Dynamic stability characteristics of liquid-filled shells

A Galerkin Finite Element formulation for the dynamic stability analysis of liquid-filled shells is given in this paper. The coupling among the axial and circumferential modes is investigated. The dynamic stability characteristics of two liquid-filled storage tanks subjected to vertical, horizontal and rocking seismic excitations are presented. It is shown that a tall tank tends to buckle at distinct frequencies; and for cos θ-type ground excitation, cos 2θ, cos 3θ and cos 4θ are the dominant modes of failure. On the other hand, in a broad tank, buckling regions overlap each other. In particular, for cos θ-type ground excitation, the dominant buckling modes are cos 6θ to cos 9θ, and also cos 12θ to cos 14θ.     

Effects of the dynamic cross-interaction in the seismic analysis of multiple embedded foundations

A boundary element formulation of the substructure deletion method is presented for the seismic analysis of the dynamic cross-interaction between multiple embedded foundations. This approach is particularly suitable for three-dimensional foundations of any arbitrary geometrical shape and spatial location, since it requires only the discretization of the foundations’ surfaces. The surrounding soil is represented by a homogeneous viscoelastic half-space while the foundations are assumed to be rigid and subjected to incoming SH-, P-, and SV-waves arbitrarily inclined in both the horizontal and vertical planes. The proposed methodology is tested for the case of two identical embedded square foundations for different values of the foundations’ embedment and distance. The effects of the cross-interaction are outlined in the components of the impedance matrix and of the foundation input motion. © 1997 John Wiley & Sons, Ltd.     

地震作用下立式储液罐罐壁“象足”变形仿真分析

基于ANSYS软件建立了考虑液体晃动和罐底提离立式储液罐有限元模型,分别进行了水平地震和竖向地震作用下罐壁“象足”变形分析。分析表明:立式储液罐罐壁“象足”变形主要是由罐壁纵向压应力超过临界应力而产生的局部屈曲破坏,并非强度破坏。因罐底提离导致的罐底与基础反复撞击加大了作用在罐壁上的应力,使罐壁底部“象足”变形不断发展,最终导致罐壁撕裂。在完全相同地震加速度作用下,水平地震作用比竖向地震作用罐壁更早更容易进入屈曲状态,产生“象足”变形。     

Failure of masonry arches under impulse base motion

Recent seismic events have caused damage or collapse of invaluable historical buildings, further proving the vulnerability of unreinforced masonry (URM) structures to earthquakes. This study aims to understand failure of masonry arches—typical components of URM historic structures—subjected to horizontal ground acceleration impulses. An analytical model is developed to describe the dynamic behaviour of the arch and is used to predict the combinations of impulse magnitudes and durations which lead to its collapse. The model considers impact of the rigid blocks through several cycles of motion, illustrating that failure can occur at lower ground accelerations than previously believed. The resulting failure domains are of potential use for design and assessment purposes. Predictions of the analytical model are compared with results of numerical modelling by the distinct element method, and the good agreement between results validates the analytical model and at the same time confirms the potential of the distinct element framework as a method of evaluating complex URM structures under dynamic loading. Copyright © 2007 John Wiley & Sons, Ltd.     

地震作用下立式储液罐罐壁"象足"变形仿真分析

基于ANSYS软件建立了考虑液体晃动和罐底提离立式储液罐有限元模型,分别进行了水平地震和竖向地震作用下罐壁"象足"变形分析.分析表明:立式储液罐罐壁"象足"变形主要是由罐壁纵向压应力超过临界应力而产生的局部屈曲破坏,并非强度破坏.因罐底提离导致的罐底与基础反复撞击加大了作用在罐壁上的应力,使罐壁底部"象足"变形不断发展,最终导致罐壁撕裂.在完全相同地震加速度作用下,水平地震作用比竖向地震作用罐壁更早更容易进入屈曲状态,产生"象足"变形.     

Dynamic analysis of flexible rectangular fluid containers subjected to horizontal ground motion

In this paper, an analytical method is proposed to determine the dynamic response of 3‐D rectangular liquid storage tanks with four flexible walls, subjected to horizontal seismic ground motion. Fluid–structure interaction effects on the dynamic responses of partially filled fluid containers, incorporating wall flexibility, are accounted for in evaluating impulsive pressure. The velocity potential in which boundary conditions are satisfied is solved by the method of separation of variables using the principle of superposition. The impulsive pressure distribution is then computed. Solutions based on 3‐D modeling of the rectangular containers are obtained by applying the Rayleigh–Ritz method using the vibration modes of flexible plates with suitable boundary conditions. Trigonometrical functions that satisfy boundary conditions of the storage tank such that the flexibility of the wall is thoroughly considered are used to define the admissible vibration modes. The analysis is then performed in the time domain. Moreover, an analytical procedure is developed for deriving a simple formula that evaluates convective pressure and surface displacements in a similar rigid tank. The variation of dynamic response characteristics with respect to different tank parameters is investigated. A mechanical model, which takes into account the deformability of the tank wall, is developed. The parameters of such a model can be obtained from developed charts, and the maximum seismic loading can be predicted by means of a response spectrum characterizing the design earthquake. Accordingly, a simplified but sufficiently accurate design procedure is developed to improve code formulas for the seismic design of liquid storage tanks. Copyright © 2013 John Wiley & Sons, Ltd.     

Earthquake simulation test of circular reinforced concrete bridge column under multidirectional seismic excitation

1 Introduction Since the 1971 San Fernando earthquake, a signi?cant amount of research has been conducted on the ductility capacity of reinforced concrete bridge columns, resulting in signi?cant advances in the seismic design of bridges. Since most tests have been done in static or quasistatic conditions and unidirectional loading conditions, however, no method that properly evaluates the effect of multidirectional dynamic loading has been developed, and design recommendations on this effect a…     

Fluid–structure interaction analysis of 3-D rectangular tanks by a variationally coupled BEM–FEM and comparison with test results

A variationally coupled BEM–FEM is developed which can be used to analyse dynamic response, including free-surface sloshing motion, of 3-D rectangular liquid storage tanks subjected to horizontal ground excitation. The tank structure is modelled by the finite element method and the fluid region by the indirect boundary element method. By minimizing a single Lagrange function defined for the entire system, the governing equation with symmetric coefficient matrices is obtained. To verify the newly developed method, the analysis results are compared with the shaking-table test data of a 3-D rectangular tank model and with the solutions by the direct BEM–FEM. Analytical studies are conducted on the dynamic behaviour of 3-D rectangular tanks using the method developed. In particular, the characteristics of the sloshing response, the effect of the rigidity of adjacent walls on the dynamic response of the tanks and the orthogonal effects are investigated. © 1998 John Wiley & Sons, Ltd.     

Response of tanks to vertical seismic excitations

A method for analyzing the earthquake response of elastic, cylindrical liquid storage tanks under vertical excitations is presented. The method is based on superposition of the free axisymmetrical vibrational modes obtained numerically by the finite element method. The validity of these modes has been checked analytically and the formulation of the load vector has been confirmed by a static analysis. Two forms of ground excitations have been used: step functions and recorded seismic components. The radial and axial displacements are computed and the corresponding stresses are presented. Both fixed and partly fixed tanks are considered to evaluate the effect of base fixation on tank behaviour. Finally, tank response under the simultaneous action of both vertical and lateral excitations is calculated to evaluate the relative importance of the vertical component of ground acceleration on the overall seismic behaviour of liquid storage tanks.     

弦支穹顶结构的抗震性能研究

弦支穹顶是一种受力性能优良的结构体系，它综合了单层网壳结构和索穹顶结构的优点，详细分析了影响弦支穹顶结构自振特性的各类参数，指出了边界条件对结构抗震性能的决定性影响。研究表明：当采用径向滑动边界时，即边界节点竖向和法向受到约束而容许径向在水平面滑动时，局部布索的弦支穹顶具有较佳的抗震性能；当边界条件相同时，弦支穹顶在水平地震和竖向地震作用下反应相似，只是程度上不同。     

Vertical coherency function model of spatial ground motion

Many studies have focused on horizontal ground motion, resulting in many coherency functions for horizontal ground motion while neglecting related problems arising from vertical ground motion. However, seismic events have demonstrated that the vertical components of ground motion sometimes govern the ultimate failure of structures. In this paper, a vertical coherency function model of spatial ground motion is proposed based on the Hao model and SMART 1 array records, and the validity of the model is demonstrated. The vertical coherency function model of spatial ground motion is also compared with the horizontal coherency function model, indicating that neither model exhibits isotropic characteristics. The value of the vertical coherency function has little correlation with that of the horizontal coherency function. However, the coherence of the vertical ground motion between a pair of stations decreases with their projection distance and the frequency of the ground motion. When the projection distance in the wave direction is greater than 800 meters, the coherency between the two points can be neglected.     

Numerical investigation of stochastic response of an elevated water tank to random underground blast loading

This paper presents a stochastic finite element seismic response study of a water tank subjected to random underground blast-induced ground motion. Such tanks contain water and hazardous chemical substances, which implies significant risk to human life, serious environmental pollution, and considerable economic loss. The random blast-induced ground motion is represented by power spectral density function and applied to each support point of the three dimensional finite element model of the elevated water tank–fluid interaction system. A parametric study is conducted to estimate the effects of the blast-induced ground motion on the stochastic response of the elevated water tank system. Therefore, the analyses are carried out for different values of the charge weight and the distance from the charge centre. Additionally, in order to investigate the effect of the fluid on the stochastic response of the elevated water tank, three cases with different water levels are considered in the analyses. Finally, it is observed that underground blast loading considerably changes the stochastic behavior of the elevated water tank system.     

竖向断层对场地地面运动的影响

本文采用二维显式有限元结合透射边界的数值方法,考虑均匀弹性半空间内存在着不同宽度及深度的断层,由下向上分别垂直和斜(30°)入射一个脉冲波,研究非发震断层地面运动的一些特点。通过计算断层内外地震地面运动传递函数的幅值谱,并与自由场反应对比,以说明竖向断层对地震波传播和附近地面运动的影响,在此基础上进一步对断层周边一般结构抗震设计是否要考虑断层影响提出了几点建议。     

Finite element analysis of the seismic response of anchored and unanchored liquid storage tanks

The seismic response of liquid-filled cylindrical storage tanks has been investigated using finite element techniques implemented in the general purpose structural analysis computer code ANSYS. Both added mass concepts and displacement-based fluid finite elements were employed to allow for the effects of the liquid. Simplified response spectrum modal analyses of a tank making use of the axisymmetric harmonic displacement patterns of the principal modes of deformation were found to give accurate predictions of the tank behaviour with a rigidly anchored base. Time history analyses of three-dimensional finite element models of unanchored and flexibly anchored tanks, with gap conditions between the tank base and the supporting floor to allow lift-off of the base, indicated that stresses in the tank and resultant loads on the floor can be much greater than for a rigidly restrained tank. These results demonstrate the importance of carefully considering the restraint conditions when performing seismic design calculations on storage tanks.     

Sliding response of gravity dams including vertical seismic accelerations

Seismic safety assessment of gravity dams has become a major concern in many regions of the world while the effects of vertical seismic accelerations on the response of structures remain poorly understood. This paper first investigates the effect of including vertical accelerations in the sliding response analysis of gravity dams subjected to a range of historical ground motion records separated in two groups according to their source-to-site distance. Analyses showed that the incidence of vertical accelerations on the sliding response of gravity dams is significantly higher for near-source records than for farsource records. The pseudo-static 30% load combination rule, commonly used in practice to account for the non-simultaneous occurrence of the peak horizontal and vertical accelerations, yielded good approximations of the minimum safety factors against sliding computed from time-history analyses. A method for empirically estimating the vertical response spectra based on horizontal spectra, accounting for the difference in frequency content and amplitudes between the two components is investigated. Results from analyses using spectrum compatible horizontal and vertical synthetic records also approximated well the sliding response of a gravity dam subjected to series of simultaneous horizontal and vertical historical earthquake records.     

Seismic soil–structure interaction of massive flexible strip-foundations embedded in layered soils by hybrid BEM–FEM

A study on the seismic response of massive flexible strip-foundations embedded in layered soils and subjected to seismic excitation is presented. Emphasis is placed on the investigation of the system response with the aid of a boundary element–finite element formulation proper for the treatment of such soil–structure interaction problems. In the formulation, the boundary element method (BEM) is employed to overcome the difficulties that arise from modeling the infinite soil domain, and the finite element method (FEM) is applied to model the embedded massive flexible strip-foundation. The numerical solution for the soil–foundation system is obtained by coupling the FEM with the BEM through compatibility and equilibrium conditions at the soil–foundation and soil layer interfaces. A parametric study is conducted to investigate the effects of foundation stiffness and embedment on the seismic response.     

Stability of elastic frames subjected to earthquake excitations

Dynamic stability of elastic multistorey frame structures subjected to vertical earthquake ground accelerations is studied. Different stationary, non-stationary, white and non-white random models for earthquake strong motion are considered. The concepts of mean-square and almost-sure stability are reviewed and the corresponding stability theorems are presented. Several general criteria regarding the dynamic stability of the equilibrium state of multistorey frames subjected to random excitations are developed. A few examples concerning the stability of single and multi-degree-of-freedom structures under earthquake excitations are presented. The stability of motion of frames under combined horizontal–vertical acceleration is also briefly discussed.     

膜型网壳结构抗震性能研究

本文采用子空间迭代法分析了单层膜型网壳结构的自振特性;推导了大跨空间结构几何非线性地震响应时程分析的计算过程,编制相应的计算程序,用振型分解反应谱法与时程法进行了结构地震响应特性分析。研究表明:膜型网壳结构的抗震性能比较好;用反应谱法分析时,水平地震作用下截断振型取15、竖向地震作用下取60可满足工程设计要求;用反应谱法计算结构竖向地震响应是安全可靠的,但进行水平地震响应分析时,最终还需用时程法进行验算。     

地震体波斜入射下的断层台阶地震反应分析

应用显式有限元法对倾斜断层台阶在地震体波斜入射下的地震反应进行了数值模拟。模拟结果表明，P波入射时的竖向运动分量和SV波入射时的水平向运动分量在台阶上角点处存在极大值、在台阶下角点处存在极小值，同时在上下台面还出现由角点激发、向台阶外传播的转换体波与面波。这一结果说明，在断层台阶场地建设重大工程时应离开上角点一定距离，并考虑上下水平表面地面运动的差异性。     

竖向地震作用对储液罐地震响应的影响分析

地震作用下大型储液罐的安全问题日益引起重视。基于ANSYS软件建立储罐液体耦合有限元模型,考虑罐底非线性接触效应,以El-Centro南北向和竖直向记录地震波为输入,研究水平激励以及水平和竖向同时激励两种工况下储罐的动力响应。研究结果表明,两种工况下靠近罐底1.2m处均发生了"象足"变形,竖向激励下水平相对位移增加了14%。竖向激励使得罐壁环向应力和轴向压应力均有不同程度的增加。竖向地震激励对液面的竖向晃动影响较小。储液罐底板在地震作用下发生了竖向提离和永久滑移,竖向激励时增长幅度均在10%左右。同时罐体基底剪力在竖向地震作用下也有所增大。储罐抗震设计时应考虑竖向地震分量的影响,研究结论可为立式储罐的抗震设计提供一定的参考和依据。