This paper presents a nonlinear model for piezoelastic laminated plates with damage effect of the intra-layers and inter-laminar interfaces. Discontinuity of displacement and electric potential on the interfaces are d...This paper presents a nonlinear model for piezoelastic laminated plates with damage effect of the intra-layers and inter-laminar interfaces. Discontinuity of displacement and electric potential on the interfaces are depicted by three shape functions. By using the Hamilton variation principle, the three-dimensional nonlinear dynamic equations of piezoelastic laminated plates with damage effect are derived. Then, by using the Galerkin method, a mathematical solution is presented. In the numerical studies, effects of various factors on the natural frequencies and nonlinear amplitude-frequency response of the simply-supported peizoelastic laminated plates with interfacial imperfections are discussed. These factors include different damage models, thickness of the piezoelectric layer, side-to-thickness ratio, and length-to-width ratio.展开更多
This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochas...This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.展开更多
Based on the concept of stiffness degradation, a damage index of the whole frame and the storey is proposed for the frame seismic performance evaluation. The index is compatible with the non-linear static analysis （e...Based on the concept of stiffness degradation, a damage index of the whole frame and the storey is proposed for the frame seismic performance evaluation. The index is compatible with the non-linear static analysis （e. g. the pushover analysis）, and the structural damage is considered via plastic hinges. Simultaneously, a practical approach is developed to obtain the relationships between the proposed index and earthquake intensities based on the capacity spectrum method. The proposed index is then illustrated through two low-rise reinforced concrete frames, and it is also compared with some other indices. The results indicate that the proposed index is on the safe side and not sensitive to the lateral load pattern. The storey index is helpful to reflect the storey damage and to uncover the position of the weak storey. Finally, the relationship between performance levels and damage index values is also proposed through statistical analysis for the performance-based seismic evaluation.展开更多
It is possible for certain building structures to encounter both the seismic load and blast load during their service life.With the development of the economy and the increase of security demand,the need for design of...It is possible for certain building structures to encounter both the seismic load and blast load during their service life.With the development of the economy and the increase of security demand,the need for design of building structures against multi-hazard is becoming more and more obvious.Therefore,the damage analysis of building structures under the combined action of multiple hazards has become a very urgent requirement for disaster prevention and reduction.In this paper,the refined finite element model of reinforced concrete(RC)columns is established by using the explicit dynamic analysis software LS-DYNA.Combined with the Monte Carlo method,the damage law of RC columns under the combined action of random single earthquake or explosion disaster and multi-hazard is studied,and the damage groups are distinguished according to the damage index.Based on the support vector machine(SVM)algorithm,the dividing line between different damage degree groups is determined,and a rapid method for determining the damage degree of RC columns under the combined seismic and blast loads is proposed.Finally,suggestions for the design of RC column against multi-disaster are put forward.展开更多
基金supported by the National Natural Science Foundation of China (No. 10572049)
文摘This paper presents a nonlinear model for piezoelastic laminated plates with damage effect of the intra-layers and inter-laminar interfaces. Discontinuity of displacement and electric potential on the interfaces are depicted by three shape functions. By using the Hamilton variation principle, the three-dimensional nonlinear dynamic equations of piezoelastic laminated plates with damage effect are derived. Then, by using the Galerkin method, a mathematical solution is presented. In the numerical studies, effects of various factors on the natural frequencies and nonlinear amplitude-frequency response of the simply-supported peizoelastic laminated plates with interfacial imperfections are discussed. These factors include different damage models, thickness of the piezoelectric layer, side-to-thickness ratio, and length-to-width ratio.
基金National Natural Science Foundation of China for Innovative Research Groups Under Grant No.50321803 & 50621062National Natural Science Foundation of China Under Grant No.50808113 & 10872148
文摘This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.
基金The National Basic Research Program of China(973 Program)(No.2007CB714200)
文摘Based on the concept of stiffness degradation, a damage index of the whole frame and the storey is proposed for the frame seismic performance evaluation. The index is compatible with the non-linear static analysis （e. g. the pushover analysis）, and the structural damage is considered via plastic hinges. Simultaneously, a practical approach is developed to obtain the relationships between the proposed index and earthquake intensities based on the capacity spectrum method. The proposed index is then illustrated through two low-rise reinforced concrete frames, and it is also compared with some other indices. The results indicate that the proposed index is on the safe side and not sensitive to the lateral load pattern. The storey index is helpful to reflect the storey damage and to uncover the position of the weak storey. Finally, the relationship between performance levels and damage index values is also proposed through statistical analysis for the performance-based seismic evaluation.
基金supported by the National Natural Science Foundation of China (Grant Nos.51878445,51938011 and 51908405)。
文摘It is possible for certain building structures to encounter both the seismic load and blast load during their service life.With the development of the economy and the increase of security demand,the need for design of building structures against multi-hazard is becoming more and more obvious.Therefore,the damage analysis of building structures under the combined action of multiple hazards has become a very urgent requirement for disaster prevention and reduction.In this paper,the refined finite element model of reinforced concrete(RC)columns is established by using the explicit dynamic analysis software LS-DYNA.Combined with the Monte Carlo method,the damage law of RC columns under the combined action of random single earthquake or explosion disaster and multi-hazard is studied,and the damage groups are distinguished according to the damage index.Based on the support vector machine(SVM)algorithm,the dividing line between different damage degree groups is determined,and a rapid method for determining the damage degree of RC columns under the combined seismic and blast loads is proposed.Finally,suggestions for the design of RC column against multi-disaster are put forward.
