with overlap. 1.
Langley: “Distribution of eigenvalues of linear stochastic systems
 Proceedings of the ninth International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP 9
, 2003
"... ABSTRACT: Dynamic characteristics of linear structural systems are governed by the natural frequencies and the modeshapes. In this paper the statistical properties of the eigenvalues of linear dynamic systems are considered. It is assumed that the mass and the stiffness matrices are smooth, continu ..."
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Cited by 6 (1 self)
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ABSTRACT: Dynamic characteristics of linear structural systems are governed by the natural frequencies and the modeshapes. In this paper the statistical properties of the eigenvalues of linear dynamic systems are considered. It is assumed that the mass and the stiffness matrices are smooth, continuous and at least twice differentiable functions of a random parameter vector. The random parameter vector is assumed to be standard Gaussian or can be transformed to standard Gaussian. Two approaches are proposed to obtain moments, cumulants and probability density functions of the eigenvalues. The first approach is based on a perturbation expansion of the eigenvalues about an optimal point which is best is some sense. This optimal point is obtained by using the concepts borrowed from structural reliability analysis. The second approach is based on asymptotic analysis. Moments of the eigenvalues are obtained by asymptotic expansion of a multidimensional integral involving the joint probability density function of the random variables. Based on theses methods, two simple expressions of the probability density functions of the eigenvalues are derived. A numerical example is given to compare the proposed methods with Monte Carlo simulations. 1
A Global Sensitivity Approach for the Dynamic Response of Printed Wiring Boards
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Stochastic finite element simulation of uncertain structures subjected to earthquake
"... In present study, the stochastic finite element simulation based on the efficient Neumann expansion technique is extended for the analysis of uncertain structures under seismically induced random ground motion. The basic objective is to investigate the possibility of applying the Neumann expansion ..."
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In present study, the stochastic finite element simulation based on the efficient Neumann expansion technique is extended for the analysis of uncertain structures under seismically induced random ground motion. The basic objective is to investigate the possibility of applying the Neumann expansion technique coupled with the Monte Carlo simulation for dynamic stochastic systems upto that extent of parameter variation after which the method is no longer gives accurate results compared to that of the direct Monte carlo simulation. The stochastic structural parameters are discretized by the local averaging method and then simulated by Cholesky decomposition of the respective covariance matrix. The earthquake induced ground motion is treated as stationary random process defined by respective power spectral density function. Finally, the finite element solution has been obtained in frequency domain utilizing the advantage of Neumann expansion technique.
Stochastic finite elements: where is the physics?
, 2011
"... The micromechanics based on the HillMandel condition indicates that the majority of stochastic finite element methods hinge on random field (RF) models of material properties (such as Hooke’s law) having no physical content, or even at odds with physics. At the same time, that condition allows one ..."
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The micromechanics based on the HillMandel condition indicates that the majority of stochastic finite element methods hinge on random field (RF) models of material properties (such as Hooke’s law) having no physical content, or even at odds with physics. At the same time, that condition allows one to set up the RFs of stiffness and compliance tensors in function of the mesoscale and actual random microstructure of the given material. The mesoscale is defined through a Statistical Volume Element (SVE), i.e. a material domain below the Representative Volume Element (RVE) level. The paper outlines a procedure for stochastic scaledependent homogenization leading to a determination of mesoscale onepoint and twopoint statistics and, thus, a construction of analytical RF models.
PROBABILISTIC ANALYSIS OF STATIC RESPONSE FOR TURBINE BLADE WITH PARAMETRIC UNCERTAINTY
"... ABSTRACT A probabilistic analysis method is developed for static response of the turbine blade with parametric uncertainty. The material, geometric parameters and loadings of blade exhibit notable random fluctuations, so the conventional deterministic analysis of blade can't provide complete i ..."
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ABSTRACT A probabilistic analysis method is developed for static response of the turbine blade with parametric uncertainty. The material, geometric parameters and loadings of blade exhibit notable random fluctuations, so the conventional deterministic analysis of blade can't provide complete information. The Stochastic analysis can tackle the uncertainties in blade parameters and obtain the probabilistic characteristics of the response. In this paper, the study focuses on the 3D stochastic finite element method (3DSFEM) of the static response for turbine blade. The perturbation stochastic finite element method (PSFEM) is used to calculate probabilistic characteristics of the static response of the turbine blade. The random response of a turbine blade subjected to the steam pressure and the centrifugal force is analyzed using perturbation stochastic finite element method. The example shows that the present method is valid.
Changqing Bai A Partition Expansion Method for Nonlinear Response Analysis of Stochastic Dynamic Systems With Local Nonlinearity
"... This paper focuses on the problem of nonlinear dynamic response variability resulting from stochastic system properties and random loads. An efficient and accurate method, which can be employed to analyze the dynamic responses of random finite element systems with local nonlinearity, is presented i ..."
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This paper focuses on the problem of nonlinear dynamic response variability resulting from stochastic system properties and random loads. An efficient and accurate method, which can be employed to analyze the dynamic responses of random finite element systems with local nonlinearity, is presented in this paper. This method, dubbed as the partition expansion method, is based on the partitioned time integration algorithm in conjunction with the Neumann expansion technique within the framework of the Monte Carlo simulation. Two numerical examples involving structural and mechanical stochastic vibration problems are employed to illustrate the advantage of the proposed method with respect to accuracy and efficiency. By comparing the results obtained by the direct Monte Carlo simulation, the dynamic response statistics can be accurately determined using the proposed method with four order expansion while the computational efforts are significantly reduced. The comparison of computing time indicates that the proposed method is efficient and practical for analyzing the statistical quantities of stochastic dynamic systems with local nonlinearity.