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1.
Based on the approximation by polynomial‐fraction, a series of systematic lumped‐parameter models are developed in this paper for efficiently representing the dynamic behaviour of unbounded soil. Concise formulation is first employed to represent the dynamic flexibility function of foundation with a ratio of two polynomials. By defining an appropriate quadratic error function, the optimal coefficients of the polynomials can be directly solved from a system of linear equations. Through performing partial‐fraction expansion on this polynomial‐fraction and designing two basic discrete‐element models corresponding to the partial fractions, systematic lumped‐parameter models can be conveniently established by connecting these basic units in series. Since the systematic lumped‐parameter models are configured without introducing any mass, the foundation input motion can be directly applied to these models for their applications to the analysis of seismic excitation. The effectiveness of these new models is strictly validated by successfully simulating a semi‐infinite bar on an elastic foundation. Subsequently, these models are applied for representing the dynamic stiffness functions for different types of foundation. Comparison of the new models with the other existing lumped‐parameter models is also made to illustrate their advantages in requiring fewer parameters and featuring a more systematic expansion. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

2.
The paper presents a lumped parameter model for the approximation of the frequency‐dependent dynamic stiffness of pile group foundations. The model can be implemented in commercial software to perform linear or nonlinear dynamic analyses of structures founded on piles taking into account the frequency‐dependent coupled roto‐translational, vertical, and torsional behaviour of the soil‐foundation system. Closed‐form formulas for estimating parameters of the model are proposed with reference to pile groups embedded in homogeneous soil deposits. These are calibrated with a nonlinear least square procedure, based on data provided by an extensive non‐dimensional parametric analysis performed with a model previously developed by the authors. Pile groups with square layout and different number of piles embedded in soft and stiff soils are considered. Formulas are overall well capable to reproduce parameters of the proposed lumped system that can be straightforwardly incorporated into inertial structural analyses to account for the dynamic behaviour of the soil‐foundation system. Some applications on typical bridge piers are finally presented to show examples of practical use of the proposed model. Results demonstrate the capability of the proposed lumped system as well as the formulas efficiency in approximating impedances of pile groups and the relevant effect on the response of the superstructure.  相似文献   

3.
Soil-structure interaction analysis is usually carried out in the frequency domain, because the compliance functions of the half-space are known only in the frequency domain. Since non-linear analysis cannot be carried out in the frequency domain, a system with frequency independent parameters is used to represent the half-space soil medium so that a nonlinear analysis in the time domain becomes possible. The objective of this paper is to propose a system with lumped parameters, which are independent of frequency, to represent the half-space soil medium. The proposed frequency independent system consists of a number of real discrete structure elements; thus the existing dynamic analysis programs may be adoptable with little modification. In this paper, the parameters are found by minimizing the sum of the squares of deviations between the steady-state responses of the theoretical half-space model and those of the lumped parameter system over a specified frequency range. Once the parameters have been found, the lumped parameter system can be used in practical applications for time domain dynamic analysis of either linear or non-linear structures. In comparison with the dynamic response of the theoretical half-space model, the lumped parameter system yields satisfactory results.  相似文献   

4.
The computational demand of the soil‐structure interaction analysis for the design and assessment of structures, as well as for the evaluation of their life‐cycle cost and risk exposure, has led the civil engineering community to the development of a variety of methods toward the model order reduction of the coupled soil‐structure dynamic system in earthquake regions. Different approaches have been proposed in the past as computationally efficient alternatives to the conventional finite element model simulation of the complete soil‐structure domain, such as the nonlinear lumped spring, the macroelement method, and the substructure partition method. Yet no approach was capable of capturing simultaneously the frequency‐dependent dynamic properties along with the nonlinear behavior of the condensed segment of the overall soil‐structure system under strong earthquake ground motion, thus generating an imbalance between the modeling refinement achieved for the soil and the structure. To this end, a dual frequency‐dependent and intensity‐dependent expansion of the lumped parameter modeling method is proposed in the current paper, materialized through a multiobjective algorithm, capable of closely approximating the behavior of the nonlinear dynamic system of the condensed segment. This is essentially the extension of an established methodology, also developed by the authors, in the inelastic domain. The efficiency of the proposed methodology is validated for the case of a bridge foundation system, wherein the seismic response is comparatively assessed for both the proposed method and the detailed finite element model. The above expansion is deemed a computationally efficient and reliable method for simultaneously considering the frequency and amplitude dependence of soil‐foundation systems in the framework of nonlinear seismic analysis of soil‐structure interaction systems.  相似文献   

5.
动力基础系统非线性本构关系的研究   总被引：1，自引：1，他引：0  
采用理想集总参数计算体系,以三次幂多项式模型反映动力地基的非线性特性,将非线性幂函数作为循环荷载作用下系统位移-力关系的主干骨线,在此基础上按照Masing二倍法则,将骨线拓展为位移一力的滞回曲线,建立了动力基础双曲线滞回动力学模型。提出了非线性广义刚度函数的概念,建立了动力基础系统在不同振动形式下的非线性本构关系。  相似文献   

6.
This paper proposes a simple lattice model for collapse analysis of RC bridges subjected to earthquakes by using the extended distinct element method (EDEM). In the model, a concrete element consists of lumped masses connected to one another by springs, and a reinforcement bar is represented by a discrete model or an integrated model. The proposed lattice model is simple but its parameters are reasonably defined. It has fewer element nodes and connecting springs, which will be of benefit by shortening the CPU time. The processes to determine the initial stiffness of concrete and steel springs, the parameters of the constitutive model and the fracture criteria for springs are described. A re‐contact spring model is also proposed to simulate the re‐contact of the concrete after fracture of springs; and a general grid searching method is used to decrease the CPU time for judging re‐contact after fracture. The lattice model is assessed by numerical simulations and experiments. As an application, a damaged single‐column pier subjected to the Kobe Earthquake in 1995 is analysed by EDEM with the proposed model. The simulation results indicate that the proposed model predicts well qualitatively the collapse process of RC bridges. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

7.
In this paper, different formulations of a macro‐element model for non‐linear dynamic soil‐structure interaction analyses of structures lying on shallow foundations are first reviewed, and secondly, a novel formulation is introduced, which combines some of the characteristics of previous approaches with several additional features. This macro‐element allows one to model soil‐footing geometric (uplift) and material (soil plasticity) non‐linearities that are coupled through a stiffness degradation model. Footing uplift is introduced by a simple non‐linear elastic model based on the concept of effective foundation width, whereas soil plasticity is treated by means of a bounding surface approach in which a vertical load mapping rule is implemented. This mapping is particularly suited for the seismic loading case for which the proposed model has been conceived. The new macro‐element is subsequently validated using cyclic and dynamic large‐scale laboratory tests of shallow foundations on dense sand, namely: the TRISEE cyclic tests, the Public Works Research Institute and CAMUS IV shaking table tests. Based on this comprehensive validation process against a set of independent experimental results, a unique set of macro‐element parameters for shallow foundations on dense sand is proposed, which can be used to perform predictive analyses by means of the present model. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

8.
Exact representation of unbounded soil contains the single output–single input relationship between force and displacement in the physical or transformed space. This relationship is a global convolution integral in the time domain. Rational approximation to its frequency response function (frequency‐domain convolution kernel) in the frequency domain, which is then realized into the time domain as a lumped‐parameter model or recursive formula, is an effective method to obtain the temporally local representation of unbounded soil. Stability and identification for the rational approximation are studied in this paper. A necessary and sufficient stability condition is presented based on the stability theory of linear system. A parameter identification method is further developed by directly solving a nonlinear least‐squares fitting problem using the hybrid genetic‐simplex optimization algorithm, in which the proposed stability condition as constraint is enforced by the penalty function method. The stability is thus guaranteed a priori. The infrequent and undesirable resonance phenomenon in stable system is also discussed. The proposed stability condition and identification method are verified by several dynamic soil–structure‐interaction examples. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

9.
A new uncertainty estimation method, which we recently introduced in the literature, allows for the comprehensive search of model posterior space while maintaining a high degree of computational efficiency. The method starts with an optimal solution to an inverse problem, performs a parameter reduction step and then searches the resulting feasible model space using prior parameter bounds and sparse‐grid polynomial interpolation methods. After misfit rejection, the resulting model ensemble represents the equivalent model space and can be used to estimate inverse solution uncertainty. While parameter reduction introduces a posterior bias, it also allows for scaling this method to higher dimensional problems. The use of Smolyak sparse‐grid interpolation also dramatically increases sampling efficiency for large stochastic dimensions. Unlike Bayesian inference, which treats the posterior sampling problem as a random process, this geometric sampling method exploits the structure and smoothness in posterior distributions by solving a polynomial interpolation problem and then resampling from the resulting interpolant. The two questions we address in this paper are 1) whether our results are generally compatible with established Bayesian inference methods and 2) how does our method compare in terms of posterior sampling efficiency. We accomplish this by comparing our method for two electromagnetic problems from the literature with two commonly used Bayesian sampling schemes: Gibbs’ and Metropolis‐Hastings. While both the sparse‐grid and Bayesian samplers produce compatible results, in both examples, the sparse‐grid approach has a much higher sampling efficiency, requiring an order of magnitude fewer samples, suggesting that sparse‐grid methods can significantly improve the tractability of inference solutions for problems in high dimensions or with more costly forward physics.  相似文献   

10.
波动在有限元离散模型中传播时,会出现许多不同于连续介质中波动的现象.本文引用经典物理学中晶格动力学的分析方法,由有限元离散形式的出平面波动方程得到频散关系,在此基础上,讨论了集中质量有限元模型中各种可能的出平面运动形式,并分析了考虑时域离散化影响下各种形式可能存在的频率范围.  相似文献   

11.
In this paper, we present a methodology to perform geophysical inversion of large‐scale linear systems via a covariance‐free orthogonal transformation: the discrete cosine transform. The methodology consists of compressing the matrix of the linear system as a digital image and using the interesting properties of orthogonal transformations to define an approximation of the Moore–Penrose pseudo‐inverse. This methodology is also highly scalable since the model reduction achieved by these techniques increases with the number of parameters of the linear system involved due to the high correlation needed for these parameters to accomplish very detailed forward predictions and allows for a very fast computation of the inverse problem solution. We show the application of this methodology to a simple synthetic two‐dimensional gravimetric problem for different dimensionalities and different levels of white Gaussian noise and to a synthetic linear system whose system matrix has been generated via geostatistical simulation to produce a random field with a given spatial correlation. The numerical results show that the discrete cosine transform pseudo‐inverse outperforms the classical least‐squares techniques, mainly in the presence of noise, since the solutions that are obtained are more stable and fit the observed data with the lowest root‐mean‐square error. Besides, we show that model reduction is a very effective way of parameter regularisation when the conditioning of the reduced discrete cosine transform matrix is taken into account. We finally show its application to the inversion of a real gravity profile in the Atacama Desert (north Chile) obtaining very successful results in this non‐linear inverse problem. The methodology presented here has a general character and can be applied to solve any linear and non‐linear inverse problems (through linearisation) arising in technology and, particularly, in geophysics, independently of the geophysical model discretisation and dimensionality. Nevertheless, the results shown in this paper are better in the case of ill‐conditioned inverse problems for which the matrix compression is more efficient. In that sense, a natural extension of this methodology would be its application to the set of normal equations.  相似文献   

12.
A simple non‐linear control law is proposed for reducing structural responses against seismic excitations. This law defines control force dynamics by one differential equation involving a non‐linear term that restrains the control force amplitude. If non‐linearity is neglected, the control force becomes the force in a Maxwell element, so it is called the non‐linear‐Maxwell‐element‐type (NMW) control force. The NMW control force vs. deformation relation plots hysteretic curves. The basic performance of an SDOF model with the NMW control force is examined for various conditions by numerical analyses. Furthermore, the control law is extended to fit an MDOF structural model, and an application example is shown. The computational results show that the NMW control force efficiently reduces structural responses. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

13.
The terms ‘downward’ and ‘upward’ (synonymous with ‘top‐down’ and ‘bottom‐up’ respectively) are sometimes used when describing methods for developing hydrological models. A downward approach is used here to develop a lumped catchment‐scale model for subsurface stormflow at the 0·94 km2 Slapton Wood catchment. During the development, as few assumptions as possible are made about the behaviour of subsurface stormflow at the catchment scale, and no assumptions are made about its behaviour at smaller scales. (In an upward approach, in contrast, the modelling would be based on assumptions about, and data for, the behaviour at smaller scales, such as the hillslope, plot, and point scales.) The model has a single store with a relatively simple relationship between discharge and storage, based on equations describing hysteretic patterns seen in a graph of discharge against storage. Double‐peaked hydrographs have been observed at the catchment outlet. Rainfall on the channel and infiltration‐excess and saturation‐excess runoff give a rapid response, and shallow subsurface stormflow gives a delayed response. Hydrographs are successfully simulated for the large delayed responses observed in 1971–1980 and 1989–1991, then a lumped model for the rapid response is coupled to the lumped hysteretic model and some double‐peaked hydrographs simulated. A physical interpretation is developed for the lumped hysteretic model, making use of information on patterns of perched saturation observed in 1982 on a hillslope at the Slapton Wood catchment. Downward and upward approaches are complementary, and the most robust way to develop and improve lumped catchment models is to iterate between downward and upward steps. Possible next steps are described. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

14.
Impact stiffness is an important parameter of the contact‐element models for the analysis and prediction of the pounding responses of highway bridges subjected to seismic excitations. This paper presents a pounding experiment to investigate the inconsistencies between the theoretical and experimental values of the impact stiffness both for the linear impact model and Kelvin impact model presented in literature. The analysis of the impact acceleration and acoustic emission signals indicates that accelerometer performance and the non‐uniform pounding are two important factors that affect the pounding responses. Based on this observation, a phenomenological contact‐element model is proposed based on the actual contact state of highway bridges during the impact. To evaluate the effectiveness of the proposed impact model, a numerical simulation is subsequently conducted. A comparison of the results indicates that the proposed impact model can effectively predict the pounding responses of highway bridges. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

15.
Non‐linear structural identification problems have raised considerable research efforts since decades, in which the Bouc–Wen model is generally utilized to simulate non‐linear structural constitutive characteristic. Support vector regression (SVR), a promising data processing method, is studied for versatile‐typed structural identification. First, a model selection strategy is utilized to determine the unknown power parameter of the Bouc–Wen model. Meanwhile, optimum SVR parameters are selected automatically, instead of tuning manually. Consequently, the non‐linear structural equation is rewritten in linear form, and is solved by the SVR technique. A five‐floor versatile‐type structure is studied to show the effectiveness of the proposed method, in which both power parameter known and unknown cases are investigated. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

16.
Growing human pressure and potential change in precipitation pattern induced by climate change require a more efficient and sustainable use of water resources. Hydrological models can provide a fundamental contribution to this purpose, especially as increasing availability of meteorological data and forecast allows for more accurate runoff predictions. In this article, two models are presented for describing the flow formation process in a sub‐alpine catchment: a distributed parameter, physically based model, and a lumped parameter, empirical model. The scope is to compare the two modelling approaches and to assess the impact of hydrometeorological information, either observations or forecast, on water resources management. This is carried out by simulating the real‐time management of the regulated lake that drains the catchment, using the inflow predictions provided by the two models. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

17.
Building structures damaged by a seismic event may be exposed to the risk of aftershocks or another event within a certain period. In this paper, the seismic assessment of damaged piloti‐type RC buildings was carried out to evaluate probabilistic retrofitting effects under successive earthquakes. First, a framework to evaluate the effectiveness of retrofitting was proposed, and then the proposed methodology was demonstrated with a structure retrofitted with buckling‐restrained braces (BRBs). For consideration of realistic successive earthquakes, past records measured at the same station were combined. Within the framework, a series of nonlinear time history analyses were performed for an as‐is model subjected to single earthquake, a damaged model subjected to successive earthquakes, and a damaged model retrofitted with BRBs subjected to successive earthquakes. In addition, fragility analysis was systematically applied in the framework for evaluation of effectiveness of the retrofitting strategy. The proposed framework was capable of quantifying the influence of successive earthquakes and evaluating the effectiveness of BRB retrofitting by considering the severity of the first earthquake damage and the hysteresis behavior of the retrofit element. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

18.
The implicit dissipative generalized‐ α method is analyzed using discrete control theory. Based on this analysis, a one‐parameter family of explicit direct integration algorithms with controllable numerical energy dissipation, referred to as the explicit KR‐α method, is developed for linear and nonlinear structural dynamic numerical analysis applications. Stability, numerical dispersion, and energy dissipation characteristics of the proposed algorithms are studied. It is shown that the algorithms are unconditionally stable for linear elastic and stiffness softening‐type nonlinear systems, where the latter indicates a reduction in post yield stiffness in the force–deformation response. The amount of numerical damping is controlled by a single parameter, which provides a measure of the numerical energy dissipation at higher frequencies. Thus, for a specific value of this parameter, the resulting algorithm is shown to produce no numerical energy dissipation. Furthermore, it is shown that the influence of the numerical damping on the lower mode response is negligible. It is further shown that the numerical dispersion and energy dissipation characteristics of the proposed explicit algorithms are the same as that of the implicit generalized‐ α method. A numerical example is presented to demonstrate the potential of the proposed algorithms in reducing participation of undesired higher modes by using numerical energy dissipation to damp out these modes. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

19.
The time delay resulting from the servo hydraulic systems can potentially destabilize the real‐time dynamic hybrid testing (RTDHT) systems. In this paper, the discrete‐time root locus technique is adopted to investigate the delay‐dependent stability performance of MDOF RTDHT systems. Stability analysis of an idealized two‐story shear frame with two DOFs is first performed to illustrate the proposed method. The delay‐dependent stability condition is presented for various structural properties, time delay, and integration time steps. Effects of delay compensation methods on stability are also investigated. Then, the proposed method is applied to analyze the delay‐dependent stability of a single shaking table RTDHT system with an 18‐DOF finite element numerical substructure, and corresponding RTDHTs are carried out to verify the theoretical results. Furthermore, the stability behavior of a finite element RTDHT system with two physical substructures, loaded by twin shaking tables, is theoretically and experimentally investigated. All experimental results convincingly demonstrate that the delay‐dependent stability analysis on the basis of the discrete‐time root locus technique is feasible. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

20.
Rayleigh damping is commonly used to provide a source of energy dissipation in analyses of structures responding to dynamic loads such as earthquake ground motions. In a finite element model, the Rayleigh damping matrix consists of a mass‐proportional part and a stiffness‐proportional part; the latter typically uses the initial linear stiffness matrix of the structure. Under certain conditions, for example, a non‐linear analysis with softening non‐linearity, the damping forces generated by such a matrix can become unrealistically large compared to the restoring forces, resulting in an analysis being unconservative. Potential problems are demonstrated in this paper through a series of examples. A remedy to these problems is proposed in which bounds are imposed on the damping forces. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

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