Neumann enriched polynomial chaos approach for stochastic finite element problems

Pryse, S.E.; Adhikari, Sondipon

doi:10.1016/j.probengmech.2021.103157

Cited by 7 publications

(2 citation statements)

References 37 publications

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“…Representation of the solutions by PCE Random processes and fields are represented by chaotic PC polynomials, which are created by expanding a series of orthogonal polynomials via a sequence of random variables with definite coefficients [13], [15], [16], [18], [30]. Norbert Wiener presented the PC notion based on the homogeneous PC theory for Gaussian random variables as follows:…”

Section: 4mentioning

confidence: 99%

Generalization of spectral stochastic finite element method for analysis of structures with elastoplastic materials

rahimibondarabadi¹,

mousaviamjad²

2022

Preprint

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The significance of the influence of uncertainty and stochastic approach-related problems on engineering system analysis is now evident and irrefutable. On the other hand, considering the factors that apply these uncertainties in the findings should need a significant amount of computing cost and effort, which is why researchers are always looking for approaches that combine high calculation accuracy with speed. One of the most useful tools for analyzing systems with uncertainty in computational stochastic mechanics is the spectral stochastic finite element method. In the present paper, by applying uncertainty to the applied loads and elastic modulus, this method has been developed to analyze the structures with nonlinear materials, and a method called the nonlinear spectral stochastic finite element method (NLSSFEM) has been proposed. The results obtained from the used method have been compared with the results obtained from the Monte Carlo simulation method. The accuracy of calculations and the speed of access to the solution of the proposed method are evaluated as desirable.

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Section: 4mentioning

confidence: 99%

Generalization of spectral stochastic finite element method for analysis of structures with elastoplastic materials

rahimibondarabadi¹,

mousaviamjad²

2022

Preprint

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“…In computational mechanics, stochastic discretization techniques have been employed for variational theory for nonlinear problems with stochastic coefficients [59,60,61], inelastic media under uncertainty [62], elastic-plastic material with uncertain parameters [63], fatigue crack propagation due to the inherent uncertainties according to the material properties [64], nonlinear fracture mechanics of concrete [65], and stochastic fracture response and crack growth analysis of laminated composites [66]. In addition to MC-FEM, different numerical methods, such as polynomial chaos expansion (PCE) [67], the method of time-separated stochastic mechanics (TSM) [68,69,70] and stochastic finite element method [71,72,73,74] with applications to fracture mechanics.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic failure mechanisms via Monte Carlo simulations of complex microstructures

Noii,

Khodadadian,

Aldakheel

2022

Preprint

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A probabilistic approach to phase-field brittle and ductile fracture with random material and geometric properties is proposed within this work. In the macroscopic failure mechanics, materials properties and exactness of spatial quantities (of different phases in the geometrical domain) are assumed to be homogeneous and deterministic. This is unlike the lower-scale with strong fluctuation in the material and geometrical properties. Such a response is approximated through some uncertainty in the model problem. The presented contribution is devoted to providing a mathematical framework for modeling uncertainty through stochastic analysis of a microstructure undergoing brittle/ductile failure. Hereby, the proposed model employs various representative volume elements with random distribution of stiff-inclusions and voids within the composite structure. We develop an allocating strategy to allocate the heterogeneities and generate the corresponding meshes in two-and three-dimensional cases. Then the Monte Carlo finite element technique is employed for solving the stochastic PDE-based model and approximate the expectation and the variance of the solution field of brittle/ductile failure by evaluating a large number of samples. For the prediction of failure mechanisms, we rely on the phase-field approach which is a widely adopted framework for modeling and computing the fracture phenomena in solids. Incremental perturbed minimization principles for a class of gradient-type dissipative materials are used to derive the perturbed governing equations. This analysis enables us to study the highly heterogeneous microstructure and monitor the uncertainty in failure mechanics. Several numerical examples are given to examine the efficiency of the proposed method.

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Dynamic response of gyroscopic flexible structures with interval parameters

Guo

et al. 2023

Acta Mech. Sin.

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Neumann enriched polynomial chaos approach for stochastic finite element problems

Cited by 7 publications

References 37 publications

Generalization of spectral stochastic finite element method for analysis of structures with elastoplastic materials

Generalization of spectral stochastic finite element method for analysis of structures with elastoplastic materials

Probabilistic failure mechanisms via Monte Carlo simulations of complex microstructures

Dynamic response of gyroscopic flexible structures with interval parameters

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