Uncertainties In Material Properties Research Articles

Uncertainty Analysis of a Dynamic Model of a Novel Remotely Piloted Airship

As the sophistication of finite element models increases, the need to investigate the effects of uncertainties in model inputs becomes increasingly important in the interests of developing a robust model. A novel design of an unmanned airship is under development at the Politecnico di Torino, Italy. Structural and fluid. structure interaction models were developed to ascertain the response of the structure under operational and aerodynamic loading; however, uncertainties in material properties (due to variation with temperature), pressure, and aerodynamic loading necessitated an uncertainty analysis. Since the computational expense of a large finite element model makes Monte Carlo methods impractical, a probabilistic Bayesian uncertainty analysis was performed, whereby the output of the model is sampled over a set of input points and the response of the model is emulated by a Gaussian process. Quantities pertaining to uncertainty analysis were then inferred, allowing a reliable uncertainty analysis to be performed for considerably less computational expense than conventional Monte Carlo methods. The results showed that uncertainty in model stress and deflection is indeed significant, although the highly nonlinear response of the fluid. structure interaction model required a high sampling density in order to accurately emulate its response. Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Bayesian sensitivity analysis of a model of the aortic valve

Understanding the mechanics of the aortic valve has been a focus of attention for many years in the biomechanics literature, with the aim of improving the longevity of prosthetic replacements. Finite element models have been extensively used to investigate stresses and deformations in the valve in considerable detail. However, the effect of uncertainties in loading, material properties and model dimensions has remained uninvestigated. This paper presents a formal statistical consideration of a selected set of uncertainties on a fluid-driven finite element model of the aortic valve and examines the magnitudes of the resulting output uncertainties. Furthermore, the importance of each parameter is investigated by means of a global sensitivity analysis. To reduce computational cost, a Bayesian emulator-based approach is adopted whereby a Gaussian process is fitted to a small set of training data and then used to infer detailed sensitivity analysis information. From the set of uncertain parameters considered, it was found that output standard deviations were as high as 44% of the mean. It was also found that the material properties of the sinus and aorta were considerably more important in determining leaflet stress than the material properties of the leaflets themselves.

Prediction of the confidence interval for stability analysis of chain pillars in coal mines

The conventional deterministic approach based (DAB) methods are simple and widely used to determine an adequate chain pillar size in coal mines where geological settings, coal characterizations and mining methods have been explored. It is evident that such deterministic methods have some intrinsic limitations in handling uncertainties in material properties, non-regular geometries and different mining operations. In the deterministic stability analysis of a chain pillar, the safety factors as well as all input parameters are deterministic. Although, these parameters generally exhibit uncertainty and should lead to a probabilistic expression for the safety factor. The probabilistic analysis provides a confidence interval to express the reliability of chain pillars stability. In this paper, safety factor is defined as a probabilistic function and the failure probability of designed chain pillar of Tabas coal mine is then evaluated using the First Order Second Moment (FOSM) and the Advanced Second Moment (ASM) methods. The results of the probabilistic stability analysis show that the confidence interval for designed pillars with both mentioned methods applied are similar and their values vary from 84% to 88%. The results of such analyses can be used as a basis for decision-making about the size of chain pillars and reduce the risk of pillars stability as well as the uncertainties. However, a trade-off between cost is essential for making the final decision.

Climate change impact and risks of concrete infrastructure deterioration

Atmospheric CO2 is a major cause of reinforcement corrosion in bridges, buildings, wharves, and other concrete infrastructure in Australia, United States, United Kingdom and most other countries. The increase in CO2 levels associated with global warming will increase the likelihood of carbonation-induced corrosion. Moreover, temperature rises will increase corrosion rates. Clearly, the impact of climate change on existing and new infrastructure is considerable, as corrosion damage is disruptive to society and costly to repair. The paper describes a probabilistic and reliability-based approach that predicts the probability of corrosion initiation and damage (severe cracking) for concrete infrastructure subjected to carbonation and chloride-induced corrosion resulting from elevated CO2 levels and temperatures. The atmospheric CO2 concentration and local temperature and relative humidity changes with time over the next 100 years in the Australian cities of Sydney and Darwin are projected based on nine General Circulation Models (GCMs) under (i) high CO2 emission scenario, (ii) medium CO2 emission scenario, and (iii) CO2 emission reduction scenario based on policy intervention. The probabilistic analysis included the uncertainty of CO2 concentration, deterioration processes, material properties, dimensions, and predictive models. It was found that carbonation-induced damage risks can increase by over 400% over a time period to 2100 for some regions in Australia. Damage risks for chloride-induced corrosion increase by no more than 15% over the same time period due to temperature increase, but without consideration of ocean acidity change in marine exposure. Corrosion loss of reinforcement is not significant. The results were most sensitive to increases in atmospheric CO2.

Non-probabilistic Reliability Based Topology Optimization Design of Two-material Structures

Using the convex model description and the quantified definition of the non-probabilistic reliability,topology optimization of two-material structures considering uncertainties in material properties,geometry and loads is studied.Based on the extended penalization scheme of relative density,a continuous minimax optimization problem,which satisfies the material volume constraint and the reliability requirement,is presented for finding the united distribution of two candidate materials.The minimax problem is solved in the sequential approximate programming manner by embedding a direct iterative formula and the method of moving asymptotes(MMA).The computation cost is thus greatly decreased since the original problem is transformed into a series of deterministic ones.Numerical examples show that system uncertainties may have considerable effects on the optimal united layout of two-material structures.The results prove that a powerful approach for the topology design of two-material structures is furnished by the proposed numerical technique.

Stochastic Aeroelastic Analysis of Composite Helicopter Rotor

The effect of uncertainty in composite material properties on the aeroelastic response, vibratory loads, and stability of a hingeless helicopter rotor is investigated. The uncertainty impact on rotating natural frequencies of the blade is studied with Monte Carlo simulations and first-order reliability methods. The stochastic aeroelastic analyses in hover and forward flight are carried out with Monte Carlo simulations. The flap, lag, and torsion responses show considerable scatter from their baseline values, and the uncertainty impact varies with the azimuth angle. Furthermore, the blade response shows finite probability of resonance-type conditions caused by modal frequencies approaching multiples of the rotor speed. The 4/rev vibratory forces show large deviations from their baseline values. The lag mode damping shows considerable scatter due to uncertain material properties with an almost 40% probability of instability in hover.

Genetic algorithm for reliability-based design optimisation of composite drive shaft

The laminated composite material is widely used in structural and automotive applications because of its high specific strength and stiffness. However, such material is strongly anisotropic and sensitive to the change in loading conditions. Therefore, it is necessary to consider the effect of such variations by applying the structural reliability theory. In this paper, reliability-based design optimisation methodology for finding the optimal design of composite drive shaft with a specific risk and reliability is presented. The effect of the uncertainties in material and geometric properties is considered to quantify the probability of failure. The application of genetic algorithm to determine the critical design parameters is explored. The reliability of various designs is estimated using Monte Carlo procedure to determine the optimal stacking sequence which meets the target reliability.

Predicting plastic deformation and work hardening during V-band formation

V-band clamps are manufactured using a cold roll forming process consisting of six passes which plastically deform an initially flat strip by bending to produce the band's V-section. In this paper a new method of validating numerically predicted plastic deformation in a cold formed metal strip is presented. Tensile testing of samples of the band's material was used to obtain a direct link between plastic strain and work hardness of this particular material. Using this correlation, the equivalent plastic strain (PEEQ) values predicted by finite element simulations were converted into hardness values. These values were compared to experimental work, in which samples of each pass of the roll forming process were taken to determine the work hardness in the cross section of the V-band using a micro-hardness machine. The error in strain predicted by the numerical method and hardness obtained by testing was found to be between 0.4% and 16.9%. This error was mainly due to uncertainty in material properties and the accuracy of the measurement technique. Compared to the more classical approach of measuring strain distribution with strain gauges, this method is more precise and accurate, as it is able to pick up even small changes in strain distribution.

Robust Optimization of Thermal-Dynamic Coupling Systems Using a Kriging Model

Thermally induced vibration of theflexible appendages of large-scale space structuresmay cause adverse effects to astronautical activities. This kind of unexpected response could be controlled to an admissible level through some optimal design methods. Because uncertainties in material properties and structural dimensions are inevitable in practice, they should also be considered during the optimization process to ensure the robust performance of the resultant structure. However, traditional robust design schemes based on either a direct Monte Carlo method or a perturbation-based stochastic finite elementmethod are usually too time-consuming to accomplish this task, because highly nonlinear analysis needs to be repeatedly conducted for this transient problem during the optimization process. To solve this problem, a robust optimization scheme based on the kriging model is developed in this paper. Because of the kriging approximation, only a few thermal–dynamic coupling analyses are needed to construct a satisfactory approximation function of the structural response. Based on this function, the mean value and the standard deviation of the structural response can be obtained efficiently, which greatly facilitates the calculation of the Pareto front for this kind of robust optimal design.

A Probabilistic Detectability-Based Structural Sensor Network Design Methodology for Prognostics and Health Management


 
 
 Significant technological advances in sensing and communication promote the use of large sensor networks to monitor structural systems, identify damages, and quantify damage levels. Prognostics and health management (PHM) technique has been developed and applied for a variety of safety-critical engineering structures, given the critical needs of the structure health state awareness. The PHM performance highly relies on real-time sensory signals which convey the structural health relevant information. Designing an optimal structural sensor network (SN) with high detectability is thus of great importance to the PHM performance. This paper proposes a generic SN design framework using a detectability measure while accounting for uncertainties in material properties and geometric tolerances. Detectability is defined to quantify the performance of a given SN. Then, detectability analysis will be developed based on structural simulations and health state classification. Finally, the generic SN design framework can be formulated as a mixed integer nonlinear programming (MINLP) using the detectability measure and genetic algorithms (GAs) will be employed to solve the SN design optimization problem. A power transformer study will be used to demonstrate the feasibility of the proposed generic SN design methodology.
 
 

A Computational Approach for Model Update of an LS-DYNA Energy-Absorbing Cell

NASA and its contractors are working on structural concepts for absorbing impact energy of aerospace vehicles. Recently, concepts in the form of multi-cell honeycomb-like structures designed to crush under load have been investigated for both space and aeronautics applications. Efforts to understand these concepts are progressing from tests of individual cells to tests of systems with hundreds of cells. Because of fabrication irregularities, geometry irregularities, and material properties uncertainties, the problem of reconciling analytical models, in particular LS-DYNA models, with experimental data is a challenge. A first look at the correlation results between single cell load/deflection data with LS-DYNA predictions showed problems which prompted additional work in this area. This paper describes a computational approach that uses analysis of variance, deterministic sampling techniques, response surface modeling, and genetic optimization to reconcile test with analysis results. Analysis of variance provides a screening technique for selection of critical parameters used when reconciling test with analysis. In this study, complete ignorance of the parameter distribution is assumed and, therefore, the value of any parameter within the range that is computed using the optimization procedure is considered to be equally likely. Mean values from tests are matched against LS-DYNA solutions by minimizing the square error using a genetic optimization. The paper presents the computational methodology along with results obtained using this approach.

Moving on from Kirkpatrick (1994): estimating ‘safety factors’ for flying vertebrates

The most cited work (by far) to provide safety factor estimates for the wing bones of flying vertebrates is inaccurate. Kirkpatrick ([Kirkpatrick, 1994][1]) presented extremely low measurements for the material properties of wing bones and anomalous estimates of applied loading that deflate

Probabilistic Design Approach for Cyclic Fatigue Life Prediction of Microelectronic Interconnects

Deterministic approaches may predict the life of solder joint interconnects used in microelectronic devices far different from the test results and field environment. This difference is caused by uncertainties introduced in finite element and damage modeling with different random variables such as material properties, geometry, damage model constants, and many others. This paper presents a methodology to include these uncertainties in the life prediction approach for solder joint materials. The approach is implemented in predicting the life of ball grid array Pb-free solder joints under thermo-mechanical cyclic loading using the energy partitioning (E-P) damage model. The sensitivity of the finite element results to uncertainties in elastic and inelastic material properties are investigated using this probabilistic approach. In addition final life prediction sensitivity to uncertainties in damage model constants are studied and compared with the effect of uncertainties in material properties. The analyses show that from material properties, creep coefficient and activation energy are two factors that have significant effect in fluctuating the prediction results. Coefficient of thermal expansion was also found to have a strong effect. When compared with the damage model constants, material properties are found to have a negligible effect suggesting a more cautious use of the damage models and constants. Damage model exponents show a more significant effect than damage model coefficients.

Structural modeling uncertainties and their influence on seismic assessment of existing RC structures

The structural modeling uncertainty may be comparable to that of the ground motion representation in the seismic assessment of existing buildings. This work aims to characterize the uncertainties in material properties and in construction details and to propagate them to estimate the structural performance conditional on code-based seismic demand and capacity definitions. A prior probability distribution for the uncertain parameters is constructed based on the state of knowledge about the building before any in situ test is conducted. The uncertainties in the parameters are then propagated using simulation in order to obtain a probability distribution for structural resistance. The simulation-based methods allow for suitable grouping of uncertain parameters in order to build a simplified model of correlation across structural parameters. The results of tests and inspections are used both to update the prior probability distributions for parameters and also to update the structural reliability in a Bayesian framework. The updated probability distributions take into account the increased level of information eventually gathered as a results of destructive and/or non-destructive tests and inspections on the structure.

The Robust Optimization for Large-Scale Space Structures Subjected to Thermal Loadings

Large-scale space structures may experience unexpected thermal-elastic deformation due to thermal loadings in space. This thermal response could be minimized by using optimization method in design phase and the uncertainty of material properties should also be considered to ensure the reliable performance of the produced structure. For this purpose, the robust optimization is applied to this kind of structures in this paper. Firstly, a perturbation based stochastic finite element program is developed, which is tailored for the problem of thermal-elastic deformation of thin-walled structures subjected to incident thermal flux and energy emission through radiation. Based on this program, a robust design scheme is formulated as a two-objective optimization problem, in which all required sensitivities are calculated analytically. Then, the Pareto front of this problem is effectively determined by using the adaptive weighted sum method. Finally, numerical examples are presented to illustrate the validity and capability of this proposed method.

Effect of matrix cracking and material uncertainty on composite plates

A laminated composite plate model based on first order shear deformation theory is implemented using the finite element method. Matrix cracks are introduced into the finite element model by considering changes in the A, B and D matrices of composites. The effects of different boundary conditions, laminate types and ply angles on the behavior of composite plates with matrix cracks are studied. Finally, the effect of material property uncertainty, which is important for composite material on the composite plate, is investigated using Monte Carlo simulations. Probabilistic estimates of damage detection reliability in composite plates are made for static and dynamic measurements. It is found that the effect of uncertainty must be considered for accurate damage detection in composite structures. The estimates of variance obtained for observable system properties due to uncertainty can be used for developing more robust damage detection algorithms.

Stochastic homogenization analysis for thermal expansion coefficients of fiber reinforced composites using the equivalent inclusion method with perturbation-based approach

This paper describes a perturbation-based stochastic homogenization analysis method for a thermal expansion coefficient of a fiber reinforced composite material using the equivalent inclusion method. The proposed method is formulated for evaluation of the probabilistic characteristics of the homogenized thermal expansion coefficients considering uncertainties in material properties and geometry of a component material. As a numerical example, the probabilistic characteristics of the homogenized thermal expansion coefficients of a unidirectional fiber reinforced plastic are analyzed. With comparison between the results of the proposed method and the results of the Monte-Carlo simulation, validity, accuracy and effectiveness of the proposed method are investigated.

Statistical Applications and Stochastic Analysis for Performance-Related Specification of Asphalt Quality Assurance

Performance-related specification (PRS) is known as the most advanced specification type in asphalt pavement quality assurance (QA). One major feature of PRS QA is the consideration of material variability in performance prediction models through the application of several essential statistical techniques. The uncertainty in material properties can consequently be encoded in the evaluation of asphalt mix quality. For this reason, it is of critical significance to use the statistical applications correctly in PRS QA. One product of the NCHRP 9-22 project is a computerized quality assurance tool, quality-related specification software (QRSS). This computer program can quantitatively evaluate the as-constructed asphalt mix quality against the as-designed mix quality to predict service life. To quantify stochastically the quality of both the as-designed and as-built mixes with the consideration of material variability, several essential statistical techniques were applied to the QA procedure. This paper presents the techniques used and the applications implemented in the QRSS. It includes statistical methods to estimate variance of a multivariate function (e.g., Monte Carlo simulation and Rosenblueth method), conversion methods from distress to service life, expression of predicted distress as well as its service life by using probability distributions, and a method to quantify the relative difference in predicted service life between as-designed and as-constructed mixes with the use of cumulative frequency distributions.

Influence of Random Variation in Volume Fraction of Fiber on Stochastic Property of Equivalent Elastic Property of Unidirectional Fiber Reinforced Composite Material

This paper describes stochastic analysis on a homogenized elastic property of a unidirectional fiber reinforced composite material considering uncertainty in material and geometrical properties of component materials. The influence of the microscopic uncertainties on the stochastic characteristics of a homogenized elastic property is analyzed with the perturbation-based analysis using the equivalent inclusion method. Especially, influence of a volume fraction variation on the stochastic characteristics is discussed in this paper. Also, as an example of a design considering the influence of a volume fraction variation, a limit of the random variation of the volume fraction of fiber for controlling a random variation of a homogenized elastic property of a composite to be less than random variations of elastic properties of component materials is discussed.

Level set based robust shape and topology optimization under random field uncertainties

A robust shape and topology optimization (RSTO) approach with consideration of random field uncertainty in loading and material properties is developed in this work. The proposed approach integrates the state-of-the-art level set methods for shape and topology optimization and the latest research development in design under uncertainty. To characterize the high-dimensional random-field uncertainty with a reduced set of random variables, the Karhunen–Loeve expansion is employed. The univariate dimension-reduction (UDR) method combined with Gauss-type quadrature sampling is then employed for calculating statistical moments of the design response. The combination of the above techniques greatly reduces the computational cost in evaluating the statistical moments and enables a semi-analytical approach that evaluates the shape sensitivity of the statistical moments using shape sensitivity at each quadrature node. The applications of our approach to structure and compliant mechanism designs show that the proposed RSTO method can lead to designs with completely different topologies and superior robustness.