• Structural Engineering and Mechanics
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• v.15 no.6
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• pp.669-683
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• 2003

The stochastic optimal nonlinear control of coupled adjacent building structures is studied based on the stochastic dynamical programming principle and the stochastic averaging method. The coupled structures with control devices under random seismic excitation are first condensed to form a reduced-order structural model for the control analysis. The stochastic averaging method is applied to the reduced model to yield stochastic differential equations for structural modal energies as controlled diffusion processes. Then a dynamical programming equation for the energy processes is established based on the stochastic dynamical programming principle, and solved to determine the optimal nonlinear control law. The seismic response mitigation of the coupled structures is achieved through the structural energy control and the dimension of the optimal control problem is reduced. The seismic excitation spectrum is taken into account according to the stochastic dynamical programming principle. Finally, the nonlinear controlled structural response is predicted by using the stochastic averaging method and compared with the uncontrolled structural response to evaluate the control efficacy. Numerical results are given to demonstrate the response mitigation capabilities of the proposed stochastic optimal control method for coupled adjacent building structures.

• Structural Engineering and Mechanics
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• v.31 no.5
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• pp.621-624
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• 2009

The time delay in active and semi-active controls is an important research subject. Many researches on the time-delay control for deterministic systems have been made (Hu and Wang 2002, Yang et al. 1990, Abdel-Mooty and Roorda 1991, Pu 1998, Cai and Huang 2002), while the study on that for stochastic systems is very limited. The effects of the time delay on the control of nonlinear systems under Gaussian white noise excitations have been studied by Bilello et al. (2002). The controlled linear systems with deterministic and random time delay subjected to Gaussian white noise excitations have been treated by Grigoriu (1997). Recently, a stochastic averaging method for quasi-integrable Hamiltonian systems with time delay has been proposed (Liu and Zhu 2007). In the present paper, a stochastic optimal time-delay control method for stochastically excited nonlinear structural systems is proposed based on the stochastic averaging method for quasi Hamiltonian systems with time delay and the stochastic dynamical programming principle. An example of stochastically excited and controlled hysteretic column is given to illustrate the proposed control method.

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

• Interaction and multiscale mechanics
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• v.1 no.3
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• pp.369-379
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• 2008

A combined stochastic diffusion and mean-field model is developed for a systematic study of the grain growth in a pure single-phase polycrystalline material. A corresponding Fokker-Planck continuity equation is formulated, and the interplay/competition of stochastic and curvature-driven mechanisms is investigated. Finite difference results show that the stochastic diffusion coefficient has a strong effect on the growth of small grains in the early stage in both two-dimensional columnar and three-dimensional grain systems, and the corresponding growth exponents are ~0.33 and ~0.25, respectively. With the increase in grain size, the deterministic curvature-driven mechanism becomes dominant and the growth exponent is close to 0.5. The transition ranges between these two mechanisms are about 2-26 and 2-15 nm with boundary energy of 0.01-1 J $m^{-2}$ in two- and three-dimensional systems, respectively. The grain size distribution of a three-dimensional system changes dramatically with increasing time, while it changes a little in a two-dimensional system. The grain size distribution from the combined model is consistent with experimental data available.

• Structural Engineering and Mechanics
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• v.6 no.5
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• pp.473-484
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• 1998

The first and second moments of response variables for SDOF systems with hysteretic nonlinearity are obtained by a direct linearization procedure. This adaptation in the implementation of well-known statistical linearization methods, provides concise, model-independent linearization coefficients that are well-suited for numerical solution. The method may be applied to systems which incorporate any hysteresis model governed by a differential constitutive equation, and may be used for zero or non-zero mean random vibration. The implementation eliminates the effort of analytically deriving specific linearization coefficients for new hysteresis models. In doing so, the procedure of stochastic analysis is made independent from the task of physical modeling of hysteretic systems. In this study, systems with three different hysteresis models are analyzed under various zero and non-zero mean Gaussian White noise inputs. Results are shown to be in agreement with previous linearization studies and Monte Carlo Simulation.

• Structural Engineering and Mechanics
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• v.3 no.3
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• pp.273-287
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• 1995

Stochastic response of systems to random excitation can be estimated by direct integration methods in the time domain such as the stochastic central difference method (SCDM). In this paper, the SCDM is applied to compute the variance and covariance in response of linear and nonlinear structures subjected to random excitation. The accuracy of the SCDM is assessed using two-DOF systems with both deterministic and random material properties excited by white noise. For the former case, closed-form solutions can be obtained. Numerical results also are presented for a simply supported geometrically nonlinear beam. The stiffness of this beam is modeled as a random field, and the beam is idealized by the stochastic finite element method. A perturbation technique is applied to formulate the equations of motion of the system, and the dynamic structural response statistics are obtained in a time domain analysis. The effect of variations in structural parameters and the numerical stability of the SCDM also are examined.

• Structural Engineering and Mechanics
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• v.32 no.1
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• pp.1-20
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• 2009

The present contribution addresses uncertainty quantification and uncertainty propagation in structural mechanics using stochastic analysis. Presently available procedures to describe uncertainties in load and resistance within a suitable mathematical framework are shortly addressed. Monte Carlo methods are proposed for studying the variability in the structural properties and for their propagation to the response. The general applicability and versatility of Monte Carlo Simulation is demonstrated in the context with computational models that have been developed for deterministic structural analysis. After discussing Direct Monte Carlo Simulation for the assessment of the response variability, some recently developed advanced Monte Carlo methods applied for reliability assessment are described, such as Importance Sampling for linear uncertain structures subjected to Gaussian loading, Line Sampling in linear dynamics and Subset simulation. The numerical example demonstrates the applicability of Line Sampling to general linear uncertain FE systems under Gaussian distributed excitation.

• Smart Structures and Systems
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• v.5 no.1
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• pp.69-79
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• 2009

A non-clipped semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers is developed based on the stochastic averaging method and stochastic dynamical programming principle. A nonlinear stochastic control structure is first modeled as a semi-actively controlled, stochastically excited and dissipated Hamiltonian system. The control force of an MR damper is separated into passive and semi-active parts. The passive control force components, coupled in structural mode space, are incorporated in the drift coefficients by directly using the stochastic averaging method. Then the stochastic dynamical programming principle is applied to establish a dynamical programming equation, from which the semi-active optimal control law is determined and implementable by MR dampers without clipping in terms of the Bingham model. Under the condition on the control performance function given in section 3, the expressions of nonlinear and linear non-clipped semi-active optimal control force components are obtained as well as the non-clipped semi-active LQG control force, and thus the value function and semi-active nonlinear optimal control force are actually existent according to the developed strategy. An example of the controlled stochastic hysteretic column is given to illustrate the application and effectiveness of the developed semi-active optimal control strategy.

• Structural Engineering and Mechanics
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• v.6 no.4
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• pp.377-394
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• 1998

Slit shear walls an reinforced concrete shear wall structures with purposely built-in vertical slits. If the slits are inserted with visco-elastic damping materials, the shear walls will become viscoelastic sandwich beams. When adequately designed, this kind of structures can be quite effective in resisting earthquake loads. Herein, a simple analysis method is developed for the evaluation of the stochastic responses of visco-elastic slit shear walls. In the proposed method, the stiffness and mass matrices are derived by using Rayleigh-Ritz method, and the responses of the structures are calculated by means of complex modal analysis. Apart from slit shear walls, this analysis method is also applicable to coupled shear walls and cantilevered sandwich beams. Numerical examples are presented and the results clearly show that the seismic responses of shear wall structures can be substantially reduced by incorporating vertical slits into the walls and inserting visco-elastic damping materials into the slits.

• Geomechanics and Engineering
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• v.14 no.6
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• pp.589-600
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• 2018

For foundations in permafrost regions, the displacement characteristics are uncertain because of the randomness of temperature characteristics and mechanical parameters, which make the structural system have an unexpected deviation and unpredictability. It will affect the safety of design and construction. In this paper, we consider the randomness of temperature characteristics and mechanical parameters. A stochastic analysis model for the uncertain displacement characteristic of foundations is presented, and the stochastic coupling program is compiled by Matrix Laboratory (MATLAB) software. The stochastic displacement fields of an embankment in a permafrost region are obtained and analyzed by Neumann stochastic finite element method (NSFEM). The results provide a new way to predict the deformation characteristics of foundations in permafrost regions, and it shows that the stochastic temperature has a different influence on the stochastic lateral displacement and vertical displacement. Construction disturbance and climate warming lead to three different stages for the mean settlement of characteristic points. For the stochastic settlement characteristic, the standard deviation increases with time, which imply that the results of conventional deterministic analysis may be far from the true value. These results can improve our understanding of the stochastic deformation fields of embankments and provide a theoretical basis for engineering reliability analysis and design in permafrost regions.