Simulation of the earthquake-induced pounding of seismically isolated buildings

Seismic isolation can significantly reduce the induced seismic loads to a relatively stiff building by inserting flexibility at its base to avoid resonance with the predominant frequencies of common earthquakes. Sometimes the width of the provided seismic gap to facilitate the large relative displacements at the isolation level of a seismically isolated building is limited. Hence, there is a possibility of poundings of the building with adjacent structures during strong earthquakes. This work investigates, through numerical simulations using a specially developed software, how potential poundings of seismically isolated buildings with adjacent structures affects the effectiveness of seismic isolation.     

Performance of a multi-story structure with a resilient-friction base isolation system

Complex frequency response functions and excitation-response relations for stationary random process are formulated to estimate responses of multi-story superstructures isolated with resilient-friction base isolation (R-FBI) system. The equivalent linearization technique is also used to linearize the nonlinear governing equations of motion of R-FBI system occurred between the parallel actions of the resiliency of rubber and friction of Teflon-coated plates. In this approach, the spectral density functions for both the relative displacement response and absolute acceleration response of N degrees of freedom systems are derived. The applicability and accuracy of the proposed methodology are examined by comparing the resulting responses obtained from this study with those calculated from time history analysis based method. These two studies demonstrate good agreement in terms of characteristics of peak responses. Extensive sensitivity analysis to find the influence of various important structural parameters on the behavior of structures isolated with R-FBI system is also carried out.     

双向地震激励下隔震结构抗倾覆特性的数值分析

为研究叠层橡胶支座隔震建筑的抗倾覆性能,建立隔震结构在双向地震激励下倾覆力矩时域响应动力分析模型.在对该模型进行简化的基础上,利用结构设计反应谱探讨结构高宽比和结构基本周期等因素对隔震结构抗倾覆力矩与倾覆力矩比值的影响.给出多层和小高层隔震结构在双向地震作用下的抗倾覆安全因数随地震烈度、场地土类别的变化规律.利用本课题...     

A study of suspended roofs for near-source seismic motions

The non-linear behavior of multi-suspended roof systems for seismic loads is studied. The study is based on a formulation that can be easily employed for a preliminary design of multi-suspended roofs subjected to seismic loads. Specifically, applying Lagrange’s equations, the corresponding set of equations of motion for discrete models of multiple suspension roofs is obtained and numerical integration of the equations of motion is performed via the Runge–Kutta scheme. For representative realistic combinations of geometric, stiffness and damping parameters, a non-linear analysis is employed to study the behavior of suspended roofs for near-source and far-field seismic motions. The analysis demonstrates that: (i) code-specified design loads could dramatically underestimate the response of suspended roofs subjected to near-source ground motions and (ii) flexible roofing systems are greatly affected by near-source ground motions, a behavior that is not observed for stiff systems.     

Integrated design optimization of base-isolated concrete buildings under spectrum loading

Base isolation has become a practical control strategy for protecting structures against seismic hazards. Most previous studies on the optimum design of base-isolated structures have been focused on the design optimization of either the base isolation or the superstructure. It is necessary to simultaneously optimize both the base isolation and the superstructure as a whole to seek the most cost-efficient design for such structures. This paper presents an effective numerical optimization technique for the seismic design of base-isolated concrete building structures under spectrum loading. Attempts have been made to automate the integrated spectrum analysis and design optimization procedure and to minimize the total cost of the base-isolated building subject to design performance criteria in terms of the interstory drifts of the superstructure and the lateral displacement of the isolation system. In the optimal design problem formulation, the cost of the superstructure can be expressed in terms of concrete member sizes while assuming all these members to be linearly elastic under earthquake actions. However, the isolation system is assumed to behave nonlinearly, and its cost can be related to the effective horizontal stiffness of each isolator. Using the principle of virtual work, the lateral drift responses of concrete base-isolated buildings can be explicitly formulated and the integrated optimization problem can be solved by the optimality criteria method. The technique is capable of achieving the optimal balance between the costs of the superstructure and the isolation system while the design performance criteria can be simultaneously satisfied. One practical building example with and without base isolation is used to illustrate the effectiveness of the optimal design technique.     

毗邻建筑非平稳随机地震响应LQG控制问题的闭合解

研究了毗邻建筑在非平稳随机地震激励下的LQG控制问题,首先建立了主动液压传动装置连接的毗邻建筑在地震激励下的动力方程,然后采用复模态分析得到系统的动力特性,包括模态频率和模态阻尼比;通过引入成形滤波器来描述地震功率谱密度函数,最终利用虚拟激励法和留数定理推导出LQC;控制问题的闭合解,算例结果表明：只要适当选择LQG控制器参数,LQG控制可有效地减小两栋建筑的地震响应,并且其响应达到稳态的速度比无控时要快得多。     

Simulation and automation of calculations of buildings (structures) on seismic effects

In many countries there are standards as one-dimensional, console systems for calculations of buildings, which stay in contradiction with the experience of destructive earthquakes. This scientific work offers an explanation for the transfer from one-dimensional to three-dimensional models of different complexity in standards. Discretely-continuous and discrete models of buildings have already been worked out as unified three-dimensional systems with floors deforming in their own plane.

We have considered models of seismic effects, which take into account the effect of the running seismic wave under the ground and the effect of non-uniformity of oscillation field along an extended building or a structure. We pointed out paradoxes in calculations while using three-dimensional models of buildings and “zero-dimensional” (normative) models of soil seismic effects on their grounds. In relation to this problem, we have executed the correction of the formula for determination of seismic forces.

Variational methods of making up the solving equations have been developed for calculation of oscillations of buildings as dynamic systems of large dimension. The structural analysis of buildings, of hydraulic structures, of bridges and of ship hulls has expediently proved to choose own vectors of rigidity matrixes separated out of a three-dimensional object of flat elements as possible displacements. It is the key to “rolling-up” extensive solving equations with thousands of the unknowns and “compressing” the three-dimensional object in one or two directions.

In order to simplify the calculations, we use so-called principle of partial symmetry, connected with mechanisms of deformation of cross- or longitudinal-sections of a three-dimensional construction. The principle can be considered as transformations leaving mathematical objects (tensors) invariant. In mathematical plan the symmetry causes break-up of solving equations into the independent blocks.

In an effort to adjust sequentially solutions, a hierarchical chain of mathematical simulation models of different levels was built, in which own vectors of flat elements are considered as hypotheses of deformation. We have developed program complex “PRIS” to automize calculations of buildings by three-dimensional models. The spectral methods of calculations are generalized for universal three-dimensional models of buildings to use standards of different countries in the developed program complex.     

Assessing the suitability of equivalent linear elastic analysis of seismically isolated multi-storey buildings

Although seismic isolation systems exhibit non-linear inelastic behavior, simplified linear elastic analysis is frequently used for the analysis of multi-storey seismically isolated buildings. Equivalent linearized models, which are proposed in the literature, are assessed through parametric studies, using a specially-developed software. The aim is to obtain an insight on their suitability and identify how that may be affected by certain parameters. The results indicate that the estimation of the effective characteristics influences considerably the computed response. Linear elastic analysis may be used in the preliminary design. However, for analysis and research purposes, the more accurate bilinear inelastic analysis should be used.     

Dynamic analysis of structures with friction devices using discrete-time state-space formulation

The seismic response of a structural system equipped with friction-type energy dissipation devices is generally nonlinear. The main reason for this nonlinearity is the friction mechanism that possesses two possible motion states, referred to as stick and slip states. The essential force and kinematic conditions of a friction damper, in these two states, are different. In this paper, by employing a state-space formulation and a linear integration scheme, the discrete-time solution of dynamic response of a structural system equipped with multiple friction devices, which can be in either a stick or slip state, was derived in a single and unified form. The nonlinear friction forces, in each time step of analysis, were solved by satisfying both the force and kinematic conditions of certain motion states. Based on a derived discrete-time solution, a numerical analysis procedure was proposed, which allows the time interval of analysis to remain constant, even at the transition of stick and slip states; thus, it is a systematic and efficient method for numerical implementation. The solution of the method was compared with the analytical free-vibration response of a single DOF system, and also with the harmonic and seismic responses simulated by other conventional numerical methods. These examples demonstrate the accuracy and stability of the proposed method.     

An efficient and robust integration technique for applied random vibration analysis

The mode-based finite element formulation of the equations of motion is usually adopted for linear random vibration analysis (RVA). In general, the RVA of large systems requires a large number of numerical integrations which is very time-consuming for a reasonable level of desired accuracy. Moreover, conventional numerical integration methods may fail to converge when the integrands are highly oscillatory due to slow propagation velocities. In this paper, a robust general-purpose RVA integration technique which can overcome these drawbacks is presented. Multi-point base and nodal excitations including wave passage effect and frequency-independent spatial correlation can be taken into account in the analysis. The proposed technique is based on the closed-form solutions for polynomial-type power spectral density functions and has been verified to be efficient and accurate for many engineering problems. This paper describes the implementation details, presents two examples taken from engineering applications and demonstrates the dramatic time-saving in the computation compared to numerical integration solutions. Response statistics, such as standard deviation of structural responses, are computed and displayed over the entire structures for these examples.     

Application of Micro-GA for optimal cost base isolation design of bridges subject to transient earthquake loads

Seismic isolation and energy dissipation systems are innovative strategies for seismic design and upgrade or retrofit of bridges. In a retrofit design, base isolation devices can be easily incorporated into existing bridges to replace conventional bearings and to improve the overall structural performance. In this paper, an optimal cost base isolation design or retrofit design method for bridges subject to transient earthquake loads is studied. The goal of this study is to push forward the concept of retrofit design optimization of structures using this isolation design as an example. This is achieved by combining nonlinear time history analyses with an optimization procedure to select base isolators that minimize the cost of the isolation system while satisfying certain design requirements. An improved genetic algorithm (GA), Micro-GA, is employed to search for the optimal solutions for such discrete optimization problems. An example of the optimal design of a highway bridge is presented and the minimum cost expense of the isolation system is achieved with improved structural response under multiple transient earthquake loads.     

Nonlinear analysis for seismic upgrade studies of existing essential facilities

The need to perform cost-effective seismic upgrades of essential facilities has made the use of nonlinear finite-element techniques an attractive option. These techniques allow for the analysis of full buildings with large, nonlinear deformations. For reinforced concrete structures, this includes concrete crushing and cracking, and steel reinforcement yielding. These nonlinear models can predict the response of buildings subjected to strong motion earthquakes with a greater degree of accuracy than simple linear or ‘quasi’ nonlinear models.     

Dynamic wave-soil-structure interaction analysis in the time domain

In recent papers [Zhang X, Wegner JL, Haddow, JB. Three dimensional soil-structure-wave interaction analysis in time domain. Earthq Eng Struct Dynam 1999;36:1501-24; Wegner, JL, Zhang X. Free vibration analysis of a three-dimensional soil-structure system. Earthq Eng Struct Dynam 2001;30:43-57], a new numerical procedure was developed and implemented into a three-dimensional dynamic soil-structure interaction analysis program (DSSIA-3D). In this novel procedure, a substructure method is used in which the unbounded soil is modeled by the scaled boundary finite-element method and the structure is modeled by a standard FEM. This results in an improvement over current methods. In this paper, we apply DSSIA-3D to obtain the dynamic response of tall buildings, with multi-level basements, subjected to realistic seismic excitations, including P-, SV-, and SH-waves, at various angles of incidence. Numerical results are obtained for the dynamic response of the soil-structure system, which depends upon frequency content, wave pattern and input angle of ground motion.     

Seismic optimum design of triple friction pendulum bearing subjected to near-fault pulse-like ground motions

Triple Friction Pendulum Bearing (TFPB) as a novel seismic isolator, provides different combinations of stiffness and damping during its course of motion. The adaptive behavior of TFPBs is one of the practical solutions for unsuitable performance of seismic isolation systems under near-fault ground motions. Selecting the TFPB’s design variables (curvature radii, friction coefficients and displacement capacity of sliding surfaces) is complicated process while finding the optimized combination of these variables depends on input ground motion characteristics and seismic performance objectives of the superstructure. Here first, comprehensive nonlinear dynamic analyses are performed to identify influence of the design variables on superstructure response (roof acceleration and displacement of isolated level). Next, a specific numerical optimization method based on Genetic Algorithms (GA) is applied to determine the optimum values of the design variables that minimize superstructure demands. In this process, near-fault ground motions are employed with ranges of pulse periods and hazard levels as input excitations. According to GA results, the derived optimum design variables of TFPB have significantly distinct intervals for different target responses such as story drift and TFPB displacement. Therefore response targets (single objective functions) are combined to make a new fitness function. The proposed optimization method for determining design variables and design intervals can be used for investigating many other types of superstructures with similar behaviors.     

Analysis of nonlinear, dynamic coupled thermoviscoelasticity problems by the finite element method

This investigation deals with the numerical solution of a class of nonlinear problem in transient, coupled, thermoviscoelastidty. Equations of motion and heat conduction are derived for finite elements of thermomechanically simple materials and these are adapted to special classes of thermorheologically simple materials. The analysis involves the solution of large systems of nonlinear integrodifferential equations in the nodal displacements and temperatures and their histories. As a representative example, the general equations are applied to the problem of transient response of a thick-walled hollow cylinder subjected to time-varying internal and external pressures, temperatures, and heat fluxes. The integration scheme used to solve the nonlinear equations employs a linear acceleration assumption, representation of nonlinear integral terms by Simpson's rule, and the iterative solution of large systems of nonlinear algebraic equations at each reduced time step by the Newton-Raphson method. Various numerical results are given and are compared with the linearized, isothermal, and quasi-static solutions.     

Parametric identification of seismic isolators using differential evolution and particle swarm optimization

The objective of a base isolation system is to decouple the building from the damaging components of the earthquake by placing isolators between the superstructure and the foundation. The correct identification of these devices is, therefore, a critical step towards reliable simulations of base-isolated systems subjected to dynamic ground motion. In this perspective, the parametric identification of seismic isolators from experimental dynamic tests is here addressed. In doing so, the focus is on identifying Bouc–Wen model parameters by means of particle swarm optimization and differential evolution. This paper is especially concerned with the assessment of these non-classical parametric identification techniques using a standardized experimental protocol to set out the dynamic loading conditions. A critical review of the obtained outputs demonstrates that particle swarm optimization and differential evolution can be effectively exploited for the parametric identification of seismic isolators.     

A review of homogenization and topology optimization III-topology optimization using optimality criteria

This is the first part of a three-paper review of homogenization and topology optimization, viewed from an engineering standpoint and with the ultimate aim of clarifying the ideas so that interested researchers can easily implement the concepts described. In the first paper we focus on the theory of the homogenization method where we are concerned with the main concepts and derivation of the equations for computation of effective constitutive parameters of complex materials with a periodic micro structure. Such materials are described by the base cell, which is the smallest repetitive unit of material, and the evaluation of the effective constitutive parameters may be carried out by analysing the base cell alone. For simple microstructures this may be achieved analytically, whereas for more complicated systems numerical methods such as the finite element method must be employed. In the second paper, we consider numerical and analytical solutions of the homogenization equations. Topology optimization of structures is a rapidly growing research area, and as opposed to shape optimization allows the introduction of holes in structures, with consequent savings in weight and improved structural characteristics. The homogenization approach, with an emphasis on the optimality criteria method, will be the topic of the third paper in this review.     

Constitutive and Geometric Nonlinear Models for the Seismic Analysis of RC Structures with Energy Dissipators

Nowadays, the use of energy dissipating devices to improve the seismic response of RC structures constitutes a mature branch of the innovative procedures in earthquake engineering. However, even though the benefits derived from this technique are well known and widely accepted, the numerical methods for the simulation of the nonlinear seismic response of RC structures with passive control devices is a field in which new developments are continuously preformed both in computational mechanics and earthquake engineering. In this work, a state of the art of the advanced models for the numerical simulation of the nonlinear dynamic response of RC structures with passive energy dissipating devices subjected to seismic loading is made. The most commonly used passive energy dissipating devices are described, together with their dissipative mechanisms as well as with the numerical procedures used in modeling RC structures provided with such devices. The most important approaches for the formulation of beam models for RC structures are reviewed, with emphasis on the theory and numerics of formulations that consider both geometric and constitutive sources on nonlinearity. In the same manner, a more complete treatment is given to the constitutive nonlinearity in the context of fiber-like approaches including the corresponding cross sectional analysis. Special attention is paid to the use of damage indices able of estimating the remaining load carrying capacity of structures after a seismic action. Finally, nonlinear constitutive and geometric formulations for RC beam elements are examined, together with energy dissipating devices formulated as simpler beams with adequate constitutive laws. Numerical examples allow to illustrate the capacities of the presented formulations.