• Structural Engineering and Mechanics
• /
• v.62 no.6
• /
• pp.703-708
• /
• 2017

The goal of this study is to evaluate behavior uncertainties of structures by using interval finite element analysis based on interval factor method as a specific non-stochastic tool. The interval finite element method, i.e., interval FEM, is a finite element method that uses interval parameters in situations where it is not possible to get reliable probabilistic characteristics of the structure. The present method solves the uncertainty problems of a 2D solid structure, in which structural characteristics are assumed to be represented as interval parameters. An interval analysis method using interval factors is applied to obtain the solution. Numerical applications verify the intuitive effectiveness of the present method to investigate structural uncertainties such as displacement and stress without the application of probability theory.

• Smart Structures and Systems
• /
• v.19 no.4
• /
• pp.431-439
• /
• 2017

This investigation is aimed to develop a model of experimental-computation determination of a support moment of a cantilever beam loaded with concentrated force at its end including the optimal choice of coordinates of deflection data points and parameters of transformation of deflection data in case of insufficient accuracy of the assignment of initial parameters (support settlement, angle of rotation of the bearing section) and cantilever beam length. The influence of distribution and characteristics of sensors on the cantilever beam on the accuracy of determining the support moment which improves in the course of transition from the uniform distribution of sensors to optimal non-uniform distribution is shown. On the basis of the theory of inverse problems the method of transformation reduction at numerical differentiation of deflection functions has been studied. For engineering evaluation formulae of uncertainty estimate to determine a support moment of a cantilever beam at predetermined uncertainty of measurements using sensors have been obtained.

• Structural Engineering and Mechanics
• /
• v.53 no.6
• /
• pp.1127-1141
• /
• 2015

The optimum design of liquid column dampers in seismic vibration control considering system parameter uncertainty is usually performed by minimizing the unconditional response of a structure without any consideration to the variation of damper performance due to uncertainty. However, the system so designed may be sensitive to the variations of input system parameters due to uncertainty. The present study is concerned with robust design optimization (RDO) of liquid column vibration absorber (LCVA) considering random system parameters characterizing the primary structure and ground motion model. The RDO is obtained by minimizing the weighted sum of the mean value of the root mean square displacement of the primary structure as well as its standard deviation. A numerical study elucidates the importance of the RDO procedure for design of LCVA system by comparing the RDO results with the results obtained by the conventional stochastic structural optimization procedure and the unconditional response based optimization.

• Geomechanics and Engineering
• /
• v.3 no.2
• /
• pp.153-167
• /
• 2011

Traditional design methods of bearing capacity of shallow foundations are deterministic in the sense that they do not explicitly consider the inherent uncertainty associated with the factors affecting bearing capacity. To account for such uncertainty, available deterministic methods rather employ a fixed global factor of safety that may lead to inappropriate bearing capacity predictions. An alternative stochastic approach is essential to provide a more rational estimation of bearing capacity. In this paper, the likely distribution of predicted bearing capacity of strip footings subjected to vertical loads is obtained using a stochastic approach based on the Monte Carlo simulation. The approach accounts for the uncertainty associated with the soil shear strength parameters: cohesion, c, and friction angle, ${\phi}$, and the cross correlation between c and ${\phi}$. A set of stochastic design charts that assure target reliability levels of 90% and 95%, are developed for routine use by practitioners. The charts negate the need for a factor of safety and provide a more reliable indication of what the actual bearing capacity might be.

• Smart Structures and Systems
• /
• v.26 no.3
• /
• pp.311-318
• /
• 2020

The goal of this study is to analytically and non-stochastically generate structural uncertainty behaviors of isotropic beams and laminated composite plates under plane stress conditions by using an interval finite element method. Uncertainty parameters of structural properties considering resistance and load effect are formulated by interval arithmetic and then linked to the finite element method. Under plane stress state, the isotropic cantilever beam is modeled and the laminated composite plate is cross-ply lay-up [0/90]. Triangular shape with a clamped-free boundary condition is given as geometry. Through uncertainties of both Young's modulus for resistance and applied forces for load effect, the change of structural maximum deflection and maximum von-Mises stress are analyzed. Numerical applications verify the effective generation of structural behavior uncertainties through the non-stochastic approach using interval arithmetic and immediately the feasibility of the present method.

• Structural Engineering and Mechanics
• /
• v.78 no.5
• /
• pp.529-543
• /
• 2021

Inevitable source-uncertainties in geometry configuration, boundary condition, and material properties may deviate the structural dynamics from its expected responses. This paper aims to examine the influence of these uncertainties on the vibration of functionally graded beams. Finite element procedures are presented for Timoshenko beams and utilized to generate reliable datasets. A prerequisite to the uncertainty quantification of the beam vibration using Monte Carlo simulation is generating large datasets, that require executing the numerical procedure many times leading to high computational cost. Utilizing artificial neural networks to model beam vibration can be a good approach. Initially, the optimal network for each beam configuration can be determined based on numerical performance and probabilistic criteria. Instead of executing thousands of times of the finite element procedure in stochastic analysis, these optimal networks serve as good alternatives to which the convergence of the Monte Carlo simulation, and the sensitivity and probabilistic vibration characteristics of each beam exposed to randomness are investigated. The simple procedure presented here is efficient to quantify the uncertainty of different stochastic behaviors of composite structures.

• Structural Engineering and Mechanics
• /
• v.25 no.3
• /
• pp.275-289
• /
• 2007

In this paper a brief overview of methods to assess the reliability of mechanical systems and structures is presented. A selection of computational procedures, stochastic structural dynamics, stochastic fatigue crack growth and reliability based optimization are discussed. It is shown that reliability based methods may form the basis for a rational decision making.

• Structural Monitoring and Maintenance
• /
• v.3 no.4
• /
• pp.349-375
• /
• 2016

The tension of an arch bridge hanger is estimated using a number of experimentally identified modal frequencies. The hanger is connected through metallic plates to the bridge deck and arch. Two different categories of model classes are considered to simulate the vibrations of the hanger: an analytical model based on the Euler-Bernoulli beam theory, and a high-fidelity finite element (FE) model. A Bayesian parameter estimation and model selection method is used to discriminate between models, select the best model, and estimate the hanger tension and its uncertainty. It is demonstrated that the end plate connections and boundary conditions of the hanger due to the flexibility of the deck/arch significantly affect the estimate of the axial load and its uncertainty. A fixed-end high fidelity FE model of the hanger underestimates the hanger tension by more than 20 compared to a baseline FE model with flexible supports. Simplified beam models can give fairly accurate results, close to the ones obtained from the high fidelity FE model with flexible support conditions, provided that the concept of equivalent length is introduced and/or end rotational springs are included to simulate the flexibility of the hanger ends. The effect of the number of experimentally identified modal frequencies on the estimates of the hanger tension and its uncertainty is investigated.

• Structural Engineering and Mechanics
• /
• v.25 no.3
• /
• pp.311-330
• /
• 2007

Model-based predictions of structural behavior are negatively affected by uncertainties of various type and in various stages of the structural analysis. The present paper focusses on dynamic analysis and addresses the effects of uncertainties concerning material and geometric parameters, mainly in the context of modal analysis of large-scale structures. Given the large number of uncertain parameters arising in this case, highly scalable simulation-based methods are adopted, which can deal with possibly thousands of uncertain parameters. In order to solve the reliability problem, i.e., the estimation of very small exceedance probabilities, an advanced simulation method called Line Sampling is used. In combination with an efficient algorithm for the estimation of the most important uncertain parameters, the method provides good estimates of the failure probability and enables one to quantify the error in the estimate. Another aspect here considered is the uncertainty quantification for closely-spaced eigenfrequencies. The solution here adopted represents each eigenfrequency as a weighted superposition of the full set of eigenfrequencies. In a case study performed with the FE model of a satellite it is shown that the effects of uncertain parameters can be very different in magnitude, depending on the considered response quantity. In particular, the uncertainty in the quantities of interest (eigenfrequencies) turns out to be mainly caused by very few of the uncertain parameters, which results in sharp estimates of the failure probabilities at low computational cost.

• Structural Engineering and Mechanics
• /
• v.63 no.1
• /
• pp.47-53
• /
• 2017

The fundamental goal of this study is to minimize the uncertainty of the median fragility curve and to assess the structural vulnerability under earthquake excitation. Bayesian Inference with Markov Chain Monte Carlo (MCMC) simulation has been presented for efficient collapse response assessment of the independent intake water tower. The intake tower is significantly used as a diversion type of the hydropower station for maintaining power plant, reservoir and spillway tunnel. Therefore, the seismic fragility assessment of the intake tower is a pivotal component for estimating total system risk of the reservoir. In this investigation, an asymmetrical independent slender reinforced concrete structure is considered. The Bayesian Inference method provides the flexibility to integrate the prior information of collapse response data with the numerical analysis results. The preliminary information of risk data can be obtained from various sources like experiments, existing studies, and simplified linear dynamic analysis or nonlinear static analysis. The conventional lognormal model is used for plotting the fragility curve using the data from time history simulation and nonlinear static pushover analysis respectively. The Bayesian Inference approach is applied for integrating the data from both analyses with the help of MCMC simulation. The method achieves meaningful improvement of uncertainty associated with the fragility curve, and provides significant statistical and computational efficiency.