Stochastic finite element analysis of shells with combined random material and geometric properties

Stefanou, George; Papadrakakis, Manolis

doi:10.1016/j.cma.2003.10.001

Cited by 129 publications

(71 citation statements)

References 21 publications

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“…Spectral representation has also been successfully implemented in the framework of Monte Carlo simulation (MCS) for the solution of realistic problems with the stochastic finite element approach e.g. [4,20,99,133,[135][136][137][138]145,146,173].…”

Section: The Spectral Representation Methodsmentioning

confidence: 99%

“…Expressions for the stochastic matrix of several kinds of finite elements (2D and 3D beam, plane stress/strain, plate, shell) are existing in the literature [31,138,184,72,4,173]. It is worth noting that, in the case of dynamic problems, the mass and damping matrices can be random as well e.g.…”

Section: Formulation Of the Stochastic Finite Element Matrixmentioning

confidence: 99%

“…12). A comparison between the local average and weighted integral methods in the calculation of the response variability of plane stress/strain, plate and thin shell structures can be found in [184,72,4,173], respectively (see also Fig. 13).…”

Section: Discretization Of Stochastic Processes and Fieldsmentioning

confidence: 99%

“…Thus, direct MCS is today a powerful (and perhaps the only universal) tool for treating complex SFEM applications. This is why it is often used as a reference approach for validating the results of other methods [4,9,44,51,138,173,176,177,179].…”

Section: Direct Mcsmentioning

confidence: 99%

“…These methods have been extensively used by several researchers in the framework of SFEM leading to results of different levels of accuracy e.g. [4,25,31,72,111,173,184]. A thorough comparison of the midpoint, interpolation and local average methods for the case of 2D-1V homogeneous Gaussian stochastic fields with three different correlation structures (exponential, square exponential and sinusoidal) and various correlation length parameters, has been presented in [102] (Fig.…”

Section: Discretization Of Stochastic Processes and Fieldsmentioning

confidence: 99%

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The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

861

407

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a b s t r a c tA powerful tool in computational stochastic mechanics is the stochastic finite element method (SFEM). SFEM is an extension of the classical deterministic FE approach to the stochastic framework i.e. to the solution of static and dynamic problems with stochastic mechanical, geometric and/or loading properties. The considerable attention that SFEM received over the last decade can be mainly attributed to the spectacular growth of computing power rendering possible the efficient treatment of large-scale problems. This article aims at providing a state-of-the-art review of past and recent developments in the SFEM area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future.

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Section: The Spectral Representation Methodsmentioning

confidence: 99%

Section: Formulation Of the Stochastic Finite Element Matrixmentioning

confidence: 99%

Section: Discretization Of Stochastic Processes and Fieldsmentioning

confidence: 99%

Section: Direct Mcsmentioning

confidence: 99%

Section: Discretization Of Stochastic Processes and Fieldsmentioning

confidence: 99%

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The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

861

407

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Stochastic projection schemes for deterministic linear elliptic partial differential equations on random domains

Mohan

Nair

Keane

2010

Numerical Meth Engineering

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SUMMARYWe present stochastic projection schemes for approximating the solution of a class of deterministic linear elliptic partial differential equations defined on random domains. The key idea is to carry out spatial discretization using a combination of finite element methods and stochastic mesh representations. We prove a result to establish the conditions that the input uncertainty model must satisfy to ensure the validity of the stochastic mesh representation and hence the well posedness of the problem. Finite element spatial discretization of the governing equations using a stochastic mesh representation results in a linear random algebraic system of equations in a polynomial chaos basis whose coefficients of expansion can be non-intrusively computed either at the element or the global level. The resulting randomly parametrized algebraic equations are solved using stochastic projection schemes to approximate the response statistics. The proposed approach is demonstrated for modeling diffusion in a square domain with a rough wall and heat transfer analysis of a three-dimensional gas turbine blade model with uncertainty in the cooling core geometry. The numerical results are compared against Monte-Carlo simulations, and it is shown that the proposed approach provides high-quality approximations for the first two statistical moments at modest computational effort.

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Interval spectral stochastic finite element analysis of structures with aggregation of random field and bounded parameters

Minh

Gao

Song

et al. 2016

Numerical Meth Engineering

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Summary This paper presents the study on non‐deterministic problems of structures with a mixture of random field and interval material properties under uncertain‐but‐bounded forces. Probabilistic framework is extended to handle the mixed uncertainties from structural parameters and loads by incorporating interval algorithms into spectral stochastic finite element method. Random interval formulations are developed based on K–L expansion and polynomial chaos accommodating the random field Young's modulus, interval Poisson's ratios and bounded applied forces. Numerical characteristics including mean value and standard deviation of the interval random structural responses are consequently obtained as intervals rather than deterministic values. The randomised low‐discrepancy sequences initialized particles and high‐order nonlinear inertia weight with multi‐dimensional parameters are employed to determine the change ranges of statistical moments of the random interval structural responses. The bounded probability density and cumulative distribution of the interval random response are then visualised. The feasibility, efficiency and usefulness of the proposed interval spectral stochastic finite element method are illustrated by three numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

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Stochastic finite element analysis of shells with combined random material and geometric properties

Cited by 129 publications

References 21 publications

The stochastic finite element method: Past, present and future

The stochastic finite element method: Past, present and future

Stochastic projection schemes for deterministic linear elliptic partial differential equations on random domains

Interval spectral stochastic finite element analysis of structures with aggregation of random field and bounded parameters

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