The stochastic finite element method: Past, present and future

By George Stefanou. 2009

1,055 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e80520b2121bb24936442ae382c4322bf21c0b95

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Citations in the corpus

Reliability in composites – a selective review and survey of current development (2012, background): “In a numerical scheme, particularly in the context of finite element modeling, the stochastic finite element modeling (SFEM) are receiving special attention for reliability, due to the technological advances in the available computational power [50].”
Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison (2011, neutral): “[11, 27, 13, 17, 23]).”
Arbitrary polynomial chaos expansion method for uncertainty quantification and global sensitivity analysis in structural dynamics (2020, methodology): “10 [7, 64] Density of arch rib ( r D ) Weibull 7850 (kg/m 3 ) 0.”
Doubly Spectral Stochastic Finite-Element Method for Linear Structural Dynamics (2011, methodology): “Problems of structural dynamics in which the uncertainty in specifying the stiffness and mass of the structure are modeled within the framework of random fields and can be treated by using the stochastic finite-element method (Ghanem and Spanos 1991; Sudret and Der-Kiureghian 2000; Stefanou 2009; No”
Dynamic analysis of bridge–vehicle system with uncertainties based on the finite element model (2010, background): “However, it suffers from the curse of exponentially increased dimension in the polynomial chaos expansion for the solution when a large number of Karhunen–Loéve components is required to represent the system parameters and excitation [25].”
Perturbation-based stochastic multi-scale computational homogenization method for the determination of the effective properties of composite materials with random properties (2016, methodology): “The stochastic finite element method is an efficient technique for uncertainty quantification [14].”
Reengineering Aircraft Structural Life Prediction Using a Digital Twin (2011, background): “SFEM comprises three basic steps: discretization of the stochastic fields representing the uncertain input parameters, formulation of the stochastic matrix at the element and then at the global level, and, finally, the response variability calculation [37].”
Towards efficient uncertainty quantification in complex and large-scale biomechanical problems based on a Bayesian multi-fidelity scheme (2014, background): “Various approaches to solve this kind of stochastic boundary value problem have been proposed in recent decades (Spanos and Zeldin 1998; Stefanou 2009; Panayirci and Schuëller 2011; Xiu 2010; Eldred 2009).”