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1.
The use of unconditionally stable implicit time integration techniques for pseudodynamic tests has been recently proposed and advanced by several researchers. Inspired by such developments, a pseudodynamic test scheme based on an unconditionally stable implicit time integration algorithm and dual displacement control is presented in this paper. The accuracy of the proposed scheme is proved with error-propagation analysis. It is shown by numerical examples and verification tests that the error-correction method incorporated can eliminate the spurious higher-mode response, which can often be excited by experimental errors. The practicality of the proposed scheme lies in the fact that the implementation is as easy as that of explicit schemes and that the convergence criteria required are compatible with the accuracy limits of ordinary test apparatus. 相似文献
2.
In pseudodynamic tests, experimental feedback errors are accumulated in the step-by-step integration procedure. In this paper, the growth of cumulative experimental errors is examined. Approximate cumulative error bounds are derived for linear single- and multi-degree-of-freedom systems, based on realistic models of random and systematic feedback errors. These studies show that the rate of cumulative error growth with respect to the integration time step increases rapidly with the natural frequency of the specimen and the integration time interval used. Hence, the higher modes of a multi-degree-of-freedom system are more sensitive to experimental errors than the lower ones. Furthermore, it is shown that some systematic errors are extremely undesirable. Rational criteria for assessing the reliability of pseudodynamic test results are presented. 相似文献
3.
The convergence and energy-dissipation characteristics of an unconditionally stable implicit time integration scheme that has been adopted for pseudodynamic testing are examined in this paper. A convergence criterion is derived for general multiple-degree-of-freedom softening systems. Furthermore, it is shown that undesired loading and unloading cycles can be avoided in numerical iterations by scaling down the incremental corrections. Finally, it is proved that the total energy dissipation introduced by the residual convergence errors and proposed numerical correction is always positive for any softening structures. 相似文献
4.
This paper presents the implementation details of a real‐time pseudodynamic test system that adopts an implicit time integration scheme. The basic configuration of the system is presented. Physical tests were conducted to evaluate the performance of the system and validate a theoretical system model that incorporates the dynamics and nonlinearity of a test structure and servo‐hydraulic actuators, control algorithm, actuator delay compensation methods, and the flexibility of an actuator reaction system. The robustness and accuracy of the computational scheme under displacement control errors and severe structural softening are examined with numerical simulations using the model. Different delay compensation schemes have been implemented and compared. One of the schemes also compensates for the deformation of an actuator reaction system. It has been shown that the test method is able to attain a good performance in terms of numerical stability and accuracy. However, it has been shown that test results obtained with this method can underestimate the inelastic displacement drift when severe strain softening develops in a test structure. This can be attributed to the fact that the numerical damping effect introduced by convergence errors becomes more significant as a structure softens. In a real‐time test, a significant portion of the convergence errors is caused by the time delay in actuator response. Hence, a softening structure demands higher precision in displacement control. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
5.
Two types of implicit time-stepping algorithms have been proposed recently for pseudodynamic tests. The first type consists of an algorithm which relies on Newton iterations to satisfy the equations of motion. The second type consists of an algorithm which is based on the Operator-Splitting technique and does not require any numerical iteration. While one or the other has been preferred by some researchers, these time-stepping algorithms have not been analysed and compared under a uniform setting. In this paper, a concise summary of these schemes is presented, and they are evaluated in a consistent manner in terms of numerical dissipation, frequency distortion and experimental errors. The analytical results are validated by numerical simulations as well as experimental results. It is shown that the algorithm based on Newton iterations can control experimental error effects effectively by means of an error-correction procedure. The algorithm based on the Operator-Splitting technique demonstrates similar performance provided the I-Modification is adopted. 相似文献
6.
In a pseudodynamic test, errors in restoring-force feedback are introduced into numerical computations. Some of these errors can excite the higher-frequency response of the specimen. In this paper, the use of viscous and numerical dampings to eliminate spurious higher-frequency effects is studied. Since the tangent stiffness of a non-linear specimen cannot be measured accurately, initial-stiffness-dependent viscous damping is considered. In addition, an explicit integration algorithm with desired numerical damping properties is proposed and examined. The analytical and numerical studies presented indicate that viscous-damping properties can be substantially changed by non-linear deformations. For this reason, the use of numerical damping appears to be more advantageous. 相似文献
7.
Converting the second-order differential equation to a first-order equation by integrating it with respect to time once as the governing equation of motion for a structural system can be very promising in the pseudodynamic testing. This was originally found and developed by Chang. The application of this time-integration technique to the Newmark explicit method is implimented and investigated in this paper. The main advantages of using the integral form of Newmark explicit method instead of the commonly used Newmark explicit method in a pseudodynamic test are: a less-error propagation effect, a better capability in capturing the rapid changes of dynamic loading and in eliminating the adverse linearization errors. All these improvements have been verified by theoretical studies and experimental tests. Consequently, for a same time step this time-integration technique may result in less-error propagation and achieve more accurate test results than applying the original form of Newmark explicit method in a pseudodynamic test due to these significant improvements. Thus, the incorporation of this proposed time-integration technique into the direct integration method for pseudodynamic testings is strongly recommended. © 1998 John Wiley & Sons, Ltd. 相似文献
8.
Shuenn-Yih Chang 《地震工程与工程振动(英文版)》2009,8(1):77-86
Two important extensions of a technique to perform a nonlinear error propagation analysis for an explicit pseudodynamic algorithm (Chang, 2003) are presented. One extends the stability study from a given time step to a complete step-by-step integration procedure. It is analytically proven that ensuring stability conditions in each time step leads to a stable computation of the entire step-by-step integration procedure. The other extension shows that the nonlinear error propagation results, which are derived for a nonlinear single degree of freedom (SDOF) system, can be applied to a nonlinear multiple degree of freedom (MDOF) system. This application is dependent upon the determination of the natural frequencies of the system in each time step, since all the numerical properties and error propagation properties in the time step are closely related to these frequencies. The results are derived from the step degree of nonlinearity. An instantaneous degree of nonlinearity is introduced to replace the step degree of nonlinearity and is shown to be easier to use in practice. The extensions can be also applied to the results derived from a SDOF system based on the instantaneous degree of nonlinearity, and hence a time step might be appropriately chosen to perform a pseudodynamic test prior to testing. 相似文献
9.
A structure may exhibit a severe strain-softening behaviour when subjected to strong earthquake excitation. Pseudodynamic testing of such structures using an implicit time-integration algorithm may be conceived of as a problem, since the Newton-type iterations, which are often required when structural non-linearity develops, may not converge under these circumstances. An unconditionally stable implicit time-integration algorithm implemented with Newton-type iterations is analysed to provide an insight into this problem. A simple convergence condition is derived to detect possible divergence. The condition is shown to be a sufficient criterion for convergence for general multiple-degree-of-freedom structures, and it is used later on to develop an adaptive time-stepping strategy to avoid divergence under severe strain-softening conditions. The implementation of this technique for pseudodynamic testing is presented. As demonstrated by numerical examples, the algorithm proves to be effective and reliable. 相似文献
10.
Real‐time hybrid testing combines experimental testing and numerical simulation, and provides a viable alternative for the dynamic testing of structural systems. An integration algorithm is used in real‐time hybrid testing to compute the structural response based on feedback restoring forces from experimental and analytical substructures. Explicit integration algorithms are usually preferred over implicit algorithms as they do not require iteration and are therefore computationally efficient. The time step size for explicit integration algorithms, which are typically conditionally stable, can be extremely small in order to avoid numerical stability when the number of degree‐of‐freedom of the structure becomes large. This paper presents the implementation and application of a newly developed unconditionally stable explicit integration algorithm for real‐time hybrid testing. The development of the integration algorithm is briefly reviewed. An extrapolation procedure is introduced in the implementation of the algorithm for real‐time testing to ensure the continuous movement of the servo‐hydraulic actuator. The stability of the implemented integration algorithm is investigated using control theory. Real‐time hybrid test results of single‐degree‐of‐freedom and multi‐degree‐of‐freedom structures with a passive elastomeric damper subjected to earthquake ground motion are presented. The explicit integration algorithm is shown to enable the exceptional real‐time hybrid test results to be achieved. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
11.
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
12.
实时子结构实验Chang算法的稳定性和精度 总被引：7，自引：0，他引：7
与慢速拟动力子结构实验相比,实时子结构实验的优点在于它能真实地反映速度相关型试件的特性。实时子结构实验的逐步积分算法通常借用拟动力算法,但是目前液压伺服作动器很难实现速度反馈控制,因而试件速度不能实现原算法的假定值,这样一来算法的稳定性和计算精度将发生改变。台湾学者S.Y.Chang提出一种无条件稳定的显式拟动力算法,本文分析了这种方法应用于实时子结构实验时的稳定性和计算精度。研究发现在实时子结构实验中该方法由无条件稳定变成了有条件稳定的,精度也发生了改变。 相似文献
13.
This paper describes a modal weighting technique that improves the stability characteristics of explicit time-integration schemes used in structural dynamics. The central difference method was chosen as the trial algorithm because of its simplicity, both in terms of formulation and ease of numerical stability and convergence analysis. It is shown how explicit algorithms may be reformulated in order to make them stable for any integration time by attenuating high-frequency oscillation modes that are generated by mesh geometry rather than generic dynamical features. We discuss results from trial calculations obtained from mathematical models that represent hysteretic restoring force elements and an application on a physical, four-degree-of-freedom, base-isolated structure using the pseudodynamic technique. © 1998 John Wiley & Sons, Ltd. 相似文献
14.
Shuenn-Yih Chang 《地震工程与结构动力学》1997,26(9):917-929
There is no second-order accurate, dissipative, explicit method in the currently available step-by-step integration algorithms. Two new families of second-order accurate, dissipative, explicit methods have been successfully developed for the direct integration of equations of motion in structural dynamics. These two families of methods are numerically equivalent and possess the desired numerical dissipation which can be continuously controlled. These two families of algorithms are very useful for pseudodynamic tests since the favourable numerical damping can be used to suppress the spurious growth of high-frequency modes due to the presence of numerical and/or experimental errors in performing a pseudodynamic test. © 1997 by John Wiley & Sons, Ltd. 相似文献
15.
This paper studies the stability of the central difference method (CDM) for real‐time substructure test considering specimen mass. Because the standard CDM is implicit in terms of acceleration, to avoid iteration, an explicit acceleration formulation is assumed for its implementation in real‐time dynamic substructure testing. The analytical work shows that the stability of the algorithm decreases with increasing specimen mass if the experimental substructure is a pure inertia specimen. The algorithm becomes unstable however small the time integration interval is, when the mass of specimen equal or greater than that of its numerical counterpart. For the case of dynamic specimen, the algorithm is unstable when there is no damping in the whole test structure; a damping will make the algorithm stable conditionally. Part of the analytical results is validated through an actual test. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
16.
大刚度结构力控制拟动力实验方法 总被引：3，自引：2，他引：3
由于受到拟动力实验加载系统和量测系统精度限制，对大刚度结构采用位移控制的拟动力实验方法已失效，本文提出了适用于大风度结构的力控制拟动力试验方法，阐述了方法的原理与步骤，并用实验实例验证了该方法是可行的和可靠的。 相似文献
17.
Shuenn-Yih Chang 《地震工程与工程振动(英文版)》2009,8(3):329-340
Two explicit integration algorithms with unconditional stability for linear elastic systems have been successfully developed for pseudodynamic testing.Their numerical properties in the solution of a linear elastic system have been well explored and their applications to the pseudodynamic testing of a nonlinear system have been shown to be feasible. However,their numerical properties in the solution of a nonlinear system are not apparent.Therefore,the performance of both algorithms for use in the solution... 相似文献
18.
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
19.
An inelastic substructure technique for the pseudodynamic test method is described. This technique requires testing of only a critical component of a multi-degree-of-freedom structure, while the remaining portion is modelled using standard inelastic analytical procedures. This is an economical method to investigate the seismic behaviour of a structure, provided a critical subassembly is found. This paper describes the development of a substructure algorithm which is verified with a numerically simulated test. The method was used to evaluate the seismic performance of moment-resisting steel frames. Modelling for an eight-storey, three-bay frame is discussed, and the boundary conditions between the analytical portion and the experimental component are evaluated. The results indicate that the selection of the critical subassembly was adequate and that the pseudodynamic response was significantly dependent on the behaviour of this experimental component. Furthermore, experimental results suggest that this information would have been difficult to obtain from quasi-static testing or from standard inelastic dynamic analysis. Therefore, this substructure pseudodynamic technique was an economical tool to investigate the seismic behaviour of ductile frames. 相似文献
20.
Hybrid simulation is a powerful test method for evaluating the seismic performance of structural systems. This method makes it feasible that only critical components of a structure be experimentally tested. This paper presents a newly proposed integration algorithm for seismic hybrid simulation which is aimed to extend its capabilities to a wide range of systems where existing methods encounter some limitations. In the proposed method, which is termed the variable time step (VTS) integration method, an implicit scheme is employed for hybrid simulation by eliminating the iterative phase on experimental element, the phase which is necessary in regular implicit applications. In order to study the effectiveness of the VTS method, a series of numerical investigations are conducted which show the successfulness of the VTS method in obtaining accurate, stable and converged responses. Then, in a comparative approach, the improved accuracy of the VTS method over commonly used integration methods is demonstrated. The stability of the VTS method is also studied and the results show that it provides conditional stability; however, its stability limit is well beyond the accuracy limit. The effect of time delay on the VTS method results is also investigated and it is shown that the VTS method is quite successful in handling this experimental error. 相似文献