Uncertainties In Material Properties Research Articles

Modeling of frontal polymerization of carbon fiber and dicyclopentadiene woven composites with stochastic material uncertainty

A novel finite element modeling framework is proposed for simulating dicyclopentadiene (DCPD) frontal polymerization in carbon fiber (CF) woven composites. A mesoscale CF/DCPD representative volume element (RVE) model was developed with two triggering directions, resulting in out-of-plane and in-plane DCPD polymerization. The Arrhenius equation coupled with a modified Prout-Tompkins autocatalytic model was used to evaluate the dynamic DCPD polymerization process. The rate and degree of DCPD cure were calculated by the material property uncertainties of DCPD with and without random void inclusions (3 % used as a reference in this work). The DCPD frontal polymerization in CF/DCPD composite was strongly influenced by the triggering direction. In the RVE model considered in this work, DCPD frontal polymerization was slightly faster in the in-plane (warp/weft yarn) directions than the out-of-plane (thickness) direction; polymerization occurs first in DCPD resin and is followed by CF/DCPD interface. Material property uncertainty and void inclusion had significant effects on both out-of-plane and in-plane DCPD polymerization. A large variation in DCPD material properties and the presence of void inclusions significantly delayed the rate and degree of DCPD frontal polymerization. This work provides the preliminary estimation of the frontal polymerization of DCPD-based composites and guides the structural applications of these materials.

Robust design of a low cost flat plate collector under uncertain design parameters

The high expenses of electrical energy needed for heating water can be significantly decreased by using flat plate collectors. Therefore, the design of flat plate collectors having optimal performance has received a lot of attention in recent research projects. However, due to the existence of uncertainties in material properties, geometry and environmental conditions, it is imperative to incorporate uncertainty analysis into the design optimization to obtain reliable results. In this work, a multi-criteria robust design based on multi-objective optimization of the flat plate collector system is developed. Firstly, a determinist optimization (non-consideration of uncertain design parameters in this optimization strategy) of flat plate collector design is conducted. The obtained results showed that the determinist optimization leads to a flat plate collector design with 30% efficiency sensitivity and 27% total cost sensitivity to design parameters uncertainty. As an alternative, the multi-criteria robust design based on multi-objective optimization is developed. For this goal, a combined multi-objective colonial competitive algorithm and polynomial chaos expansion method is developed and used. This multi-criteria robust optimization considers simultaneously four objectives functions including the flat plate collector efficiency, the flat plate collector total cost, and their sensitivities to uncertain design parameters. It is noted that the multi-criteria robust design based on multi-objective optimization offers a robust flat plate collector with performances sensitivity to design parameters uncertainty less than 4.5%. Furthermore, when compared to the literature results, the performances sensitivities of flat plate collector design, obtained by the multi-criteria robust design based on multi-objective optimization, were reduced until 64%.

Fragility curves accounting for uncertainties in material parameters and ground motion characteristics using a data driven surrogate model

This study uses a statistical surrogate model to develop fragility curves for an infilled reinforced concrete frame building, considering uncertainties in both material properties and ground motion parameters. The focal point of this study is a school building in Nepal damaged during the 2015 Gorkha earthquake. The school was instrumented, and its seismic response was simulated using a nonlinear numerical model. The model, developed following a recently proposed framework and extensively validated with the field data, is used in a parametric study conducted to identify the most influential material parameters (MPs). The model is then used in incremental dynamic analyses conducted to provide data for the calibration of a surrogate model. The three-staged least square statistical modeling approach is adopted to relate the influential MPs and ground motion intensity measures with important response quantities related to the peak and residual first-story drift ratios. The surrogate model is employed to generate fragility curves accounting for the two sources of uncertainty. The results indicate that accounting for uncertainties associated with the MPs can alter the fragility curves, causing a shift in the prediction of the median and dispersion of intensity measures.

Stochastic virtual element methods for uncertainty propagation of stochastic linear elasticity

This paper presents stochastic virtual element methods for propagating uncertainty in linear elastic stochastic problems. We first derive stochastic virtual element equations for 2D and 3D linear elastic problems that may involve uncertainties in material properties, external forces, boundary conditions, etc. A stochastic virtual element space that couples the deterministic virtual element space and the stochastic space is constructed for this purpose and used to approximate the unknown stochastic solution. Two numerical frameworks are then developed to solve the derived stochastic virtual element equations, including a Polynomial Chaos approximation based approach and a weakly intrusive approximation based approach. In the Polynomial Chaos based framework, the stochastic solution is approximated using the Polynomial Chaos basis and solved via an augmented deterministic virtual element equation that is generated by applying the stochastic Galerkin procedure to the original stochastic virtual element equation. In the weakly intrusive approximation based framework, the stochastic solution is approximated by a summation of a set of products of random variables and deterministic vectors, where the deterministic vectors are solved via converting the original stochastic problem to deterministic virtual element equations by the stochastic Galerkin approach, and the random variables are solved via converting the original stochastic problem to one-dimensional stochastic algebraic equations by the classical Galerkin procedure. This method avoids the curse of dimensionality in high-dimensional stochastic problems successfully since all random inputs are embedded into one-dimensional stochastic algebraic equations whose computational effort weakly depends on the stochastic dimension. Numerical results on 2D and 3D problems with low- and high-dimensional random inputs demonstrate the good performance of the proposed methods.

Multi-hazard assessment of transmission line systems subjected to independent non-concurrent turbulent winds and ground accelerations

The design of transmission lines is based on the Load and Resistance Factor Design approach, considering that their collapse limit state is governed by climatic actions (wind and ice). Even so, accident reports indicate the regular observation of moderate to severe damage of towers after strong ground motions, affecting the structure’s capacity to withstand future load events. Therefore, integrating the concepts of Performance-Based and Multi-Hazard Design, successfully applied to buildings and still embryonic to transmission lines, seems to be promising. With such performance-based multi-hazard approaches, intermediate performances can be evaluated even when they are controlled by a non-dominant hazard. Hence, the present paper aims at performing an original multi-hazard assessment of a Chilean 230kV transmission line segment. For this purpose, direct geometric and material nonlinear time history analysis, using a finite element suitable for eccentrically loaded angle profiles (L-shaped cross-sections), is employed to construct the fragility curves. In addition, uncertainties in loads and material properties are accounted for to address the transmission line system failure probability. In the existing literature, fragility analysis has been performed through pushover approaches, whereas reliability has been assessed for a single structure rather than for the transmission line system, as recommended by line codes. Contrary to design practice, the results show that seismic loads control all limit states in TLs located from central to northern Chile. Numerical results presented in this paper are based on 5000 h of total computation time.

Optimising the inherent fire capacity of structures

This paper introduces a structural design optimisation methodology aimed at minimising the consequences of a fire. The methodology considers the trade-off between implementing passive fire protection measures and enhancing a structure’s “inherent fire capacity”, defined as its ability to retain integrity/functionality without additional fire safety measures. The feasibility of the methodology is demonstrated through the fire safety design of a single-span, steel girder bridge. The optimisation process generates multiple Pareto-optimal solutions for minimising the maximum bridge deflection after a given fire exposure time. Passive protection ensures the bridge’s functionality when facing a heavy goods vehicle fire. In the case of exposure to a car fire, solutions requiring fire protection in specific limited girder regions are identified. The decision-making process is further supported by investigating the robustness of the solutions to uncertainties in material properties and the heat flux model.

Bayesian parameter estimation for the inclusion of uncertainty in progressive damage simulation of composites

Despite gradual progress over the past decades, the simulation of progressive damage in composite laminates remains a challenging task, in part due to inherent uncertainties of material properties. This paper combines three computational methods — finite element analysis (FEA), machine learning and Markov Chain Monte Carlo — to estimate the probability density of FEA input parameters while accounting for the variation of mechanical properties. First, 15,000 FEA simulations of open-hole tension tests are carried out with randomly varying input parameters by applying continuum damage mechanics material models. This synthetically-generated data is then used to train and validate a neural network consisting of five hidden layers and 32 nodes per layer to develop a highly efficient surrogate model. With this surrogate model and the incorporation of statistical test data from experiments, the application of Markov Chain Monte Carlo algorithms enables Bayesian parameter estimation to learn the probability density of input parameters for the simulation of progressive damage evolution in fibre reinforced composites. This methodology is validated against various open-hole tension test geometries enabling the determination of virtual design allowables.

Stochastic analysis of semi-rigid steel frames using a refined plastic-hinge model and Latin hypercube sampling

This paper proposes a stochastic analysis model that combines the refined plastic-hinge analysis method with the Monte Carlo simulation to predict the realistic resistance of steel structures. The model treats the uncertainty quantifications of the material properties, geometry, and semi-rigid connections as independent random variables in the discretized stochastic fields using Latin hypercube sampling. The critical resistance of the structures in each simulation is determined using the general displacement control method and advanced analysis algorithms. The statistical approach is employed to compute the mean values and the standard deviation of the load-carrying capacity of the steel frames. The study finds that the uncertainties in material properties are the most sensitive, and the correlation of these parameters with the strength of structures is also significant. To improve the load and resistance factor design criterion, a resistance factor of 0.93 is suggested for the beam-columns in the frames under axial force, torsion, and biaxial bending moments. A stochastic response spectrum is proposed to define the boundary of strength, where a clearly defined plastic mechanism is attained. Furthermore, this study provides valuable insights into the stochastic resistance of steel frames, which are essential for practical engineering applications.

Effect of Intraluminal Thrombus Burden on the Risk of Abdominal Aortic Aneurysm Rupture.

Abdominal aortic aneurysm (AAA) is a critical health disorder, where the abdominal aorta dilates more than 50% of its normal diameter. Enlargement in abdominal aorta alters the hemodynamics and flow-induced forces on the AAA wall. Depending on the flow conditions, the hemodynamic forces on the wall may result in excessive mechanical stresses that lead to AAA rupture. The risk of rupture can be predicted using advanced computational techniques such as computational fluid dynamics (CFD) and fluid-structure interaction (FSI). For a reliable rupture risk assessment, formation of intraluminal thrombus (ILT) and uncertainty in arterial material properties should be taken into account, mainly due to the patient-specific differences and unknowns in AAAs. In this study, AAA models are computationally investigated by performing CFD simulations combined with FSI analysis. Various levels of ILT burdens are artificially generated in a realistic AAA geometry, and the peak effective stresses are evaluated to elucidate the effect of material models and ILT formation. The results indicate that increasing the ILT burden leads to lowered effective stresses on the AAA wall. The material properties of the artery and ILT are also effective on the stresses; however, these effects are limited compared to the effect of ILT volume in the AAA sac.

An Interval Prediction of Chloroprene Rubber Crack Propagation Characteristics Based on Thermal Accelerated Aging.

Thermo-oxidative aging plays an important role in changing the properties of rubber materials; it significantly decreases the fatigue life of air spring bags and further causes safety hazards. However, due to the great uncertainty of rubber material properties, an effective interval prediction model has not been established considering the effect of aging on airbag rubber properties. To solve the problem, this study proposes an interval parameter correlation model that can more accurately describe rubber crack propagation characteristics by considering material uncertainty. Furthermore, an aging prediction model of the rubber crack propagation characteristic region is established based on the Arrhenius equation. The effectiveness and accuracy of the method are verified by comparing the test and prediction results under the temperature spectrum. The method can be used to determine the variations in the interval change of the fatigue crack propagation parameters during rubber aging and can guide fatigue reliability analyses of air spring bags.

Uncertainty quantification in free vibration and aeroelastic response of variable angle tow laminated composite plate

The influence of uncertainty in material properties on free vibration and aeroelastic response of variable angle tow (VAT) laminated plates is presented in this work. Free vibration analysis is conducted by a finite element model based on third-order shear deformation theory. The FE model is further coupled with MSC. Nastran to carry out aeroelastic analysis of VAT laminates in the subsonic regime. MSC. Nastran helps to extract the aerodynamic influence coefficient matrix at discrete values of reduced frequencies using Doublet Lattice Method. The accuracy and adaptability of the highly efficient radial basis neural network (RBFN) based surrogate model developed for uncertainty analysis are checked by comparing the result with that of the Monte Carlo simulation. Stochastic analysis of natural frequencies and flutter characteristics of VAT laminates are conducted through various parametric studies. Variance-based sensitivity analysis is used to calculate the contribution of individual material properties to the free vibration and aeroelastic response of VAT laminates. Further, the influence of the highly sensitive properties on the structural failure probability is estimated. This research can be leveraged to predict the probability of failure of the structure at different levels of material uncertainty present in it.

Uncertainty quantification of wood floor system modal frequencies resulting from variable densities in members

Low-frequency vibration in a multi-story wood building is of concern because failure in mitigation of such vibration may lead to occupant discomfort. Ultimately, it may cause damage to their health. Variability in material properties of the members of a wooden floor system significantly influences vibration response characteristics such as eigenfrequencies and mode shapes. In this study, we investigate the uncertainty in low-frequency characteristics of a selected wood floor system, resulting from uncertainty in the members’ material properties. We use a surrogate model developed using polynomial chaos expansion, based on a few training samples computed using a finite element model of an experimental-scale structure comprised of seven load-bearing joists of spruce. We estimate the hyperparameters needed for accurate surrogate model development and, with these, we predict probability distributions for each of the floor-system modal frequencies. Also, we perform local and global sensitivity analyses to assess how material property variation affects the modal frequencies. Results confirm the accuracy and efficiency of the developed surrogate models in prediction of the modal frequencies, resulting from uncertainty in wood material properties. The accuracy of the results is comparable to those based on more expensive Monte Carlo simulation.

Stochastic approach for remaining fatigue life prediction considering parametric distributions

AbstractIn the present work, a stochastic framework, which combines the well‐recognized linear damage rule (LDR) and the uncertainty of material properties under constant amplitude loading, is proposed to improve the accuracy in prediction of remaining fatigue life. The uncertainty quantification approach based on parametric statistics is employed together with the Monte‐Carlo simulation method for modeling the randomness of remaining fatigue life. The impact of several commonly‐used parametric statistics is investigated, and the pertinent one is identified utilizing the Kullback‐Leibler divergence. The proposed framework is validated through the use of experimental fatigue life data under two‐step loading test.

Effect of structural repairs on the load rating and reliability of a prestressed concrete bridge

Prestressed girders often deteriorate over time due to environmental and man-made stressors, lowering the strength and serviceability of bridge structures. Although structural repairs are implemented to improve the load carrying capacity of the structure, the presence of numerous unknowns leads to high uncertainty in estimating the adequacy of repairs. For instance, the cross-section of the remaining strands, material properties, applied external loads, and workmanship assumptions made throughout the repair process introduce ambiguities when estimating the adequacy of the repairs. This study evaluates the efficiency of re-tensioning repairs of prestressed concrete bridge span girders. The repairs include field splicing, re-tensioning, of deteriorated or damaged strands by torquing a splicing coupler. The evaluation in this study considers component, system reliability, and load ratings while accounting for several uncertainties, such as structural repair, material properties, and external loads. This paper introduces an approach to account for prestressing strands damage and repair uncertainties while also accounting for other uncertainties. In this regard, five cases are studied: as-built, repaired, and three varying degrees of damage cases. First, the distribution for structural demand and capacity accounting for uncertainty in loads, material properties, and repair process is defined for each girder in the prestressed concrete bridge span. In doing so, Monte-Carlo simulation is employed to determine the distributions. Accordingly, the limit state function of the girders is defined from the obtained distributions. Then, the component reliability of each AASHTO (American Association of State Highway and Transportation Officials) Type II girder is calculated from the obtained reliability indices based on the determined limit state functions. Finally, a system reliability model of the span is developed from the component reliability of each girder. Some advantages and disadvantages of using component and system reliability index versus load rating in damaged and repaired prestressed concrete bridge girders are also discussed. Several critical conclusions are made regarding the uncertainties in structural repair, material properties and external loads, and their impact on the load rating and the component and system reliability of the prestressed concrete bridge structure girders.

Optimal Intensity Measures for Probabilistic Seismic Stability Assessment of Large Open-Pit Mine Slopes under Different Mining Depths

The dynamic stability of slopes is the key to ensure the safety of a large open-pit mine during and after a strong earthquake. This study was mainly focused on the identification of optimal intensity measures (IMs) for the probabilistic seismic stability assessment of large open-pit mine slopes within the framework of performance-based earthquake engineering (PBEE). To this end, four open-pit slopes with different mining depths were constructed as the reference cases for the numerical investigation. The randomness of input ground motions and the uncertainty of material properties of the slopes were also considered. A total of 96 ground-motion records and 29 common IMs were selected for testing. By a series of nonlinear time-history analyses, the probabilistic seismic demand models (PSDMs) between the minimum factor of safety (FOS) of slopes and all considered IMs were developed. The optimal IMs with respect to FOS were identified based on the evaluation of five criteria: correlation, efficiency, practicality, proficiency, and sufficiency. The impacts on seismic fragility and FOS response hazard of the slopes were discussed when using different IMs. The results reveal that sustained maximum velocity (SMV) and velocity spectrum intensity (VSI) are recognized as the optimal IM for a mining depth of 50 m and 100 m, respectively. However, Housner intensity (HI) is observed to have the best predictability for both the mining depths of 200 m and 300 m. Moreover, for the three most commonly used IMs, peak ground velocity (PGV) is superior to peak ground acceleration (PGA) and spectral acceleration at first mode period (Sa (T1)) for different mining depths. Finally, based on the evaluations of seismic fragility and FOS response hazard, the uncertainty of seismic stability prediction of open-pit slopes can be greatly reduced when using a more appropriate or optimal IM.

Performance-Based Characterization and Quantification of Uncertainty in Damage Plasticity Model for Seismic Fragility Assessment of Concrete Structures

Seismic probabilistic risk assessment requires explicit consideration and quantification of all sources of uncertainty. Although uncertainties in earthquakes and basic material properties, such as nominal concrete compressive strength, strain at maximum stress, and modulus of elasticity of concrete, have been considered in some studies, uncertainties in parameters used to model the nonlinear behavior of concrete are often not considered. Recent recommendations in design standards have incorporated performance-based limit states in the design and risk assessment of nuclear power plants. These recommendations have implicitly mandated that the uncertainty in the nonlinear behavior of concrete needs to be characterized and quantified in accordance with different performance limit states. This study focused on nonlinear model parameters in the concrete damage plasticity model (CDPM) and their characterization in terms of material strength parameters. Furthermore, a performance-based characterization and quantification of uncertainties in nonlinear model parameters was also conducted. Data from existing experimental studies were used to study the uncertainties in CDPM and were used as a basis for the proposed quantification.

High dimensional model representation for flood fragility analysis of highway bridge

Climate changes and global warming have increased the frequency and severity of rains, hence the vulnerability of structures due to floods. Bridges are the most affected components of the transportation infrastructure affected by floods. Analysis in a probabilistic framework is required for reliable performance assessments of bridges. However, the detailed performance assessment of bridges requires consideration of the uncertainties in geometry, material properties, and flood loading. The random structural responses due to flood loading can be obtained by stochastic analysis; conventionally, this is carried out using Monte Carlo Simulations (MCS). Due to the high computational cost required for MCS, non-statistical methods like High Dimensional Model Representation (HDMR) can be a feasible alternative to MCS. The present study is an application of the HDMR method to develop metamodels for the flood response of the highway bridge, considering the uncertainties. The structural responses due to flood at the sampling points of the HDMR are obtained by conducting finite element analysis. The HDMR could predict the random bridge responses due to flood loading fairly well compared to other popular response surface methods (like Central Composite Design, Box Behnken Design, and Full Factorial Design) with significantly fewer simulations. HDMR provides a flood response metamodel, as a function of the sensitive random parameters, with a substantial reduction in the computational effort. The efficiency of the HDMR method can be attributed to the ability of HDMR to model the nonlinear flood responses in terms of the statistical properties of random variables. The metamodels for the pier drifts developed are further utilized to generate flood fragility curves. The HDMR metamodels are found to simplify the fragility computations.

On Propagation of Material Property Uncertainty Through Signal Energy-Based Acoustic Source Localization in an Orthotropic Plate

Abstract A framework for quantifying the uncertainty propagating through the signal energy-based acoustic source localization approach in an orthotropic plate under an uncertainty in the properties of the plate material is presented. Seven mechanical properties of an orthotropic plate material, namely, density and six elastic constants, are considered as lognormally distributed and mutually independent random variables (RVs) with a fixed coefficient of variation for all seven random variables. Their means are considered such that the “mean” plate exhibits a strong anisotropy. Using Latin hypercube sampling, several design points in lognormal spaces of these random variables are selected. For each design point, an acoustic event is simulated in the corresponding plate using finite element analyses. The signal energy-based approach is applied to localize the acoustic source for each design point. The localization error for each design point is taken as the “response,” and a regression kriging metamodel is constructed through these response values at the design points. Monte Carlo (MC) points are selected in lognormal spaces of the random variables, and the response values at these Monte Carlo points are estimated using the regression kriging metamodel. The distribution parameters of the so-obtained response values are computed. Finally, a global sensitivity analysis of the random variables is carried out by computing the Sobol’ indices.

Reliability analysis of damage prediction in asphalt pavement sections using FlexPAVETM program and S-VECD fatigue model

ABSTRACT With mechanistic and mechanistic-empirical modelling of pavement performance there are a considerable number of uncertainties that are inherent in the prediction process. Many of these sources of uncertainty are challenging to quantify, but one that is technically possible to evaluate is the effect of uncertainty in the characterisation and modelling of the mechanical properties of the asphalt concrete. In this study, the Bayesian inference-based Markov Chain Monte Carlo (MCMC) was used to estimate how uncertainties from the simplified viscoelastic continuum damage (S-VECD) model parameters propagate to pavement performance simulation errors in the FlexPAVETM program. Performance predictions were evaluated based on the propagation of three different material parameter uncertainties; (1) modulus, (2) damage characteristic curves, and (3) failure criterion. These factors were systematically varied according to chosen reliability levels and using data from real-world experimental data on different asphalt mixtures. High-performance computing resources were then used to predict pavement performance on the thousands of different combinations of material property uncertainty, and a simplified prediction algorithm was developed to more easily estimate the uncertainty. The results show that the simplified uncertainty prediction model could estimate the reliability of the damage and cracking predictions from FlexPAVETM within 1.2% and 4.8%, respectively.

Influence of material uncertainties on thermo-elastic vibration characteristics of graphene reinforced functionally graded porous beams

This paper aims to study the influence of material uncertainties on thermo-elastic vibration response of functionally graded porous (FGP) beams reinforced with graphene platelets (GPLs) using the perturbation-based stochastic finite element method. The influence of material uncertainty on the vibration behavior of FGP-GPL reinforced beams subjected to thermal loading conditions have been discussed for low variability (randomness) in material design parameters (porosity content, amount of nanofillers) and material properties (Young’s modulus, density of metal matrix, and nanofillers) respectively. A C0 continuous stochastic finite element formulation based on higher-order shear deformation theory has been formulated. The convergence and validation of the present formulation have been compared with a traditional Monte-Carlo simulation to establish the accuracy of the present methodology. The homogenized effective material properties are estimated using the Halpin-Tsai micromechanics model and Voigt’s rule of mixture and are typically assumed to be varying along the thickness direction. The results highlighting the effect of uncertainty in material properties on the thermo-elastic vibration response of FGP-GPL reinforced beams have been discussed thoroughly.