Modeling physical uncertainties in dynamic stall induced fluid–structure interaction of turbine blades using arbitrary polynomial chaos

Witteveen, Jeroen; Sarkar, Saswati; Bijl, H.

doi:10.1016/j.compstruc.2007.01.004

Cited by 132 publications

(68 citation statements)

References 40 publications

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“…Here, the basis functions are stochastic and are obtained as polynomials of basic random variables, and unlike in KL, the projections are deterministic. The form of the polynomial functions, and the distribution of the random variables are based on the Askey scheme and depend on the marginal pdf of the random field [17,20]. While this approach is straightforward for scalar random fields, extending the method to higher dimensions is fraught with difficulties.…”

Section: Discussionmentioning

confidence: 99%

“…Subsequently, the force vector due to the thermal gradients, F t , is computed from Eq. (20). The effect of the spatial randomness in the elastic modulus of the material is addressed using the formulation discussed in the previous Section.…”

Section: Case 2: Random Spatial Variation In the Modulus Of Elasticitmentioning

confidence: 99%

“…The left-hand side of the three-dimensional integrals in Eqs. (19)(20)(21) as well as the integrands consist of matrices/vectors. These expressions are to be interpreted to be the generic form for computing the elements of matrices/vectors in the left-hand side of these equations.…”

Section: Case 1: Random Spatial Variations In the Modulus Of Elasticitymentioning

confidence: 99%

“…As the shape functions {S k (x, y, z)} are available numerically, the evaluation of the three-dimensional integrals in Eqs. (19)(20)(21) is carried out numerically using Gauss' quadrature scheme. The damage trajectories with time are subsequently computed corresponding to each realization.…”

Section: Case 1: Random Spatial Variations In the Modulus Of Elasticitymentioning

confidence: 99%

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3-D stochastic finite elements for thermal creep analysis of piping structures with spatial material inhomogeneities

Appalanaidu

Gupta

2017

Acta Mech

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A stochastic finite element-based methodology is developed for creep damage assessment in pipings carrying high-temperature fluids. The material properties are assumed to be spatially randomly inhomogeneous and are modelled as 3-D non-Gaussian fields. A spectral-based approach for random field discretization that preserves exactly the non-Gaussian characteristics is used in developing the stochastic finite element model. The meshing used in random field discretization is distinct from FE meshing, depends on the correlation characteristics of the random fields and is computationally efficient. The methodology enables estimating the failure probability and the most likely regions of failure in a section of a circular pipe.

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Section: Discussionmentioning

confidence: 99%

Section: Case 2: Random Spatial Variation In the Modulus Of Elasticitmentioning

confidence: 99%

Section: Case 1: Random Spatial Variations In the Modulus Of Elasticitymentioning

confidence: 99%

Section: Case 1: Random Spatial Variations In the Modulus Of Elasticitymentioning

confidence: 99%

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3-D stochastic finite elements for thermal creep analysis of piping structures with spatial material inhomogeneities

Appalanaidu

Gupta

2017

Acta Mech

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“…(18). PC coefficients for both types of polynomials in Section 2.2 and Section 2.3 are summarized in Table 3.…”

Section: Pc Coefficients Of Materials Parametersmentioning

confidence: 99%

Multidimensional Stochastic Material Modeling at Large Deformations Considering Parameter Correlations

Penner¹,

Caylak²,

Mahnken³

2017

Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. In many engineering applications the material behavior, e.g. hyper-elasticity and plasticity, is described by appropriate mathematical models. However, these become uncertain due to different types of uncertainty such as variation in the manufacturing process, measurement errors and missing or incomplete information on material properties. This contribution presents a framework for nonlinear elastic stochastic material model at large deformations. As a key idea uncertainty of the material is described by parameters, which are modeled as stochastic variables.To this end, 150 specimens for three different rubber materials are experimentally investigated in tensile tests. Based on experimental results 1000 artificial data are generated by aid of an ARMA process [1]. The artificial data are used for parameter identification of an Ogden material model for rubber materials . Furthermore, statistical analysis of material parameters including their correlations is studied. The number of material parameters define the dimension of the stochastic space. Usually, the stochastic material parameters are considered as stochastically independent. However, in our work we consider the dependency including the correlation obtained from experimental data.The hyperelastic stochastic material parameters are expanded with the multivariate PCE. In this context, the stresses depend on stochastic variables. To determine the corresponding PC coefficients for non-independent stochastic material parameters we use a Cholesky decomposition. As a numerical example we consider the static problem for uniaxial tension of the rectangular plate. This structure is investigated in order to represent the experimental setup conditions.

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An iterative polynomial chaos approach toward stochastic elastostatic structural analysis with non‐Gaussian randomness

Nath

Dutta

Hazra

2019

Numerical Meth Engineering

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Summary Stochastic analysis of structure with non‐Gaussian material property and loading in the framework of polynomial chaos (PC) is considered. A new approach for the solution of stochastic mechanics problem with random coefficient is presented. The major focus of the method is to consider reduced size of expansion in an iterative manner to overcome the problem of large system matrix in conventional PC expansion. The iterative method is based on orthogonal expansion of stochastic responses and generation of an iterative PC based on the responses of the previous iteration. The polynomials are evaluated using Gram‐Schmidt orthogonalization process. The numbers of random variables in PC expansion are reduced by considering only the dominant components of the response characteristics, which is evaluated using Karhunen‐Loève (KL) expansion. In case of random material field problem, the KL expansion is used to discretize and simulate the non‐Gaussian random field. Independent component analysis (ICA) is carried out on the non‐Gaussian KL random variables to minimize statistical dependence. The usefulness of the proposed method in terms of accuracy and computational efficiency is examined. From the numerical analysis of three different types of structural mechanics problems, the proposed iterative method is observed to be computationally more efficient and accurate than conventional PC method for solution of linear elastostatic structural mechanics problems.

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Modeling physical uncertainties in dynamic stall induced fluid–structure interaction of turbine blades using arbitrary polynomial chaos

Cited by 132 publications

References 40 publications

3-D stochastic finite elements for thermal creep analysis of piping structures with spatial material inhomogeneities

3-D stochastic finite elements for thermal creep analysis of piping structures with spatial material inhomogeneities

Multidimensional Stochastic Material Modeling at Large Deformations Considering Parameter Correlations

An iterative polynomial chaos approach toward stochastic elastostatic structural analysis with non‐Gaussian randomness

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