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Liu J.,Guangxi University | Yu B.,Guangxi University | Yang L.,Guangxi University | Yang L.,Agency of Housing and Urban Rural Development
Yingyong Lixue Xuebao/Chinese Journal of Applied Mechanics | Year: 2015

The accuracy of the FORM based on the Orthogonal and Nataf transformations is investigated through a comprehensive parametric study, considering the influences of distribution type, variability and correlation of random variables as well as the nonlinearity of performance function. The results indicate that the error of the FORM mainly comes from the nonlinearity caused by the Orthogonal and Nataf transformations when the coefficient of variation (COV) is small, while the influence of the nonlinearity of performance function is unobvious. Meanwhile, the bigger the absolute value of the skewness coefficient of random variable is, the larger the relative error of the FORM based on the above two transformations will be. For the Normal and Lognormal distribution types, the accuracy of both Orthogonal and Nataf transformations is generally satisfied. In this situation, the Orthogonal transformation is recommended due to its simpleness. For the Type-I largest distribution and Shifted Rayleigh distribution types, the accuracy of these two transformations is acceptable when the COV and correlation coefficient are small. However, if the correlation coefficient is large, the Orthogonal transformation causes a significant error, since it ignores the difference between correlation coefficients that before and after transformations. In this situation, the Nataf transformation is recommended due to its high precision. Further studies show that the FORM based on the Orthogonal and Nataf transformations can also be applied in the planar frame structure with implicit perform function, and the accuracy of these two transformations is comparable to each other. ©, 2015, Xi'an Jiaotong University. All right reserved.


Yu B.,Guangxi University | Yang L.,Guangxi University | Yang L.,Agency of Housing and Urban Rural Development | Wu M.,Guangxi University | Li B.,Nanyang Technological University
Construction and Building Materials | Year: 2014

A practical model for predicting the corrosion rate of steel reinforcement in concrete structures was proposed. The numerical model with nonlinear boundary conditions for the macrocell corrosion of steel reinforcement in concrete structures was established based on the electrochemical principles and the Bulter-Volmer equation. The influences of various parameters such as anode-to-cathode (A/C) ratio, relative humidity, concrete resistivity, cover thickness on the corrosion control mode and corrosion rate of steel reinforcement in concrete structures were then investigated. Finally, a practical model for predicting the corrosion rate of steel reinforcement in concrete structures was proposed based on a comprehensive nonlinear regression analysis with easily quantifiable engineering parameters, such as water-to-cement (W/C) ratio, chloride content, thickness of concrete cover and relative humidity. Model comparison and experimental verification demonstrate that the proposed prediction model is of good accuracy and applicability to real life scenarios in terms of capturing the corrosion behavior of steel reinforcement in different situations. © 2013 Elsevier Ltd. All rights reserved.


Yu B.,Guangxi University | Liu D.,Guangxi University | Yang L.F.,Guangxi University | Yang L.F.,Agency of Housing and Urban Rural Development
Applied Mechanics and Materials | Year: 2013

Peak displacement is one of the most important parameters for the performance based seismic design of bridge structure, while the peak displacement is often significantly impacted by the P-Δ effect. In this study, the influence of the P-Δ effect on the statistics of peak displacement of bridge structure was quantificationally investigated based on a series of nonlinear time-history analysis. The bridge structure was idealized as the single degree of freedom (SDOF) system and the hysteretic behaviour was represented by the improved Bouc-Wen model. The statistic analysis was implemented based on the inelastic dynamic responses of the SDOF system under 69 selected earthquake records. The results show that the P-Δ effect has significant impact on the mean and dispersion of peak displacement of bridge structures, especially if the normalized yield strength and the natural vibration period are small. © (2013) Trans Tech Publications, Switzerland.


Yang L.-F.,Guangxi University | Yang L.-F.,Agency of Housing and Urban Rural Development | Yang X.-F.,Guangxi University | Yu B.,Guangxi University | Li Z.-Y.,Guangxi University
Jisuan Lixue Xuebao/Chinese Journal of Computational Mechanics | Year: 2013

An improved stochastic response surface method was proposed based on the stepwise regression analysis. The correlated random variables given the marginal cumulative distribution function were transformed into the independent standard normal variables according to the Nataf transformation, while the stochastic response of complex structure was expressed as the polynomial chaos expansion of independent standard normal variables. The optimal probabilistic collocation points were selected based on the linear independent criterion and the insignificant expansion terms were eliminated efficiently by the stepwise regression analysis. The numerical results show that the proposed method can reduce the probabilistic collocation points and unknown coefficients of polynomial expansion significantly on the condition of ensuring calculation accuracy.


Yu B.,Guangxi University | Liu D.,Guangxi University | Yang L.-F.,Guangxi University | Yang L.-F.,Agency of Housing and Urban Rural Development
Zhendong yu Chongji/Journal of Vibration and Shock | Year: 2014

Residual displacement is one of the most important parameters to assess the repairability and usability of bridge structures after an earthquake, while the P-Δ effect has significant influences on the residual displacement of bridge structures. Probabilstic characteristics and empirical prediction equations of residual displacements for bridge structures were quantitatively investigated based on the large number of nonlinear time history analyses by taking the P-Δ effect and randomness of strong ground motion into account. The governing differential equation of motion for bridge structures including the P-Δ effect was developed based on the dynamic balance theory. The influences of the P-Δ effect, post-yield stiffness ratio, normalized yield strength and natural period of vibration on statistical characteristics of residual displacement were quantitatively investigated based on the inelastic dynamic responses of bridge structures under the excitation of 69 selected records of strong ground motions. The correlation between the peak and residual displacements was discussed and the prediction equation for the residual-to-peak displacement ratio was also proposed. The results show that the P-Δ effect, the post-yield stiffness ratio and the normalized yield strength have significant impact on the mean of residual displacements; the residual displacement can be described as a lognormal or Weibull distribution variable; the correlation between the residual and peak displacements is remarkable and the mean (dispersion) of the residual-to-peak displacement ratios increases (decreases) with the increase of the natural period of vibration and the stability factor.


Yang L.-F.,Guangxi University | Yang L.-F.,Agency of Housing and Urban Rural Development | Yuan Y.-H.,Guangxi University | Yu B.,Guangxi University
Gongcheng Lixue/Engineering Mechanics | Year: 2014

An improved vector cooperative response surface method (CRSM) for structural reliability analysis involving non-Gaussian correlated random variables was proposed based on the orthogonal and approximately equivalent probability transformations. First, according to the orthogonal transformation, the non-Gaussian correlated random variables were mapped into the uncorrelated non-Gaussian standardized random variables to establish global stiffness matrices and load vectors. The preconditioner was defined by the global structure stiffness matrix to form a preconditioner Krylov subspace, and the stochastic global nodal displacement vector of structure was expanded subsequently in the subspace to develop vector cooperative response surface hierarchically. The collocation points selected from combinations of the roots of polynomial chaos of one-order higher than the order of the response surface were mapped into the non-Gaussian random variable space from the independent standard normal random variable space according to approximately equivalent probability transformation. Finally, the unknown coefficients of cooperative response surface (CRS) were determined by the regression analysis and structural reliability analysis was implemented based on the limit state function constructed by the CRS. Results show that the proposed method is of high accuracy, global applicability and fast convergence for structural reliability analysis involving non-Gaussian correlated random variables.


Yu B.,Guangxi University | Liu D.,Guangxi University | Yang L.F.,Guangxi University | Yang L.F.,Agency of Housing and Urban Rural Development
Applied Mechanics and Materials | Year: 2013

Residual displacement is an important measure of post-earthquake functionality of engineering structures. Empirical equations for prediction of residual displacement of SDOF system from its peak inelastic displacement were proposed through a comprehensive statistical analysis. An inelastic seismic analysis model including the P-Δ effect was employed to assess the residual and peak inelastic displacements of SDOF system under horizontal and vertical excitations. The correlation and empirical equations between residual and peak inelastic displacements were discussed based on 69 selected earthquake records. Results show that the correlation between residual and peak inelastic displacements are of high correlation, and the mean of residual-to-peak displacement ratio increases with the increase of period of vibration or stability factor. Furthermore, the coefficient of variation of residual-to-peak displacement ratio decreases with the increase of the period of vibration dramatically for rigid systems and is generally independent of the stability factor and the normalized yield strength. © (2013) Trans Tech Publications, Switzerland.


Yu B.,Guangxi University | Yang L.,Guangxi University | Yang L.,Agency of Housing and Urban Rural Development
Applied Mechanics and Materials | Year: 2013

It is quite difficult to estimate system reliability of complex structures which involve lots of potential failure modes. A novel method for system reliability analysis of frame structure was proposed based on stochastic limit analysis. Stochastic limit load was firstly calculated based on the elastic modulus reduction method (EMRM) by taking the uncertainty of structural resistance into account. Once the limit state equation was established by the stochastic limit load, the system reliability index can be calculated by the first-order reliability method (FORM) efficiently. Numerical example illustrates the efficiency and accuracy of the proposed method by comparing with the traditional failure mode analysis approaches. © (2013) Trans Tech Publications, Switzerland.


Yang L.-F.,Guangxi University | Yang L.-F.,Agency of Housing and Urban Rural Development | Li Z.-Y.,Guangxi University
Gongcheng Lixue/Engineering Mechanics | Year: 2012

Conventional response surface methods (RSM) are of scalar type and usually developed for a specific random quantity at a given point attached to a stochastic structure. A vectorial response surface method called as a cooperative response surface method (CRSM) is presented and developed for a global nodal displacement vector so as to overcome the limitation of the conventional RSM. The Karhunen-Loève series is employed to expand the stiffness matrix and nodal force vector. A preconditioner is defined as the global stiffness matrix evaluated at the mean of the random field so that a preconditioned Krylov subspace can be determined. The nodal displacement vector could be expanded in the space and a vectorial cooperative response surface is developed so that the cooperativity still holds among the components in a displacement vector. The relationship between the compatible response surface and the polynomial chaos is presented so that the sample points can be defined. The explicit expressions are developed for the mean and covariance of the displacement vector. Examples demonstrate the high accuracy, global applicability and fast convergence of the cooperative response surface method.


Yang L.,Guangxi University | Yang L.,Agency of Housing and Urban Rural Development | Liu J.,Guangxi University | Yu B.,Guangxi University
Tumu Gongcheng Xuebao/China Civil Engineering Journal | Year: 2016

The dead load effect often plays an important role in the large-scale civil and hydraulic structures. To analyze the failure mode of structures with significant dead load effect, the traditional elasto-plastic methods have the failure path-dependent problem. To overcome the limitations of the traditional methods, a method of identifying the failure element and the failure mode is proposed by combining the strength incorporation technique with the strategy of elastic modulus adjustment, and then an elastic modulus reduction method is developed for analyzing the damage evolution and failure mode of engineering structures with significant dead load effect. Firstly, a modified computational model with updated strength and external load distribution is established by incorporating the dead load effect into the sectional strength of structural member. Next, based on the element bearing ratio (EBR) and the reference EBR defined by the homogeneous generalized yield function, a self-adaptive criterion of identifying the highly stressed elements (HSEs) is presented. Furthermore, by means of reducing the elastic modulus of HSEs, the structural stiffness damage is simulated, and the bearing capacity of the structure is determined. Finally, the potential failure elements can be identified and marked in terms of the reduction amplitude of elastic modulus of HSEs during the plastic limit state of structure, so that the failure mode can be determined. Based on two numerical examples, the good stability and convergence, high accuracy and efficiency of the proposed method can be validated. Since the proposed method can reasonably simulate the damage evolution of structure, it deserves wide applications. © 2016, Editorial Office of China Civil Engineering Journal. All right reserved.

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