Flexibility-based upper bounds on the response variability of simple beams

Papadopoulos, Vissarion; Deodatis, George; Papadrakakis, Manolis

doi:10.1016/j.cma.2004.06.040

Cited by 32 publications

(32 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…material, geometric properties, soil properties, wind, wave, earthquake loads) exhibit non-Gaussian probabilistic characteristics. NonGaussian fields are also useful for the determination of spectral-distribution-free upper bounds of the response variability of stochastic systems [134]. In particular, the simulation of highly skewed narrow-banded stochastic processes and fields is well recognized today as a testbed that reveals the limitations of the existing simulation methods [34].…”

Section: Simulation Methods For Non-gaussian Stochastic Processes Andmentioning

confidence: 99%

“…A variant of MCS called ''fast MCS" has been recently used for the efficient numerical evaluation of the variability response function [165] needed to calculate spectral-probability distribution-free upper bounds of the response variability of structural systems [134]. Numerous other variants of this approach (importance sampling, subset simulation, line sampling) have been developed in the last decade especially for the efficient solution of reliability problems where the calculation of small failure probabilities requires a very large number of samples [161].…”

Section: Direct Mcsmentioning

confidence: 99%

See 1 more Smart Citation

The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

862

407

View full text Add to dashboard Cite

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.

show abstract

Section: Simulation Methods For Non-gaussian Stochastic Processes Andmentioning

confidence: 99%

Section: Direct Mcsmentioning

confidence: 99%

The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

862

407

View full text Add to dashboard Cite

show abstract

“…Nevertheless, it is true that a consideration, which is similar to that given in this study, has also to be taken into account even when we deal with stochastic fields with a high degree of uncertainty, e.g., a non-Gaussian field having beta-distributions with lower bounds [20]. In these cases, the random sample data assume values much larger than 1.0, introducing greater discrepancy between (1 + f(x)) and 1/(1 + f(x)).…”

Section: Limitation Of Application and Further Interestmentioning

confidence: 96%

Monte Carlo simulation-compatible stochastic field for application to expansion-based stochastic finite element method

Noh

Park

2006

Computers & Structures

View full text Add to dashboard Cite

“…A number of solution procedures for solving Equation (19) have been proposed addressing small-to-medium problems. However, as the problem size grows, such a solution can become quite challenging because of the enormous memory and computational resources required.…”

Section: Solution Of the Augmented Spectral Stochastic Finite Elementmentioning

confidence: 99%

An adaptive spectral Galerkin stochastic finite element method using variability response functions

Giovanis

Papadopoulos

Stavroulakis

2015

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

SUMMARYA methodology is proposed in this paper to construct an adaptive sparse polynomial chaos (PC) expansion of the response of stochastic systems whose input parameters are independent random variables modeled as random fields. The proposed methodology utilizes the concept of variability response function in order to compute an a priori low-cost estimate of the spatial distribution of the second-order error of the response, as a function of the number of terms used in the truncated Karhunen-Loève (KL) expansion. This way the influence of the response variance to the spectral content (correlation structure) of the random input is taken into account through a spatial variation of the truncated KL terms. The criterion for selecting the number of KL terms at different parts of the structure is the uniformity of the spatial distribution of the second-order error. This way a significantly reduced number of PC coefficients, with respect to classical PC expansion, is required in order to reach a uniformly distributed target second-order error. This results in an increase of sparsity of the coefficient matrix of the corresponding linear system of equations leading to an enhancement of the computational efficiency of the spectral stochastic finite element method.

show abstract

Flexibility-based upper bounds on the response variability of simple beams

Cited by 32 publications

References 10 publications

The stochastic finite element method: Past, present and future

The stochastic finite element method: Past, present and future

Monte Carlo simulation-compatible stochastic field for application to expansion-based stochastic finite element method

An adaptive spectral Galerkin stochastic finite element method using variability response functions

Contact Info

Product

Resources

About