Stochastic elastic–plastic finite elements

Sett, Kallol; Jeremić, Boris; Kavvas, M. L.

doi:10.1016/j.cma.2010.11.021

Cited by 30 publications

(18 citation statements)

References 46 publications

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“…1.E-08 1.E-06 1.E-04 1.E-02 1.E+00 Sett et al (2011) propusieron una formulación del MEFEE que permitiría abordar el caso elasto-plástico, lo que aumentaría su interés en Geotecnia. El enfoque espectral presenta, por tanto, un potencial importante.…”

Section: Ventajas Y Limitaciones Del Métodounclassified

Método del elemento finito estocástico en geotecnia. Enfoque espectral

Pineda-Contreras¹,

Auvinet-Guichard²

2013

Ingeniería, Investigación y Tecnología

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Ingeniería Investigación y Tecnología, volumen XIV (número1), enero-marzo 2013: 11-22 ResumenEn este artículo se exponen las herramientas matemáticas que constituyen la base de la formulación del método del elemento finito estocástico espectral para problemas de elasticidad lineal. Se ilustra el potencial que presenta este mé-todo para modelar la variación espacial de las propiedades de materiales heterogéneos y en particular de los suelos, mediante un ejemplo sencillo en el que se analiza cómo se propaga la incertidumbre del módulo de deformación de un material al campo de desplazamientos calculados. Se muestra en particular la influencia de la distancia de correlación sobre la distribución de la incertidumbre. Finalmente, se evalúa la utilidad del método para las aplicaciones en geotecnia y se presentan conclusiones. Abstract This paper presents the mathematical tools in which the formulation of Spectral

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Section: Ventajas Y Limitaciones Del Métodounclassified

Método del elemento finito estocástico en geotecnia. Enfoque espectral

Pineda-Contreras¹,

Auvinet-Guichard²

2013

Ingeniería, Investigación y Tecnología

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“…FPK approach to probabilistic elasto‐plasticity has been used to simulate both monotonic and cyclic hardening and softening type uncertain material behaviors . It has also been successfully integrated with the spectral approach of the stochastic finite element (FE) method to probabilistically solve stochastic elastic‐plastic boundary value problems …”

Section: Introductionmentioning

confidence: 99%

“…8,9 It has also been successfully integrated with the spectral approach of the stochastic finite element (FE) method to probabilistically solve stochastic elastic-plastic boundary value problems. 10,11 Traditionally, in mechanics, an FPK equation is solved numerically using the finite difference or FE technique. [12][13][14] Finite difference and FE methods are based on local representations of functions such as low-order polynomials.…”

Section: Introductionmentioning

confidence: 99%

Efficient solution algorithms for multiaxial probabilistic elasto‐plastic constitutive simulations of soils

Sadrinezhad

Sett

Hariharan

2017

Num Anal Meth Geomechanics

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Summary A Fokker‐Planck‐Kolmogorov (FPK) equation approach has recently been developed to probabilistically solve any elastic‐plastic constitutive equation with uncertain material parameters by transforming the nonlinear, stochastic constitutive rate equation into a linear, deterministic partial differential equation (PDE) and thereby simplifying the numerical solution process. For an uniaxial problem, conventional numerical techniques, such as the finite difference or finite element methods, may be used to solve the resulting univariate FPK PDE. However, for a multiaxial problem, an efficient algorithm is necessary for tractability of the numerical solution of the multivariate FPK PDE. In this paper, computationally efficient algorithms, based on a Fourier spectral approach, are presented for solving FPK PDEs in (stress) space and (pseudo) time, having space‐independent but time‐dependent coefficients and both space‐ and time‐dependent coefficients, that commonly arise in probabilistic elasto‐plasticity. The algorithms are illustrated by probabilistically simulating 2 common laboratory constitutive experiments in geotechnical engineering, namely, the unconfined compression test and the unconsolidated undrained triaxial compression test.

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“…Utilizing an Eulerian-Lagrangian form of the Fokker-Planck-Kolmogorov (FPK) 65 equation [21], the aforementioned "closure problem" associated with regular perturbation methods is resolved. Afterwards, Jeremić and Sett [22] modified their approach to account for probabilistic rather than expected yielding and incorporated their developed FPK-based elastoplastic model in a Gaussian spectral stochastic finite element framework [23]. Later, Rosić [24] and 70 Arnst and Ghanem [25] presented in detail the variational theory behind the mixed-hardening stochastic plasticity problem along with stochastic versions of relevant established computational plasticity algorithms.…”

Section: Introductionmentioning

confidence: 99%

Fokker–Planck linearization for non-Gaussian stochastic elastoplastic finite elements

Karapiperis

Sett

Kavvas

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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Presented here is a finite element framework for the solution of stochastic elastoplastic boundary value problems with non-Gaussian parametric uncertainty. The framework relies upon a stochastic Galerkin formulation, where the stiffness random field is decomposed using a multidimensional polynomial chaos expansion. At the constitutive level, a Fokker-Planck-Kolmogorov (FPK) plasticity framework is utilized, under the assumption of small strain kinematics. A linearization procedure is developed that serves to update the polynomial chaos coefficients of the expanded random stiffness in the elastoplastic regime, leading to a nonlinear least-squares optimization problem. The proposed framework is illustrated in a static shear beam example of elastic-perfectly plastic as well as isotropic hardening material.

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Stochastic elastic–plastic finite elements

Cited by 30 publications

References 46 publications

Método del elemento finito estocástico en geotecnia. Enfoque espectral

Método del elemento finito estocástico en geotecnia. Enfoque espectral

Efficient solution algorithms for multiaxial probabilistic elasto‐plastic constitutive simulations of soils

Fokker–Planck linearization for non-Gaussian stochastic elastoplastic finite elements

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