Random Material Parameters Research Articles

Random seismic response analysis of truss structures with uncertain parameters

This paper presents an approach called random factor method (RFM) for the random vibration analysis of seismic response of random truss structures. An antenna and a truss bridge with random material parameters and geometric dimensions are considered to illustrate the application of the RFM in the seismic response analysis of random structures under stationary or non-stationary random earthquake excitation. Using the RFM, the structural stiffness and mass matrices can respectively be described by the product of two parts corresponding to the random factors of structural parameters and the deterministic matrix. From the expressions of structural seismic random response in the frequency domain, computational expressions for the mean value and standard deviation of the mean square value of the seismic random displacement and stress response are developed by means of the random variable’s functional moment method and the algebra synthesis method. The influences of the randomness of the structural parameters on the structural seismic responses are investigated.

Free vibration of laminated composite conical shells with random material properties

In the present study, the sensitivity of randomness in material parameters on linear free vibration response of conical shells is presented. Higher order shear deformation theory is used to model system behavior and uncertain lamina material properties are modeled as basic random variables. A finite element method is successfully combined with first-order perturbation technique to obtain the response statistics of the structure. The solution methodology is validated with the results available in the literature and an independent Monte Carlo simulation. Typical numerical results for second-order statistics of linear free vibration response of simply supported laminated composite conical shells are obtained for different lamination schemes and thickness to radius ratios.

Uncertain reliability index in finite element reliability analysis

Finite Element Reliability Analysis (FERA) has been devised to obtain the probability of structural response events based on random material, geometry and loading parameters. Previously, such analysis has not distinguished between the uncertainties rising from inherent randomness, and from model errors and insufficient knowledge about the probability distribution parameters. In this paper, we argue that this distinction is imperative for meaningful interpretation of the resulting reliability and to provide confidence in reliability assessments among practicing engineers. To this end, we identify sources of epistemic uncertainty and explicitly include them in the analysis. The quantification, representation and propagation of epistemic uncertainty by the Bayesian probabilistic approach and the fuzzy randomness approach are explored. Consequently, measures of confidence in the reliability index are obtained. We also emphasise the utilisation of importance measures to identify where data gathering or model improvement has the greatest influence. Another novelty is the implementations in the rapidly advancing OpenSees software. The extended software produces an uncertain reliability index from which point estimates or confidence bounds are extracted. A numerical example involving a non-linear finite element model of a reinforced concrete building with approximately one hundred random variables is employed to demonstrate the implementations.

Simulation of nonlinear properties of ferroelectric and piezoceramicmaterials

AbstractFerroelectric and piezoelectric materials are becoming a very significant part of smart materials that are used widely as actuators, sensors and most common applications such as vibration control, precision positioning, precision cutting and microelectromechanical systems (MEMS). Piezoceramic materials show nonlinear characteristics when they are under high electromechanical loading. In this study, nonlinear behaviour of tetragonal perovskite type piezoceramic materials is simulated using micromechanical model. In the simulations uni‐axial loading is applied. The calculations which are based on a linear constitutive model, nonlinear domain switching model and a model of probability to switch are performed at each grain. The different domain switching effects (900 or 1800 domain switching for tetragonal perovskite structure) due to energy differences, different probability functions, different statistical random generators and material parameters are analyzed. Finally, simulation results are compared with the data of experiments are giving in literature. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modal approaches for the stochastic finite element analysis of structures with material and geometric uncertainties

This paper presents two efficient modal approaches as an alternative to direct formulations for the time-harmonic dynamic analysis of structures with random material and shape parameters. In both approaches, the structural eigenproblem is solved and complemented by a sensitivity analysis to the random parameters. The modal perturbation stochastic finite element method (SFEM) then condenses the response sensitivities to assess the response variability. The mixed perturbation/Monte-Carlo SFEM assesses the response statistics by sampling the structural eigenmodes according to the perturbation estimation of their probability distribution functions (PDFs). Geometric uncertainties are handled through an appropriate shape parameterisation and a shape design sensitivity analysis. Two numerical applications examine both approaches in terms of accuracy, variability level and computational requirements. The applications involve a plate bending problem with random Young modulus or edge length and a plate with a random flatness default. Particular observations related to the influence of the parameter PDFs in simulation-based methods are also provided.

Reliability analysis of direct shear and flexural failure modes of RC slabs under explosive loading

Two loosely coupled SDOF systems are used to model the flexural and direct shear responses of one-way reinforced concrete slabs subjected to explosive loading. Incorporating the effects of random variations of the structural and blast loading properties, as well as the strain rate effect caused by rapid load application, failure probabilities of the two failure modes are analyzed. The model is capable of predicting the failure probability of the slab with random material and geometrical parameters and subjected to random blast loading. Considering the random variations of structural properties and blast loading, the failure probabilities of one-way RC slab designed according to BS 8110 (Stuctural use of concrete, parts 1 and 2 (1985)) are calculated. The effect of span length of the slab on its failure probability to blast loading is also investigated. Based on numerical results, a semi analytical boundary that separates the slab's flexural and shear failure modes is derived as a function of peak reflected pressure and duration of blasting wave.

Stochastic Simulations in Dynamic Soil-Structure Interaction

This paper deals with several numerical techniques that account for random excitations and random material parameters occurring in earthquake engineering. It focuses in sequence on the influence on the structural response of the variability of the incident field using filtering theory, on the soil variability by coupling Stochastic Finite Elements, integral operators and Monte-Carlo simulation, and finally on the influence on the site response of a random building distribution using periodic simulations. In each case, practical examples are given to help illustrate the numerical techniques and to underline the importance of randomness in earthquake engineering problems. Sommario. Questo lavoro prende in considerazione diverse tecniche numeriche che portano in conto l'aleatorieta dell'eccitazione e dei parametri del materiale in problemi di ingegneria sismica. L'attenzione viene rivolta sequen- zialmente all'influenza sulla risposta strutturale della variabilita del campo incidente utilizzando una teoria del filtro, alla variabilita del suolo analizzata tramite elementi finiti stocastici, operatori integrali e simulazioni Monte- Carlo, ed infine all'influenza sulla risposta del sito di una distribuzione aleatoria degli edifici analizzata tramite simulazioni periodiche. Per ciascun caso, vengono fomiti esempi pratici volti ad illustrare le tecniche numeriche e ad evidenziare l'importanza delle aleatorieta nei problemi di ingegneria sismica.

Spectral stochastic finite element analysis of periodic random thermal creep stress in concrete

A spectral stochastic finite element method with a numerical step-by-step algorithm for the analysis of thermal creep stresses in concrete structures is presented. The effect of concrete age on creep properties and various kinds of random factors including material parameters and the random temperature process of concrete, etc. is taken into account. In the proposed method, the complex frequency response function is introduced to reflect the influence of the temperature process and is regarded as a random function of the random material parameters of concrete. The algorithm leads to a series of incremental elastic problems in which the stresses and strains, etc. are all complex variables. The suggested method is useful for spectral analysis of the response of concrete structures with random material exposed to random environmental temperature.

A probabilistic analysis of foundation settlements

This paper deals with a settlement analysis of shallow foundations resting on a layered subsoil. Three basic sources of randomness are discussed: random shape of the subsoil (location of an interface between two strata), random material parameters and random loads. The numerical analysis is based on the finite element method coupled with stochastic versions of the perturbation and the Neumann expansion methods. Both methods lead to a simple evaluation of the response variability in terms of the mean value and the covariance matrix for foundation settlements. More sophisticated analyses introduce the probability of failure as a measure of safety. In this context, failure means either exceeding the bearing capacity or exceeding allowable displacements. The probability of failure is usually evaluated by means of FEM-oriented gradient algorithms or some versions of the Monte Carlo simulation techniques. Numerical examples are presented for a raft foundation resting on an elastic subsoil. The obtained results compare the scale of random fluctuations of soil properties or loading with the scale of foundation settlement fluctuations.

Stochastic boundary element method in elasticity

The stochastic boundary element method is developed to analyzeelasticity problems with random material and/or geometrical parameters and ran-domly perturbed boundaries. Based on the first-order Taylor series expansion, theboundary integration equations concerning the mean and deviation of the displace-ments are derived, respectively. It is found that the randomness of material param-eters is equivalent to a random body force, so the mean and covariance matricesof unknown boundary displacements and tractions can be obtained. Furthermore,the mean and covariance of displacements and stresses at inner points can also beobtained. Numerical examples show that the proposed stochastic boundary elementmethod gives satisfactory solutions, as compared with those obtained by theoreticalanalysis or other numerical methods.

Stochastic boundary element method in elasticity

The stochastic boundary element method is developed to analyze elasticity problems with random material and/or geometrical parameters and randomly perturbed boundaries. Based on the first-order Taylor series expansion, the boundary integration equations concerning the mean and deviation of the displacements are derived, respectively. It is found that the randomness of material parameters is equivalent to a random body force, so the mean and covariance matrices of unknown boundary displacements and tractions can be obtained. Furthermore, the mean and covariance of displacements and stresses at inner points can also be obtained. Numerical examples show that the proposed stochastic boundary element method gives satisfactory solutions, as compared with those obtained by theoretical analysis or other numerical methods.

Sampling analysis of concrete structures for creep and shrinkage with correlated random material parameters

The latin hypercube sampling method, which represents the most efficient way to determine the statistics of the creep and shrinkage response of structures, has previously been developed and used under the assumption that the random parameters of the creep and shrinkage prediction model are mutually independent. In reality they are correlated. On the basis of existing data, this paper establishes, by means of the method of maximum likelihood, the joint multivariate probability distribution of the random parameters involved, tests the hypothesis of mutual dependence of parameters on the basis of the χ 2- distribution , and generalizes the latin hypercube sampling method to the case of correlated multinormal random parameters. The generalization is accomplished by an orthogonal matrix transformation of the random parameters based on the eigenvectors of the inverse of the covariance matrix. This yields a set of new random parameters which are uncorrelated (independent) and can be subjected to the ordinary latin hypercube sampling, with samples of equal probabilities. Numerical examples of statistical prediction of creep and shrinkage effects in structures confirm the practical feasibility of the method and reveal a good agreement with the scatter observed in some previous experiments.

One-dimensional strain-dependent creep damage in inhomogeneous materials

A local inhomogeneous strain-dependent creep damage theory is presented and then applied using creep damage data obtained at J.R.C. Ispra for specimens of various lengths. Solutions for one-dimensional constant stress and load are obtained, and are found to be in better agreement with observation than solutions based on previous homogeneous theory. Also, the effect of random material parameters on the rupture time is considered for the constant tensile stress test, and is found to be a significant factor.

A Self‐Consistent Approach to the Ideal Magnetization in Heterogeneous Ferromagnetics

AbstractA generalization of the CPA‐like effective‐medium theory for heterogeneous media to the case of non‐linear material behaviour is proposed. The method is developed referring to the example of ideal effective magnetization of heterogeneous ferromagnetics. The treatment is based on the phenomenological description of micromagnetism. The heterogeneity is expressed by random material parameters. In comparison with the effective‐medium theory the main idea of the new procedure consists in the introduction of an additional stochastic field simulating the long‐range interaction between different grains of the heterogeneous body. In order to illustrate the method calculations are carried out for a simple ferromagnetic model system consisting of a mixture of two isotropic components.

Damped lateral vibration in an axially creeping beam with random material parameters

Damped lateral vibration in an axially creeping beam with random material parameters is considered. The temperature and imperfection density, and as a result two inelastic material parameters, are random functions of the distance along the neutral axis. It is assumed that the material of the beam is governed by a nonlinear Maxwell model, and that the initial tensile stress is much greater than the increment of stress caused by the oscillation so that a perturbation technique may be employed. Two special cases are fully analyzed: (a) the random parameters are random processes which are only slightly random, and (b) the random parameters are random variables which are largely random. Statistical results are obtained for the lateral velocity, bending moment, logarithmic decrement and circular frequency. It is found that in a specific example, where the beam is made of an aluminum alloy, the lateral velocity, bending moment and logarithmic decrement are sensitive to randomness in temperature and imperfection density, whereas the circular frequency is almost deterministic.

Damped Lateral Vibration in Axially Creeping Beam with Random Material Parameters

It is assumed that the material of the beam is governed by a nonlinear Maxwell model. The temperature and imperfection density and consequently the two inelastic material parameters are taken as random functions of the distance along the neutral axis. A perturbation about the initial axial stress is employed, analogous to the approach used in Cozzarelli, Wu, and Tang [“Lateral Vibration of a Nonlinear Viscoelastic Beam under Initial Axial-Tension,” J. Sound Vibration 13 (1970)]. As in Cozzarelli and Huang [Effect of Random Material Parameters on Nonlinear Steady Creep Solutions,” Int. J. Solids Structures 7 (1971)], the problem is separated into two uncoupled problems—a “random temperature problem” and a “random imperfection problem.” Two special cases are fully analyzed: (a) the random parameters are random processes that are only slightly raudom, and (b) the random parameters are random variables that are largely random. Statistical results are obtained for the lateral velocity, bending moment, logarithmic decrement and circular frequency.

Effect of random material parameters on nonlinear steady creep solutions

An analysis is presented concerning the effect of random material parameters on nonlinear steady creep in a 3-bar truss. Parameter randomness is in general large and is introduced through randomness in the temperature and in the density of imperfections. Analytical and numerical results are presented on the statistical properties of the material parameters and of the stress and velocity. It is shown that randomness in the material parameters will on the one hand introduce only a very slight randomness in stress and on the other hand a very significant randomness in velocity.