• Structural Engineering and Mechanics
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• v.8 no.5
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• pp.453-464
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• 1999

Safety monitoring systems of structures generally resort to detecting possible changes of dynamic system parameters. Sensitivity analysis of these dynamic system parameters may implement these techniques. Conventional structural eigenvalue problems are discussed in the scope of those systems with deterministic parameters. Large and flexible structures, such as suspension bridges, actually possess stochastic material properties and these random properties unavoidably affect the dynamic system parameters. The sensitivity matrix of structural modal parameters to basic design variables has been established in this paper. Moreover, second order statistics of natural frequencies due to the randomness of material properties have been discussed. It is concluded from numerical analysis of a modem suspension bridge that although the second order statistics of frequencies are small relatively to the change of basic design variables, such as density of mass and modulus of elasticity, the sensitivities of modal parameters to these variables at different locations change in magnitude.

• Smart Structures and Systems
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• v.9 no.6
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• pp.505-534
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• 2012

The present work deals with second order statistics of post buckling response of piezoelectric laminated composite cylindrical shell panel subjected to hygro-thermo-electro-mechanical loading with random system properties. System parameters such as the material properties, thermal expansion coefficients and lamina plate thickness are assumed to be independent of the temperature and electric field and modeled as random variables. The piezoelectric material is used in the forms of layers surface bonded on the layers of laminated composite shell panel. The mathematical formulation is based on higher order shear deformation shell theory (HSDT) with von-Karman nonlinear kinematics. A efficient $C^0$ nonlinear finite element method based on direct iterative procedure in conjunction with a first order perturbation approach (FOPT) is developed for the implementation of the proposed problems in random environment and is employed to evaluate the second order statistics (mean and variance) of the post buckling load of piezoelectric laminated cylindrical shell panel. Typical numerical results are presented to examine the effect of various environmental conditions, amplitude ratios, electrical voltages, panel side to thickness ratios, aspect ratios, boundary conditions, curvature to side ratios, lamination schemes and types of loadings with random system properties. It is observed that the piezoelectric effect has a significant influence on the stochastic post buckling response of composite shell panel under various loading conditions and some new results are presented to demonstrate the applications of present work. The results obtained using the present solution approach is validated with those results available in the literature and also with independent Monte Carlo Simulation (MCS).

• Structural Engineering and Mechanics
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• v.80 no.6
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• pp.645-655
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• 2021

Performance-based reliability analysis is a practical approach to investigate the seismic performance and stochastic nonlinear response of structures considering a random process. This is significant due to the uncertainties involved in every aspect of the analysis. Therefore, the present study aims to evaluate the performance-based reliability within a stochastic finite element (FE) framework for reinforced concrete (RC) shear walls that are considered as one of the most essential elements of structures. To accomplish this purpose, deterministic FE analyses are conducted for both squat and slender shear walls to validate numerical models through experimental results. The presented numerical analysis is performed by using the ABAQUS FE program. Afterwards, a random-effects investigation is carried out to consider the influence of different random variables on the lateral load-top displacement behavior of RC members. Using these results and through utilizing the Monte-Carlo simulation method, stochastic nonlinear analyses are also performed to generate random FE models based on input parameters and their probabilistic distributions. In order to evaluate the reliability of RC walls, failure probabilities and corresponding reliability indices are calculated at life safety and collapse prevention levels of performance as suggested by FEMA 356. Moreover, based on reliability indices, capacity reduction factors are determined subjected to shear for all specimens that are designed according to the ACI 318 Building Code. Obtained results show that the lateral load and the compressive strength of concrete have the highest effects on load-displacement responses compared to those of other random variables. It is also found that the probability of shear failure for the squat wall is slightly lower than that for slender walls. This implies that 𝛽 values are higher in a non-ductile mode of failure. Besides, the reliability of both squat and slender shear walls does not change significantly in the case of varying capacity reduction factors.

• Geomechanics and Engineering
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• v.10 no.6
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• pp.709-726
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• 2016

Corrugated-core sandwich panels are prevalent for many applications in industries. The researches performed with the aim of optimization of such structures in the literature have considered a deterministic approach. However, it is believed that deterministic optimum points may lead to high-risk designs instead of optimum ones. In this paper, an effort has been made to provide a reliable and robust design of corrugated-core sandwich structures through stochastic and probabilistic multi-objective optimization approach. The optimization is performed using a coupling between genetic algorithm (GA), Monte Carlo simulation (MCS) and finite element method (FEM). To this aim, Prob. Design module in ANSYS is employed and using a coupling between optimization codes in MATLAB and ANSYS, a connection has been made between numerical results and optimization process. Results in both cases of deterministic and probabilistic multi-objective optimizations are illustrated and compared together to gain a better understanding of the best sandwich panel design by taking into account reliability and robustness. Comparison of results with a similar deterministic optimization study demonstrated better reliability and robustness of optimum point of this study.

• Structural Engineering and Mechanics
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• v.45 no.5
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• pp.595-611
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• 2013

This paper aims to compare three collocation point methods associated with the odd order stochastic response surface method (SRSM) in a systematical and quantitative way. The SRSM with the Hermite polynomial chaos is briefly introduced first. Then, three collocation point methods, namely the point method, the root method and the without origin method underlying the odd order SRSMs are highlighted. Three examples are presented to demonstrate the accuracy and efficiency of the three methods. The results indicate that the condition that the Hermite polynomial information matrix evaluated at the collocation points has a full rank should be satisfied to yield reliability results with a sufficient accuracy. The point method and the without origin method are much more efficient than the root method, especially for the reliability problems involving a large number of random variables or requiring complex finite element analysis. The without origin method can also produce sufficiently accurate reliability results in comparison with the point and root methods. Therefore, the origin often used as a collocation point is not absolutely necessary. The odd order SRSMs with the point method and the without origin method are recommended for the reliability analysis due to their computational accuracy and efficiency. The order of SRSM has a significant influence on the results associated with the three collocation point methods. For normal random variables, the SRSM with an order equaling or exceeding the order of a performance function can produce reliability results with a sufficient accuracy. The order of SRSM should significantly exceed the order of the performance function involving strongly non-normal random variables.

• Earthquakes and Structures
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• v.2 no.2
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• pp.189-206
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• 2011

In this study, the subspace stochastic realization theories (SSR model I and SSR model II) have been applied to a real bridge for estimating its dynamic characteristics (natural frequencies, damping constants, and vibration modes) under ambient vibration. A numerical simulation is carried out for an arch-type steel truss bridge using a white noise excitation. The estimates obtained from this simulation are compared with those obtained from the Finite Element (FE) analysis, demonstrating good agreement and clarifying the excellent performance of this method in estimating the structural dynamic characteristics. Subsequently, these methods are applied to the vibration induced by both strong and weak winds as obtained by remote monitoring of the Kabashima bridge (an arch-type steel truss bridge of length 136 m, and situated in Nagasaki city). The results obtained with this experimental data reveal that more accurate estimates are obtained when strong wind vibration data is used. In contrast, the vibration data obtained from weak wind provides accurate estimates at lower frequencies, and inaccurate accuracy for higher modes of vibration that do not get excited by the wind of lower intensity. On the basis of the identified results obtained using both simulated data and monitored data from a real bridge, it is determined that the SSR model II realizes more accurate results than the SSR model I. In general, the approach investigated in this study is found to provide acceptable estimates of the dynamic characteristics of highway bridges as well as for the vibration monitoring of bridges.

• Structural Engineering and Mechanics
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• v.43 no.5
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• pp.637-655
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• 2012

In this study, stochastic responses of a cable-stayed bridge subjected to the spatially varying earthquake ground motion are investigated by the finite element method taking into account soil-structure interaction (SSI) effects. The considered bridge in the analysis is Quincy Bay-view Bridge built on the Mississippi River in between 1983-1987 in Illinois, USA. The bridge is composed of two H-shaped concrete towers, double plane fan type cables and a composite concrete-steel girder deck. In order to determine the stochastic response of the bridge, a two-dimensional lumped masses model is considered. Incoherence, wave-passage and site response effects are taken into account for the spatially varying earthquake ground motion. Depending on variation in the earthquake motion, the response values of the cable-stayed bridge supported on firm, medium and soft foundation soil are obtained, separately. The effects of SSI on the stochastic response of the cable-stayed bridge are also investigated including foundation as a rigidly capped vertical pile groups. In this approach, piles closely grouped together beneath the towers are viewed as a single equivalent upright beam. The soil-pile interaction is linearly idealized as an upright beam on Winkler foundation model which is commonly used to study the response of single piles. A sufficient number of springs on the beam should be used along the length of the piles. The springs near the surface are usually the most important to characterize the response of the piles surrounded by the soil; thus a closer spacing may be used in that region. However, in generally springs are evenly spaced at about half the diameter of the pile. The results of the stochastic analysis with and without the SSI are compared each other while the bridge is under the sway of the spatially varying earthquake ground motion. Specifically, in case of rigid towers and soft soil condition, it is pointed out that the SSI should be significantly taken into account for the design of such bridges.

• Structural Engineering and Mechanics
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• v.23 no.6
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• pp.599-613
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• 2006

A method for the dynamical analysis of FE discretized uncertain linear and nonlinear structures is presented. This method is based on the moment equation approach, for which the differential equations governing the response first and second-order statistical moments must be solved. It is shown that they require the cross-moments between the response and the random variables characterizing the structural uncertainties, whose governing equations determine an infinite hierarchy. As a consequence, a closure scheme must be applied even if the structure is linear. In this sense the proposed approach is approximated even for the linear system. For nonlinear systems the closure schemes are also necessary in order to treat the nonlinearities. The complete set of equations obtained by this procedure is shown to be linear if the structure is linear. The application of this procedure to some simple examples has shown its high level of accuracy, if compared with other classical approaches, such as the perturbation method, even for low levels of closures.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.369-376
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• 2002

The stochastic analysis of semi-infinite domain is presented using the weighted integral method, which is improved to include the higher order terms in expanding the displacement vector. To improve the weighted integral method, the Lagrangian remainder is taken into account in the expansion of the status variable with respect to the mean value of the random variables. In the resulting formulae only the 'proportionality coefficients' are introduced in the resulting equation, therefore no additional computation time and memory requirement is needed. The equations are applied in analyzing the semi-infinite domain. The results obtained by the improved weighted integral method are reasonable and are in good agreement with those of the Monte Carlo simulation. To model the semi-infinite domain, the Bettess's infinite element is adopted, where the theoretical decomposition of the strain-displacement matrix to calculate the deviatoric stiffness of the semi-infinite domains is introduced. The calculated value of mean and the covariance of the displacement are revealed to be larger than those given by the finite domain assumptions which is thought to be rational and should be considered in the design of structures on semi-infinite domains.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.1
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• pp.129-138
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• 2000

Composites are finding increasing use in a wide variety of engineering applications due to their outstanding mechanical properties. A number of studies have focused on the development of new materials as well as the response of composite structures to static and dynamic loads by assuming the external driving forces to be deterministic. However, there ate many situations in practice where the exciting forces vary randomly. In this work, the nonlinear response of laminated composite plates excited by stochastic loading is studied by the finite element method. Classical, first-order and third-order shear theories for plates are used in the finite element formulation. Since most composites exhibit significant nonlinearity in the shear stress-strain law, this is included in the present analysis.