A generalized stochastic perturbation technique for plasticity problems

Abstract

The main aim of this paper is to present an algorithm and the solution to the nonlinear plasticity problems with random parameters. This methodology is based on the finite element method covering physical and geometrical nonlinearities and, on the other hand, on the generalized nth order stochastic perturbation method. The perturbation approach resulting from the Taylor series expansion with uncertain parameters is provided in two different ways: (i) via the straightforward differentiation of the initial incremental equation and (ii) using the modified response surface method. This methodology is illustrated with the analysis of the elasto-plastic plane truss with random Young's modulus leading to the determination of the probabilistic moments by the hybrid stochastic symbolic-finite element method computations.

Parameter identification in elasto‐plasticity: distance between parameters and impact of measurement errors

“…T A B L E 3 Variances of normalized material parameters pertaining to stochastic model (7) identified using the analytical solution (16). In order to give an impression about the distribution of the parameters, the variance for each of the normalized parameters is provided in Table 3.…”

Hybrid uncertain analysis for temperature field prediction with random, fuzzy and interval parameters

“…For the large interval variables, the subinterval methodology can be used to decompose them into several subintervals with small uncertainty level first, and the eventual results can be reconstructed by the interval union operation [18]. For the random variables, the accuracy improvement in higher order Taylor expansion is rather small compared with the disproportional increase of computational cost, and the first-order Taylor series is still the most widely adopted strategy [33]. Without losing the universality, all the uncertain parameters in our current research are assumed to be expressed as variables with small uncertainty magnitude.…”

Fuzzy finite difference method for heat conduction analysis with uncertain parameters

“…When there exists substantial statistical information, the probability theory offers a powerful mathematical framework to represent such uncertainties. The probabilistic approaches, such as Monte Carlo simulation, stochastic perturbation method and stochastic spectral method, can be designated as the most valuable solution strategies [5][6][7]. Reliable application of probabilistic methods requires enough information to construct the probability density functions of uncertain parameters, which are not easily available for many complex practical problems.…”