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In this paper, a solution is presented for evolution of probability density function (PDF) of elastic–plastic stress–strain
relationship for material models with uncertain parameters. Developments in this paper are based on already derived general
formulation presented in the companion paper. The solution presented is then specialized to a specific Drucker–Prager elastic–plastic
material model. Three numerical problems are used to illustrate the developed solution. The stress–strain response (1D) is
given as a PDF of stress as a function of strain. The presentation of the stress–strain response through the PDF differs significantly
from the traditional presentation of such results, which are represented by a single, unique curve in stress–strain space.
In addition to that the numerical solutions are verified against closed form solutions where available (elastic). In cases
where the closed form solution does not exist (elastic–plastic), Monte Carlo simulations are used for verification. 相似文献
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The paper presents a computationally efficient algorithm to integrate a probabilistic, non-Gaussian parameter estimation approach for nonlinear finite element models with the performance-based earthquake engineering (PBEE) framework for accurate performance evaluations of instrumented civil infrastructures. The algorithm first utilizes a minimum variance framework to fuse predictions from a numerical model of a civil infrastructure with its measured behavior during a past earthquake to update the parameters of the numerical model that is, then, used for performance prediction of the civil infrastructure during future earthquakes. A nonproduct quadrature rule, based on the conjugate unscented transformation, forms an enabling tool to drive the computationally efficient model prediction, model-data fusion, and performance evaluation. The algorithm is illustrated and validated on Meloland Road overpass, a heavily instrumented highway bridge in El Centro, CA, which experienced three moderate earthquake events in the past. The benefits of integrating measurement data into the PBEE framework are highlighted by comparing damage fragilities of and annual probabilities of damages to the bridge estimated using the presented algorithm with that estimated using the conventional PBEE approach. 相似文献
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Efficient solution algorithms for multiaxial probabilistic elasto‐plastic constitutive simulations of soils 
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下载免费PDF全文 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. 相似文献
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A second-order exact expression for the evolution of probability density function of stress is derived for general, one-dimensional
(1-D) elastic–plastic constitutive rate equations with uncertain material parameters. The Eulerian–Lagrangian (EL) form of
Fokker–Planck–Kolmogorov (FPK) equation is used for this purpose. It is also shown that by using EL form of FPK, the so called
“closure problem” associated with regular perturbation methods used so far, is resolved too. The use of EL form of FPK also
replaces repetitive and computationally expensive deterministic elastic–plastic computations associated with Monte Carlo technique.
The derived general expressions are specialized to the particular cases of point location scale linear elastic and elastic–plastic
constitutive equations, related to associated Drucker–Prager with linear hardening. In a companion paper, the solution of
FPK equations for 1D is presented, discussed and illustrated through a number of examples. 相似文献
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In this paper, the novel concept of probabilistic yielding is used for 1‐D cyclic simulation of the constitutive behavior of geomaterials. Fokker–Planck–Kolmogorov equation‐based probabilistic elastic–plastic constitutive framework is applied for obtaining the complete probabilistic (probability density function) material response. Both perfectly plastic and hardening‐type material models are considered. It is shown that when uncertainties in material parameters are taken into consideration, even the simple, elastic‐perfectly plastic model captures some of the important features of geomaterial behavior, for example, modulus reduction with cyclic strain, which, deterministically, is only possible with more advanced constitutive models. Furthermore, it is also shown that the use of isotropic and kinematic hardening rules does not significantly improve the probabilistic material response. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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