Finite Element-based Reliability Analysis Research Articles

Finite element-based reliability analysis of RC bridge piers subjected to the combination of barge impact and blast loads

In this paper, the reliability analysis of a girder bridge pier is presented when exposed to the combinations of barge collision and blast loads based on the finite element (FE) simulations performed in LS-DYNA and the Monte Carlo algorithm performed in MATLAB. An improved reliability analysis approach is proposed for the bridge pier under combined loads using the residual dynamic resistance capacities of the impacted bridge pier when subjected to sequential blast loading rather than utilizing the static resistance capacities of the pier columns which are commonly employed by conventional fault tree analysis. In the first step of the proposed framework, the response surface method (RSM) using the Box-Behnken design (BBD) method is employed for fitting the structural response surfaces and the internal forces of the pier columns obtained from the FE simulations. Then, the reliability analysis results including the failure probability (Pf) and corresponding reliability index (β) are calculated using the Monte Carlo algorithm in MATLAB. Finally, the sensitivities of Pf and β to various barge collision and blast loading parameters are assessed, and fragility curves are plotted for the reliability analysis results. From the reliability analysis of the pier under combined loads, it is found that the failure probabilities of the pier resulting from the proposed method are greater than those from the conventional method based on the static capacities of the pier. Therefore, the conventional static-based method provides an unconservative approach and the residual dynamic capacities of the impacted and damaged pier should be considered under the sequential blast loading for reliability analysis of the pier under combined loads.

Efficient reliability analysis of structures with the rotational quasi-symmetric point- and the maximum entropy methods

This paper presents a new method for efficient structural reliability analysis. In this method, a rotational quasi-symmetric point method (RQ-SPM) is proposed for evaluating the fractional moments of the performance function. Then, the derivation of the performance function’s probability density function (PDF) is carried out based on the maximum entropy method in which constraints are specified in terms of fractional moments. In this regard, the probability of failure can be obtained by a simple integral over the performance function’s PDF. Six examples, including a finite element-based reliability analysis and a dynamic system with strong nonlinearity, are used to illustrate the efficacy of the proposed method. All the computed results are compared with those by Monte Carlo simulation (MCS). It is found that the proposed method can provide very accurate results with low computational effort.

Stochastic multi-scale finite element based reliability analysis for laminated composite structures

This paper proposes a novel multi-scale approach for the reliability analysis of composite structures that accounts for both microscopic and macroscopic uncertainties, such as constituent material properties and ply angle. The stochastic structural responses, which establish the relationship between structural responses and random variables, are achieved using a stochastic multi-scale finite element method, which integrates computational homogenisation with the stochastic finite element method. This is further combined with the first- and second-order reliability methods to create a unique reliability analysis framework. To assess this approach, the deterministic computational homogenisation method is combined with the Monte Carlo method as an alternative reliability method. Numerical examples are used to demonstrate the capability of the proposed method in measuring the safety of composite structures. The paper shows that it provides estimates very close to those from Monte Carlo method, but is significantly more efficient in terms of computational time. It is advocated that this new method can be a fundamental element in the development of stochastic multi-scale design methods for composite structures.

Stochastic finite element based reliability analysis of steel fiber reinforced concrete (SFRC) corbels

In this study, reliability analyses of steel fiber reinforced concrete (SFRC) corbels based on stochastic finite element were performed for the first time in literature. Prior to stochastic finite element analysis, an experimental database of 84 sfrc corbels was gathered from literature. These sfrc corbels were modeled by a special finite element program. Results of experimental studies and finite element analysis were compared and found to be very close to each other. Furthermore experimental crack patterns of corbel were compared with finite element crack patterns and were observed to be quite similar. After verification of the finite element models, stochastic finite element analyses were implemented by a specialized finite element module. As a result of stochastic finite element analysis, appropriate probability distribution functions (PDF's) were proposed. Finally, coefficient of variation, bias and strength reduction (resistance) factors were proposed for sfrc corbels as a consequence of stochastic based reliability analysis.

Stochastic finite element based reliability analysis of steel fiber reinforced concrete (SFRC) corbels

In this study, reliability analyses of steel fiber reinforced concrete (SFRC) corbels based on stochastic finite element were performed for the first time in literature. Prior to stochastic finite element analysis, an experimental database of 84 sfrc corbels was gathered from literature. These sfrc corbels were modeled by a special finite element program. Results of experimental studies and finite element analysis were compared and found to be very close to each other. Furthermore experimental crack patterns of corbel were compared with finite element crack patterns and were observed to be quite similar. After verification of the finite element models, stochastic finite element analyses were implemented by a specialized finite element module. As a result of stochastic finite element analysis, appropriate probability distribution functions (PDF\'s) were proposed. Finally, coefficient of variation, bias and strength reduction (resistance) factors were proposed for sfrc corbels as a consequence of stochastic based reliability analysis.

Wavelet density-based adaptive importance sampling method

This paper presents a new importance sampling method for efficient structural reliability assessment. The method utilizes the adaptive Markov chain simulation to generate samples that can adaptively populate the important region. The importance sampling density is then constructed using nonparametric wavelet density estimation technique. This approach takes advantage of the attractive properties of the Daubechies’ wavelet family (e.g., localization, various degrees of smoothness, and fast implementation) to provide good density estimations. Four examples including a finite element-based reliability analysis are given to demonstrate the proposed method. Comparisons of the new method and the classical kernel-based importance sampling are made.

Stochastic Finite Element Based Reliability Analysis of Concrete Structures in Marine Environment

The stochastic model of chloride diffusion is the foundation of evaluating concrete structures’ reliability in marine environment. In this paper, the random field of chloride diffusion coefficient was described as a group of random variables by local average theory. The chloride distribution matrix, diffusion matrix and nodal concentration vector were expanded by using the Taylor series. The stochastic finite element method was developed, and the mean and standard deviation of the chloride distribution concentration were yielded by the presented method. A numerical example demonstrated the high precision of the stochastic finite element method presented, and the service life of concrete structures could be predicted by the method.

Interval Monte Carlo methods for structural reliability

This paper considers structural reliability assessment when statistical parameters of distribution functions can not be determined precisely due to epistemic uncertainty. Uncertainties in parameter estimates are modeled by interval bounds constructed from confidence intervals. Reliability analysis needs to consider families of distributions whose parameters are within the intervals. Consequently, the probability of failure will vary in an interval itself. To estimate the interval failure probability, an interval Monte Carlo method has been developed which combines simulation process with the interval analysis. In this method, epistemic uncertainty and aleatory uncertainty are propagated separately through finite element-based reliability analysis. Interval finite element method is utilized to model the ranges of structural responses accurately. Examples are presented to compare the interval estimates of limit state probability obtained from the proposed method and the Bayesian approach.

Applications of Meta-Models in Finite Element Based Reliability Analysis of Engineering Structures

The problem of reliability analysis of randomly parametered, linear (or) nonlinear, structures Subjected to static and (or) dynamic loads is considered. A deterministic finite element model for the structure to analyze sample realization of the structure is assumed to be available. The reliability analysis is carried out within the framework of response surface methods which involves the construction of surrogate models for performance functions to be employed in reliability calculations. This construction, in the present study, has involved combining space filling optimal Latin hypercube sampling, kriging models and methods from data-based asymptotic extreme value modeling of sequence of random variables. Illustrative examples on numerical prediction of reliability of a ten-bay truss, a W-seal in an aircraft structure, and a nonlinear randomly parametered dynamical system are presented. Limited Monte Carlo simulations are used to validate the approximate procedures developed.

SFEM-based seismic risk analysis of nonlinear structures using sequential RSM

A finite element-based reliability analysis approach is proposed to estimate the risk of structures under short duration dynamic loadings including seismic loading in the time domain. The proposed approach is parallel to the deterministic finite element method, except that it can incorporate the information on the uncertainty in the essential variables present in the problem under consideration. In the algorithm, the incorporation of uncertainties of all the seismic loading and resistance-related parameters is successfully accomplished by using the concepts of response surface method, the first-order reliability method, and an iterative linear interpolation scheme. Therefore, the rational integration of these methods with a finite element formulation leads to the stochastic finite element-based algorithm. It is capable of capable of capturing any special features that can be handled by the finite element method, making it a robust reliability assessment technique. One of its distinguishing features is that actual earthquake loading time histories can be used to excite structures so that the realistic loading conditions can be simulated. Furthermore, it has the potential to estimate the risk associated with both the serviceability and the strength limit states. The algorithm has been extensively verified using the Monte Carlo simulation technique. Although two examples are given for the steel frame building structure in this paper, applicability of the proposed approach can be easily extended to other types of structures.

Stochastic finite element-based reliability analysis of space frames

In the present paper the weighted integral method in conjunction with Monte Carlo simulation is used for the stochastic finite element-based reliability analysis of space frames. The limit state analysis required at each Monte Carlo simulation is performed using a non-holonomic step-by-step elasto-plastic analysis based on the plastic node method in conjunction with efficient solution techniques. This implementation results in cost effective solutions both in terms of computing time and storage requirements. The numerical results presented demonstrate that this approach provides a realistic treatment for the stochastic finite element-based reliability analysis of large scale three-dimensional building frames.

Practical random field discretization in stochastic finite element analysis

Stochastic finite element-based reliability analysis is applied to structures with distributed parameters that can be modeled as random fields. In this method, reliability is estimated through analytical computation of the sensitivity of stochastic response to the basic random variables. The random fields are discretized into sets of correlated random variables using two methods of discretization. The sensitivity measures are further used to selectively consider only a few of the distributed parameters as random fields, to ensure computational efficiency. The issue of choosing the appropriate mesh for the discretization of the random field is addressed through mesh refinement studies. With the help of three numerical examples, the paper examines the effects of the correlation characteristics of the random field on discretization and reliability analysis, and develops guidelines for efficient application of stochastic finite element analysis to structures with distributed parameters.