An Extrema Approach to Probabilistic Creep Modeling in Finite Element Analysis

This paper introduces a computationally efficient extremum condition-based Reduced Order Modeling (ROM) approach for the probabilistic predictions of creep in finite element (FE). Component-level probabilistic simulations are needed to assess the reliability and safety of high-temperature components. Full-scale probabilistic creep models in FE are computationally expensive, requiring many hundreds of simulations to replicate the uncertainty of component failure. In this study, an extremum condition-based ROM approach is proposed. In the extremum approach, full-scale probabilistic simulations are completed in 1D across a wide range of stresses, the data is processed and extremum conditions extracted, and those conditions alone are applied in 2D/3D FE to predict the mean and range of creep-failure. The probabilistic Sinh model, calibrated for alloy 304 stainless steel, is selected . The uncertainty sources (i.e. test condition, pre-existing damage, and model constants) are evaluated and pdfs sampling are performed via Monte carlo method. The extremum conditions are chosen from numerous 1D model simulations. These conditions include extremum cases of creep ductility, rupture, and area under creep curves. Only the extremum cases are simulated for 2D model saving significant computational time and memory. The goodness-of-fit of the predicted creep response for 1D and 2D model shows satisfactory agreement with the experimental data. The accuracy of the extremum condition-based ROM will reduce significant computational burden of simulating complex engineering systems. Introduction of multi-stage Sinh, stochasticity, and spatial uncertainty will further improve the prediction.

LOCALIZATION OF COMPACT INVARIANT SETS OF DISCRETE-TIME NONLINEAR SYSTEMS

In this paper, we examine the localization problem of compact invariant sets of discrete-time nonlinear systems. The localization procedure consists in applying the iterative algorithm based on the extremum condition. An analysis of a location of compact invariant sets of the Henon system is realized for all values of its parameters.

SUMMING RADIATIVE CORRECTIONS TO THE EFFECTIVE POTENTIAL

When one uses the Coleman–Weinberg renormalization condition, the effective potential V in the massless [Formula: see text] theory with O(N) symmetry is completely determined by the renormalization group functions. It has been shown how the (p + 1) order renormalization group function determine the sum of all the N p LL order contribution to V to all orders in the loop expansion. We discuss here how, in addition to fixing the N p LL contribution to V, the (p + 1) order renormalization group functions can also be used to determine portions of the N p+n LL contributions to V. When these contributions are summed to all orders, the singularity structure of V is altered. An alternate rearrangement of the contributions to V in powers of ln ϕ, when the extremum condition V′(ϕ = v) = 0 is combined with the renormalization group equation, show that either v = 0 or V is independent of ϕ. This conclusion is supported by showing the LL , …, N 4 LL contributions to V become progressively less dependent on ϕ.

LOCALIZATION OF COMPACT INVARIANT SETS OF NONLINEAR SYSTEMS WITH APPLICATIONS TO THE LANFORD SYSTEM

In this paper, we examine the localization problem of compact invariant sets of systems with the differentiable right-side. The localization procedure consists in applying the iterative algorithm based on the first order extremum condition originally proposed by one of authors for periodic orbits. Analysis of a location of compact invariant sets of the Lanford system is realized for all values of its bifurcational parameter.