Monte Carlo techniques in computational stochastic mechanics

Hurtado, Jorge E.; Barbat, Álex H.

doi:10.1007/bf02736747

Cited by 246 publications

(99 citation statements)

References 99 publications

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“…A Monte Carlo procedure for the evaluation ofthe failure probabilitypF is now presented.21> 22 For this procedure, pF is represented by where integrals from -m to m are used for notational convenience, the indicator function 6(TWL, TSL) is defined by …”

Section: Numerical Evaluation: Monte Carlomentioning

confidence: 99%

Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links

Helton

Johnson²,

Oberkampf

2006

Reliability Engineering & System Safety

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Relationships to determine the probability that a weak link (WL)/strong link (SL) safety system will fail to function as intended in a fire environment are investigated. In the systems under study, failure of the WL system before failure of the SL system is intended to render the overall system inoperational and thus prevent the possible occurrence of accidents with potentially serious consequences. Formal developments of the probability that the WL system fails to deactivate the overall system before failure of the SL system @e., the probability of loss of assured safety, PLOAS) are presented for several WWSL configurations: (i) one WL, one SL, (ii) multiple WLs, multiple SLs with failure of any SL before any WL constituting failure of the safety system, (iii) multiple WLs, multiple SLs with failure of all SLs before any WL constituting failure of the safety system, and (iv) multiple WLs, multiple SLs and multiple sublinks in each SL with failure of any sublink constituting failure of the associated SL and failure of all SLs before failure of any WL constituting failure of the safety system. The indicated probabilities derive from time-dependent temperatures in the WL/SL system and variability (i.e., aleatory uncertainty) in the temperatures at which the individual components of this system fail and are formally defined as multidimensional integrals. Numerical procedures based on quadrature (i.e., trapezoidal rule, Simpson's rule) and also on Monte Carlo techniques (i.e., simple random sampling, importance sampling) are described and illustrated for the evaluation of these integrals. Example uncertainty and sensitivity analyses for PLOAS involving the representation of uncertainty (i.e., epistemic uncertainty) with probability theory and also with evidence theory are presented.

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Section: Numerical Evaluation: Monte Carlomentioning

confidence: 99%

Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links

Helton

Johnson²,

Oberkampf

2006

Reliability Engineering & System Safety

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“…The solution of the mathematical problem can be determined by the stochastic numerical material model, where the system response of the model renders a distribution with statistical mean and variance. A ubiquitous strategy for its solution is the Monte Carlo method [2,3]. An alternative to reduce the computational effort, is the spectral method by Ghanem and Spanos [4], which is considered in this paper.…”

Section: Introductionmentioning

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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“…Some state of the art papers and analysis have been reported in the literature in the last years (Hurtado and Barbat, 1998;Grigoriu, 2000;Schueller, 2007;Chakraverty, 2014). On the other hand, the well-known applications of a similar nature are available in both economics (Wiggins, 1987) and, traditionally, in physics (Binder and Heermann, 1997).…”

Section: Introductionmentioning

confidence: 99%

Symbolic Computing in Probabilistic and Stochastic Analysis

Kamiński

2015

International Journal of Applied Mathematics and Computer Science

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The main aim is to present recent developments in applications of symbolic computing in probabilistic and stochastic analysis, and this is done using the example of the well-known MAPLE system. The key theoretical methods discussed are (i) analytical derivations, (ii) the classical Monte-Carlo simulation approach, (iii) the stochastic perturbation technique, as well as (iv) some semi-analytical approaches. It is demonstrated in particular how to engage the basic symbolic tools implemented in any system to derive the basic equations for the stochastic perturbation technique and how to make an efficient implementation of the semi-analytical methods using an automatic differentiation and integration provided by the computer algebra program itself. The second important illustration is probabilistic extension of the finite element and finite difference methods coded in MAPLE, showing how to solve boundary value problems with random parameters in the environment of symbolic computing. The response function method belongs to the third group, where interference of classical deterministic software with the non-linear fitting numerical techniques available in various symbolic environments is displayed. We recover in this context the probabilistic structural response in engineering systems and show how to solve partial differential equations including Gaussian randomness in their coefficients.

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Monte Carlo techniques in computational stochastic mechanics

Cited by 246 publications

References 99 publications

Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links

Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links

Multidimensional Stochastic Material Modeling at Large Deformations Considering Parameter Correlations

Symbolic Computing in Probabilistic and Stochastic Analysis

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