Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Computational Partial Differential Equations: Numerical Methods and Diffpack Programming
Computational Partial Differential Equations: Numerical Methods and Diffpack Programming
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Using stochastic analysis to capture unstable equilibrium in natural convection
Journal of Computational Physics
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
Journal of Computational Physics
Uncertainty quantification using polynomial chaos expansion with points of monomial cubature rules
Computers and Structures
Efficient uncertainty quantification with the polynomial chaos method for stiff systems
Mathematics and Computers in Simulation
Hierarchical stochastic metamodels based on moving least squares and polynomial chaos expansion
Structural and Multidisciplinary Optimization
Weighted stochastic response surface method considering sample weights
Structural and Multidisciplinary Optimization
Finite element modelling and optimisation of net-shape metal forming processes with uncertainties
Computers and Structures
Multi-objective reliability-based optimization with stochastic metamodels
Evolutionary Computation
Sampling-free linear Bayesian update of polynomial chaos representations
Journal of Computational Physics
A Posteriori Error Analysis of Parameterized Linear Systems Using Spectral Methods
SIAM Journal on Matrix Analysis and Applications
Uncertainty quantification for algebraic systems of equations
Computers and Structures
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Large deformation processes are inherently complex considering the non-linear phenomena that need to be accounted for. Stochastic analysis of these processes is a formidable task due to the numerous sources of uncertainty and the various random input parameters. As a result, uncertainty propagation using intrusive techniques requires tortuous analysis and overhaul of the internal structure of existing deterministic analysis codes. In this paper, we present an approach called non-intrusive stochastic Galerkin (NISG) method, which can be directly applied to presently available deterministic legacy software for modeling deformation processes with minimal effort for computing the complete probability distribution of the underlying stochastic processes. The method involves finite element discretization of the random support space and piecewise continuous interpolation of the probability distribution function over the support space with deterministic function evaluations at the element integration points. For the hyperelastic-viscoplastic large deformation problems considered here with varying levels of randomness in the input and boundary conditions, the NISG method provides highly accurate estimates of the statistical quantities of interest within a fraction of the time required using existing Monte Carlo methods.