An interval finite element method for the analysis of structures with spatially varying uncertainties

Finite element analysis of linear-elastic structures with spatially varying uncertain properties is addressed within the framework of the interval model of uncertainty. Resorting to a recently proposed interval field model, the uncertain properties are expressed as the superposition of deterministic basis functions weighted by particular unitary intervals. An Interval Finite Element Method (IFEM) incorporating the interval field representation of uncertainties is formulated by applying an interval extension in conjunction with the standard energy approach. Uncertainty propagation analysis is performed by adopting a response surface approach which provides approximate explicit expressions of response bounds requiring only a few deterministic analyses. Then, the whole procedure is implemented in ABAQUS’ environment by coding User Subroutines and Python scripts. 2D plane stress and bending problems involving uncertain Young's modulus of the material are analyzed. The accuracy of the proposed IFEM as well as response variability under spatially dependent uncertainty are investigated

Spatially varying fuzzy multi-scale uncertainty propagation in unidirectional fibre reinforced composites

SN and SS are grateful for the support provided through the Lloyd’s Register Foundation Centre. The Foundation helps to protect life and property by supporting engineering-related education, public engagement and the application of research.Peer reviewedPostprin

An experimental investigation of the natural frequency statistics of a beam with spatially correlated random masses

Experimental investigations into the dynamic response of structures with material or geometrical random fields usually depend upon an initial characterization of this variability, with very little control over the statistics at its early manufacturing stage. This provides the need of a minimal number of samples to generate an ensemble of dynamic responses, making such experimental data scarcely found in the literature. In this work, a cantilever beam with small masses attached along its length according to a given discrete random field has an ensemble of natural frequencies measured for a number of correlation lengths. The results can be used to investigate the effects of the correlation length on the subsequent natural frequency statistics. The experimental results are compared with a wave approximation for flexural waves using a continuous random field for the mass density, in order to approximate the mass distribution. Issues concerning this approximation are discussed. In addition, results are also compared with a simple added mass approximation with assumed modes from a FE solution

Seismic fragility analysis of reinforced concrete bridges with chloride induced corrosion subjected to spatially varying ground motion

This paper studies the time-dependent seismic fragility of reinforced concrete bridges with chloride induced corrosion under spatially varying ground motions. The time-varying characteristic of the chloride corrosion current density and the uncertainties related to the structural, material and corrosion parameters are both considered in the probabilistic finite element modeling of the example RC bridge at different time steps during its life-cycle. Spatially varying ground motions at different bridge supports are stochastically simulated and used as inputs in the fragility analysis. Seismic fragility curves of the corroded RC bridge at different time steps are generated using the probabilistic seismic demand analysis (PSDA) method. Numerical results indicate that both chloride induced corrosion and ground motion spatial variations have a significant effect on the bridge structural seismic fragility. As compared to the intact bridge, the mean peak ground accelerations (PGAs) of the fragility curves of the RC bridge decrease by approximately 40% after 90 years since the initiation of corrosion. Moreover, the effect of ground motion spatial variations changes along with the process of chloride induced corrosion owing to the structural stiffness degradation. Neglecting seismic ground motion spatial variations may not lead to an accurate estimation of the lifetime seismic fragility of RC bridges with chloride induced corrosion

Decorrelation Times of Photospheric Fields and Flows

We use autocorrelation to investigate evolution in flow fields inferred by applying Fourier Local Correlation Tracking (FLCT) to a sequence of high-resolution (0.3 \arcsec), high-cadence ($\simeq 2$ min) line-of-sight magnetograms of NOAA active region (AR) 10930 recorded by the Narrowband Filter Imager (NFI) of the Solar Optical Telescope (SOT) aboard the {\em Hinode} satellite over 12--13 December 2006. To baseline the timescales of flow evolution, we also autocorrelated the magnetograms, at several spatial binnings, to characterize the lifetimes of active region magnetic structures versus spatial scale. Autocorrelation of flow maps can be used to optimize tracking parameters, to understand tracking algorithms' susceptibility to noise, and to estimate flow lifetimes. Tracking parameters varied include: time interval $\Delta t$ between magnetogram pairs tracked, spatial binning applied to the magnetograms, and windowing parameter $\sigma$ used in FLCT. Flow structures vary over a range of spatial and temporal scales (including unresolved scales), so tracked flows represent a local average of the flow over a particular range of space and time. We define flow lifetime to be the flow decorrelation time, $\tau$. For $\Delta t > \tau$, tracking results represent the average velocity over one or more flow lifetimes. We analyze lifetimes of flow components, divergences, and curls as functions of magnetic field strength and spatial scale. We find a significant trend of increasing lifetimes of flow components, divergences, and curls with field strength, consistent with Lorentz forces partially governing flows in the active photosphere, as well as strong trends of increasing flow lifetime and decreasing magnitudes with increases in both spatial scale and $\Delta t$.Comment: 48 pages, 20 figures, submitted to the Astrophysical Journal; full-resolution images in manuscript (8MB) at http://solarmuri.ssl.berkeley.edu/~welsch/public/manuscripts/flow_lifetimes_v2.pd

On the dynamic analysis of engineering structures with high and low level random uncertainties

The ability to predict the effect of dimension and thickness variability on the dynamic response of realistically uncertain engineering structures is examined in this thesis. Initially, available methods for predicting key response statistics and probabilities, for both low and high frequencies are examined to establish their strengths and limitations for specified levels of random dimension variability. For low frequency applications, the ability of Direct Integration (DI) and the First-Order Reliability Method (FORM) to predict exceedance probability is examined. For high frequency applications, the ability of the methods of Statistical Energy Analysis (SEA) and DI to predict the mean and standard deviation of the energy response is examined. The use of Extreme Value (EV) theory is included as a way to bound responses using simulated or measured responses. The strengths and limitations of Monte Carlo simulation methods are explored for both low and high frequency responses of randomly uncertain structures using both simple mode superposition plate-structure solutions and (commercially available) finite element solutions for coupled plate structures. To address, without the need to undertake expensive Monte Carlo simulation, the problem of predicting response bounds for structures with varying levels of uncertainty, a novel DI-EV method is developed and examined. It is tested first on a simple plate structure, then on a coupled plate structure, with low-level and high-level random dimension and thickness uncertainty. In addition, the method is compared with the SEA-EV method. The thesis shows that the results from the existing SEA-EV bounding approach gives good bounds only at particular frequencies and mainly for low levels of dimension variability. In contrast, the proposed DI-EV bounding approach compare extremely well with Monte Carlo simulations, which is not only at all frequencies but also with both low-level and high-level uncertainties, for simple and coupled plate structures with dimension and thickness variation