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1.
A fully implicit iterative integration procedure is presented for local and geographically distributed hybrid simulation of the seismic response of complex structural systems with distributed nonlinear behavior. The purpose of this procedure is to seamlessly incorporate experimental elements in simulations using existing fully implicit integration algorithms designed for pure numerical simulations. The difficulties of implementing implicit integrators in a hybrid simulation are addressed at the element level by introducing a safe iteration strategy and using an efficient procedure for online estimation of the experimental tangent stiffness matrix. In order to avoid physical application of iterative displacements, the required experimental restoring force at each iteration is estimated from polynomial curve fitting of recent experimental measurements. The experimental tangent stiffness matrix is estimated by using readily available experimental measurements and by a classical diagonalization approach that reduces the number of unknowns in the matrix. Numerical and hybrid simulations are used to demonstrate that the proposed procedure provides an efficient method for implementation of fully implicit numerical integration in hybrid simulations of complex nonlinear structures. The hybrid simulations presented include distributed nonlinear behavior in both the numerical and experimental substructures. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

2.
We present a comparison of methods for the analysis of the numerical substructure in a real‐time hybrid test. A multi‐tasking strategy is described, which satisfies the various control and numerical requirements. Within this strategy a variety of explicit and implicit time‐integration algorithms have been evaluated. Fully implicit schemes can be used in fast hybrid testing via a digital sub‐step feedback technique, but it is shown that this approach requires a large amount of computation at each sub‐step, making real‐time execution difficult for all but the simplest models. In cases where the numerical substructure poses no harsh stability condition, it is shown that the Newmark explicit method offers advantages of speed and accuracy. Where the stability limit of an explicit method cannot be met, one of the several alternatives may be used, such as Chang's modified Newmark scheme or the α‐operator splitting method. Appropriate methods of actuator delay compensation are also discussed. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

3.
Explicit integration procedures have been widely adapted and applied to hybrid simulations of the seismic response of structures due to their simplicity. However, these procedures are only conditionally stable and have limited recent applications of hybrid simulations to simple structural models with few degrees of freedom. A novel integration procedure is proposed herein, in which a fully implicit formulation is applied to solve the equation of motion for the hybrid model, but defaults to an explicit or noniterative formulation in steps that fail to converge. The advantages to this approach are the ensured continuity of the simulation and the reduced accumulation of errors that occur during consecutive explicit steps that may lead to instability. The implicit procedure is applied by loading the experimental substructures beyond the expected displacement for the current step, then using the displacements and forces measured through the load path in the iterative implicit scheme. This approach captures the instantaneous behaviour of experimental substructures without physically imposing iterations. Numerical and experimental simulations demonstrate the effectiveness of the proposed integration scheme for multi‐degree‐of‐freedom models, especially in utilization of longer time steps that exceed stability limits of explicit methods, prevention of excitation of higher modes, and testing of stiff systems. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

4.
Hybrid simulations that combine numerical computations and physical experiment represent an effective method of evaluating the dynamic response of structures. However, it is sometimes impossible to take all the uncertain or nonlinear parts of the structure as the physical substructure. Thus, the modeling errors of the numerical part can raise concerns. One method of solving this problem is to update the numerical model by estimating its parameters from experimental data online. In this paper, an online model updating method for the hybrid simulation of frame structures is proposed to reduce the errors of nonlinear modeling of numerical substructures. To obtain acceptable accuracy with acceptable extra computation efforts as a result of model parameter estimation, the sectional constitutive model is adopted, therein considering axial‐force and bending‐moment coupling; moreover, the unscented Kalman filter is used for parameter estimation of the sectional model. The effectiveness of the sectional model updating with the unscented Kalman filter is validated via numerical analyses and actual hybrid tests on a full‐scale steel frame structure, with one column as the experimental substructure loaded by three actuators to guarantee the consistency of the boundary conditions. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

5.
A collaborative structural analysis (CSA) system is developed, which is capable of performing highly sophisticated structural analyses utilizing beneficial features of existing individual structural analysis programs. In the system, the global equations of motion for the overall structural system are formulated in the host program. Some substructures, whose behaviors are relatively simple, are directly solved in the host program, whereas those having complex behavior are analyzed by the station programs. A time‐consuming static condensation procedure is needed for the substructures analyzed by the station programs if adopting an implicit integration scheme. The operator splitting (OS) method, which does not require tangential stiffness, can be used to improve the system efficiency. To this end, a hybrid formulation of the Newmark‐β and OS methods is proposed, and a CSA scheme based on the hybrid formulation is developed. In the CSA system adopting the hybrid formulation, the degrees of freedom whose tangential stiffness are unavailable are formulated by the OS method, whereas the rest are still formulated by the commonly used Newmark‐β method. Using the system, analyses of a three‐story‐braced steel moment‐resisting frame are conducted. In the analyses, the column bases are analyzed using the commercial finite element method software ABAQUS, and the remaining structural elements are analyzed using a frame analysis program called NETLYS. Results suggest that the hybrid formulation is very effective for the CSA system. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

6.
A series of large‐scale real‐time hybrid simulations (RTHSs) are conducted on a 0.6‐scale 3‐story steel frame building with magneto‐rheological (MR) dampers. The lateral force resisting system of the prototype building for the study consists of moment resisting frames and damped brace frames (DBFs). The experimental substructure for the RTHS is the DBF with the MR dampers, whereas the remaining structural components of the building including the moment resisting frame and gravity frames are modeled via a nonlinear analytical substructure. Performing RTHS with an experimental substructure that consists of the complete DBF enables the effects of member and connection component deformations on system and damper performance to be accurately accounted for. Data from these tests enable numerical simulation models to be calibrated, provide an understanding and validation of the in‐situ performance of MR dampers, and a means of experimentally validating performance‐based seismic design procedures for real structures. The details of the RTHS procedure are given, including the test setup, the integration algorithm, and actuator control. The results from a series of RTHS are presented that includes actuator control, damper behavior, and the structural response for different MR control laws. The use of the MR dampers is experimentally demonstrated to reduce the response of the structure to strong ground motions. Comparisons of the RTHS results are made with numerical simulations. Based on the results of the study, it is concluded that RTHS can be conducted on realistic structural systems with dampers to enable advancements in resilient earthquake resistant design to be achieved. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

7.
Real‐time hybrid simulation is a viable experiment technique to evaluate the performance of structures equipped with rate‐dependent seismic devices when subject to dynamic loading. The integration algorithm used to solve the equations of motion has to be stable and accurate to achieve a successful real‐time hybrid simulation. The implicit HHT α‐algorithm is a popular integration algorithm for conducting structural dynamic time history analysis because of its desirable properties of unconditional stability for linear elastic structures and controllable numerical damping for high frequencies. The implicit form of the algorithm, however, requires iterations for nonlinear structures, which is undesirable for real‐time hybrid simulation. Consequently, the HHT α‐algorithm has been implemented for real‐time hybrid simulation using a fixed number of substep iterations. The resulting HHT α‐algorithm with a fixed number of substep iterations is believed to be unconditionally stable for linear elastic structures, but research on its stability and accuracy for nonlinear structures is quite limited. In this paper, a discrete transfer function approach is utilized to analyze the HHT α‐algorithm with a fixed number of substep iterations. The algorithm is shown to be unconditionally stable for linear elastic structures, but only conditionally stable for nonlinear softening or hardening structures. The equivalent damping of the algorithm is shown to be almost the same as that of the original HHT α‐algorithm, while the period elongation varies depending on the structural nonlinearity and the size of the integration time‐step. A modified form of the algorithm is proposed to improve its stability for use in nonlinear structures. The stability of the modified algorithm is demonstrated to be enhanced and have an accuracy that is comparable to that of the existing HHT α‐algorithm with a fixed number of substep iterations. Both numerical and real‐time hybrid simulations are conducted to verify the modified algorithm. The experimental results demonstrate the effectiveness of the modified algorithm for real‐time testing. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

8.
Finite element(FE) is a powerful tool and has been applied by investigators to real-time hybrid simulations(RTHSs). This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time(TET) decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method(CDM), the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ(λ = 4) method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.  相似文献   

9.
Hybrid simulation combines numerical and experimental methods for cost‐effective, large‐scale testing of structures under simulated earthquake loading. Structural system level response can be obtained by expressing the equation of motion for the combined experimental and numerical substructures, and solved using time‐stepping integration similar to pure numerical simulations. It is often assumed that a reliable model exists for the numerical substructures while the experimental substructures correspond to parts of the structure that are difficult to model. A wealth of data becomes available during the simulation from the measured experiment response that can be used to improve upon the numerical models, particularly if a component with similar structural configuration and material properties is being tested and subjected to a comparable load pattern. To take advantage of experimental measurements, a new hybrid test framework is proposed with an updating scheme to update the initial modeling parameters of the numerical model based on the instantaneously‐measured response of the experimental substructures as the test progresses. Numerical simulations are first conducted to evaluate key algorithms for the selection and calibration of modeling parameters that can be updated. The framework is then expanded to conduct actual hybrid simulations of a structural frame model including a physical substructure in the laboratory and a numerical substructure that is updated during the tests. The effectiveness of the proposed framework is demonstrated for a simple frame structure but is extendable to more complex structural behavior and models. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

10.
A hybrid numerical and experimental simulation to collapse was conducted on a one‐half scale moment‐resisting frame building with two experimental substructures at different locations. An extensible hybrid test framework was used that adopts a generalized interface to encapsulate each numerical or tested substructure, through which only boundary displacements and forces are exchanged. Equilibrium and compatibility between substructures are enforced by an iterative quasi‐Newton procedure, while adopting a predictor‐and‐corrector method to avoid loading reversals on physically tested substructures. To overcome difficulties in controlling stiff axial and rotational deformations at the boundaries, the flexible test scheme employs either open‐loop or closed‐loop control at the boundaries: enforcing either compatibility or equilibrium, or both requirements at critical boundaries. The effectiveness of the extensible framework and its capability to simulate structural behavior through collapse is demonstrated by a geographically distributed test that reproduced the collapse behavior of a four‐story, two‐bay, steel moment frame previously tested on an earthquake simulator. A comparison of both experiments highlights the viability of the hybrid test as an effective tool for the performance evaluation of structural systems from the onset of damage through collapse. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

11.
This paper presents a new method, called the equivalent force control method, for solving the nonlinear equations of motion in a real‐time substructure test using an implicit time integration algorithm. The method replaces the numerical iteration in implicit integration with a force‐feedback control loop, while displacement control is retained to control the motion of an actuator. The method is formulated in such a way that it represents a unified approach that also encompasses the effective force test method. The accuracy and effectiveness of the method have been demonstrated with numerical simulations of real‐time substructure tests with physical substructures represented by spring and damper elements, respectively. The method has also been validated with actual tests in which a Magnetorheological damper was used as the physical substructure. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

12.
In real‐time hybrid simulations (RTHS) that utilize explicit integration algorithms, the inherent damping in the analytical substructure is generally defined using mass and initial stiffness proportional damping. This type of damping model is known to produce inaccurate results when the structure undergoes significant inelastic deformations. To alleviate the problem, a form of a nonproportional damping model often used in numerical simulations involving implicit integration algorithms can be considered. This type of damping model, however, when used with explicit integration algorithms can require a small time step to achieve the desired accuracy in an RTHS involving a structure with a large number of degrees of freedom. Restrictions on the minimum time step exist in an RTHS that are associated with the computational demand. Integrating the equations of motion for an RTHS with too large of a time step can result in spurious high‐frequency oscillations in the member forces for elements of the structural model that undergo inelastic deformations. The problem is circumvented by introducing the parametrically controllable numerical energy dissipation available in the recently developed unconditionally stable explicit KR‐α method. This paper reviews the formulation of the KR‐α method and presents an efficient implementation for RTHS. Using the method, RTHS of a three‐story 0.6‐scale prototype steel building with nonlinear elastomeric dampers are conducted with a ground motion scaled to the design basis and maximum considered earthquake hazard levels. The results show that controllable numerical energy dissipation can significantly eliminate spurious participation of higher modes and produce exceptional RTHS results. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

13.
This paper presents the development and validation of a real‐time hybrid simulation (RTHS) system for efficient dynamic testing of high voltage electrical vertical‐break disconnect switches. The RTHS system consists of the computational model of the support structure, the physical model of the insulator post, a small shaking table, a state‐of‐the‐art controller, a data acquisition system and a digital signal processor. Explicit Newmark method is adopted for the numerical integration of the governing equations of motion of the hybrid structure, which consists of an insulator post (experimental substructure) and a spring‐mass‐dashpot system representing the support structure (analytical substructure). Two of the unique features of the developed RTHS system are the application of an efficient feed‐forward error compensation scheme and the ability to use integration time steps as small as 1 ms. After the development stage, proper implementation of the algorithm and robustness of the measurements used in the calculations are verified. The developed RTHS system is further validated by comparing the RTHS test results with those from a conventional shaking table test. A companion paper presents and discusses a parametric study for a variety of geometrical and material configurations of these switches using the developed RTHS system. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

14.
This paper presents real‐time hybrid earthquake simulation (RTHS) on a large‐scale steel structure with nonlinear viscous dampers. The test structure includes a three‐story, single‐bay moment‐resisting frame (MRF), a three‐story, single‐bay frame with a nonlinear viscous damper and associated bracing in each story (called damped braced frame (DBF)), and gravity load system with associated seismic mass and gravity loads. To achieve the accurate RTHS results presented in this paper, several factors were considered comprehensively: (1) different arrangements of substructures for the RTHS; (2) dynamic characteristics of the test setup; (3) accurate integration of the equations of motion; (4) continuous movement of the servo‐controlled hydraulic actuators; (5) appropriate feedback signals to control the RTHS; and (6) adaptive compensation for potential control errors. Unlike most previous RTHS studies, where the actuator stroke was used as the feedback to control the RTHS, the present study uses the measured displacements of the experimental substructure as the feedback for the RTHS, to enable accurate displacements to be imposed on the experimental substructure. This improvement in approach was needed because of compliance and other dynamic characteristics of the test setup, which will be present in most large‐scale RTHS. RTHS with ground motions at the design basis earthquake and maximum considered earthquake levels were successfully performed, resulting in significant nonlinear response of the test structure, which makes accurate RTHS more challenging. Two phases of RTHS were conducted: in the first phase, the DBF is the experimental substructure, and in the second phase, the DBF together with the MRF is the experimental substructure. The results from the two phases of RTHS are presented and compared with numerical simulation results. An evaluation of the results shows that the RTHS approach used in this study provides a realistic and accurate simulation of the seismic response of a large‐scale structure with rate‐dependent energy dissipating devices. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

15.
子结构地震模拟振动台混合试验原理与实现   总被引：2，自引：0，他引：2  
为了解决地震模拟振动台承载能力及台面尺寸对大型结构试验的限制,扩展振动台的功能,本文提出了子结构地震模拟振动台混合试验方法、试验过程及实时数值积分方法,并给出了试验子结构边界条件的两种模拟形式.通过一个简单框架结构的地震模拟振动台试验和子结构混合加载试验验证了该方法的可行性,并指出了该试验方法的主要技术问题.混合试验方法通过子结构技术和振动台试验相结合,解决了目前的地震模拟振动台试验和拟动力试验在设备规模和加载速度上的局限性.  相似文献   

16.
The peer‐to‐peer (P2P) Internet online hybrid test system has been developed for the seismic simulation of a structure. In this study, the stability and accuracy of the system are investigated analytically by studying the spectral radius of the recursive matrix of the test scheme featuring a two‐round quasi‐Newton test scheme. The applicability of the system is further examined by exploring the seismic responses of a complex structure, a steel‐encased reinforced concrete (SRC) structure with a steel tower on the top. The structure is divided into two numerical substructures and one tested part for hybrid test. The numerical substructures are simulated by sophisticated finite element method (FEM) models with material nonlinearities to capture local plastifications. Two types of FEM programs, namely OpenSEES and ABAQUS, which are suitable for the SRC part and the steel tower, respectively, are employed. The results demonstrate that the P2P system is able to simulate complex structures with significant nonlinearities. As compared with the previous study in which two elastic numerical substructures were considered, increase in the number of iterations in this study is not significant, because the associated nonlinearities are limited due to the small time interval adopted in the test. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

17.
The collapse of a one‐bay, four‐story steel moment frame is simulated in this study by the proposed peer‐to‐peer (P2P) Internet online hybrid test system. The typical beam hinging mechanism, which is ensured by a strong‐column, weak‐beam design, is reproduced. The plastic hinges at the column bases are taken as the experimental portions, while the superstructure is analyzed numerically by a general‐purpose finite element program. The implicit plastic rotations of the two column bases are treated as boundary displacements. In order to account for the complex behavior of the column bases, the P2P system is modified to use the secant stiffness during iterations, and the physical specimens are designed such that the plastic hinge behavior can be obtained. For this study, the three substructures are distributed to different locations. A large ground motion is repeatedly imposed until the column bases lose their capacity to sustain the gravity load. As a result, significant deterioration is observed at both column bases. The proposed P2P system is thus demonstrated to be able to accommodate multiple‐tested substructures involving unstable behavior. The results suggest that the P2P Internet online hybrid test system provides a reliable means of studying structures up to collapse. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

18.
显-隐式组合数值积分算法结合了显式算法无需迭代和隐式算法无条件稳定的各自优点,是结构抗震拟动力试验顺利运行的关键.在对传统显式中央差分法和隐式Newmark β组合算法进行参数修正的基础上,建立了修正CD-Newmark算法,考虑阻尼的影响分析了组合算法的稳定性条件、周期失真率和数值阻尼比,分别得到了试验子结构的稳定性条件和计算子结构无条件稳定的参数合理取值范围,并对计算精度进行了分析.通过算例分析验证了算法的数值特性,从而初步解决了CD-Newmark算法存在稳定性界限过严的问题,为结构抗震拟动力混合试验提供了研究参考.  相似文献   

19.
The paper explores the GC (Gravouil and Combescure) partitioning strategy recently adopted in real-time testing (RTDS) and pseudo-dynamic testing (PsD) with dynamic substructuring. The GC method is a multi-time step subdomain algorithm able to couple any time integration schemes from the Newmark family with the appropriate time step size dependent on the subdomain. The partitioning method is numerically tested by developing an external software able to couple finite element codes based on implicit and explicit time integration schemes. A complex Finite Element mesh partitioning, exhibiting a large number of interface points, has been considered for a full-size reinforced concrete frame structure subjected to an earthquake loading: the well-known SPEAR structure pseudo-dynamically tested at the ELSA laboratory, in Ispra, Italy. Implicit and explicit parts of the structure are modelled using multi-fibre beam elements whose cross-section is divided into steel and concrete fibres associated with cyclic and nonlinear behaviours. The accuracy of the results from the Explicit/Implicit multi-time step co-computation has been proved by comparing with the results from full explicit and full implicit computations. Despite the very large duration of the earthquake excitation and the number of interface nodes involved into the mesh partitioning, the Explicit/Implicit multi-time step co-computations provide very accurate global (displacements, forces at the base) and local (maximum strains in concrete) results while reducing by a factor 2 the computation times. Finally, it has been observed that the dissipated energy at the interface coming from the GC coupling algorithm remains very low at the end of the earthquake loading, less than 2% of the external energy, for time step ratios between the large and fine time steps ranging from 20 to 200.  相似文献   

20.
杜雨峰  王涛 《地震学刊》2014,(3):370-376
采用子结构混合实验方法进行复杂结构的地震响应模拟。在混合实验中,根据结构的特征划分为多个子结构,每个子结构被封装起来,只有边界上的力和位移作为子结构间相互作用的变量,利用拟牛顿法保持整体结构的平衡和协调。目标结构为SRC框架剪力墙结构体系,结构顶部设置11层高的钢塔。在混合实验中,该结构被分为3个子结构,SRC部分为第一个子结构,采用OpenSees进行模拟;钢塔的第1层比较薄弱,是变形集中区域,采用实验进行模拟;钢塔其余部分采用ABAQUS有限元程序进行模拟。实验得到准确的地震响应,表明本文提出的混合实验方法可有效地结合多个有限元程序,充分利用各个有限元程序的优点进行复杂结构的地震响应模拟。  相似文献   

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