Dynamic behavior of single-layer latticed cylindrical shells subjected to seismic loading

The single-layer latticed cylindrical shell is one of the most widely adopted space-fl'amed structures.In this paper,free vibration properties and dynamic response to horizontal and vertical seismic waves of single-layer latticed cylindrical shells are analyzed by the finite element method using ANSYS software.In the numerical study,where hundreds of cases were analyzed,the parameters considered included rise-span ratio,length-span ratio,surface load and member section size.Moreover,to better define the actual behavior of single-layer latticed shells,the study is focused on the dynamic stress response to both axial forces and bending moments.Based on the numerical results,the effects of the parameters considered on the stresses are discussed and a modified seismic force coefficient method is suggested.In addition,some advice based on these research results is presented to help in the future design of such structures.

RESEARCH ON IMPERFECTION SENSITIVE REGION OF SINGLE-LAYER LATTICED DOMES

The concept of the imperfection sensitive region is given. The advanced stochastic imperfection method is used to research the imperfection sensitive region of single-layer latticed domes. Taking a K6 single-layer latticed dome with a diameter of 50 m as an example, its imperfection sensitive region is made up of the first 12 kinds of joints. The influence of the imperfections of support joints on the stability of the K6 single-layer latticed dome is negligible. Influences of the joint imperfections of the main rib and the secondary rib on the structural stability are similar. The initial deviations of these joints all greatly lower the critical load of the dome. Results show that the method can analyze the structural imperfection sensitive region quantitatively and accurately.

Shaking table test and numerical simulation of an isolated cylindrical latticed shell under multiple-support excitations

In order to study the infl uence of the ground motion spatial eff ect on the seismic response of large span spatial structures with isolation bearings, a single-layer cylindrical latticed shell scale model with a similarity ratio of 1/10 was constructed. An earthquake simulation shaking table test on the response under multiple-support excitations was performed with the high-position seismic isolation method using high damping rubber (HDR) bearings. Small-amplitude sinusoidal waves and seismic wave records with various spectral characteristics were applied to the model. The dynamic characteristics of the model and the seismic isolation eff ect on it were analyzed at varying apparent wave velocities, namely infi nitely great, 1000 m/s, 500 m/s and 250 m/s. Besides, numerical simulations were carried out by Matlab software. According to the comparison results, the numerical results agreed well with the experimental data. Moreover, the results showed that the latticed shell roof exhibited a translational motion as a rigid body after the installation of the HDR bearings with a much lower natural frequency, higher damping ratio and only 1/2~1/8 of the acceleration response peak values. Meanwhile, the structural responses and the bearing deformations at the output end of the seismic waves were greatly increased under multiple-support excitations.

Seismic isolation analysis of FPS bearings in spatial lattice shell structures

A theoretical model of a friction pendulum system （FPS） is introduced to examine its application for the seismic isolation of spatial lattice shell structures. An equation of motion of the lattice shell with FPS bearings is developed. Then, seismic isolation studies are performed for both double-layer and single-layer lattice shell structures under different seismic input and design parameters of the FPS. The influence of frictional coefficients and radius of the FPS on seismic performance are discussed. Based on the study, some suggestions for seismic isolation design of lattice shells with FPS bearings are given and conclusions are made which could be helpful in the application of FPS.

Damage Assessment, Repair and Field Test of Steel Lattice Shell after Fire

A real case of a steel lattice shell suffering a fire was studied. Based on the theory of field modeling, fire dynamic simulator (FDS) was used to identify the temperature field. The damage mechanism of the structure was determined by FEM analysis. After damage assessment, the shell was repaired with the pipe-encasement method. Finally, field test was employed to check the capacity of the structure after repair. The numerical study results indicate that the damage assessment agrees well with field inspection, verifying the accuracy of fire numerical simulation and FEM analysis. The field test results prove that the pipe-encasement method is secure and reasonable, and the repaired shell is safe.

NONLINEAR DYNAMICAL BIFURCATION AND CHAOTIC MOTION OF SHALLOW CONICAL LATTICE SHELL

The nonlinear dynamical equations of axle symmetry are established by the method of quasi-shells for three-dimensional shallow conical single-layer lattice shells. The compatible equations are given in geometrical nonlinear range. A nonlinear differential equation containing the second and the third order nonlinear items is derived under the boundary conditions of fixed and clamped edges by the method of Galerkin. The problem of bifurcation is discussed by solving the Floquet exponent. In order to study chaotic motion, the equations of free oscillation of a kind of nonlinear dynamics system are solved. Then an exact solution to nonlinear free oscillation of the shallow conical single-layer lattice shell is found as well. The critical conditions of chaotic motion are obtained by solving Melnikov functions, some phase planes are drawn by using digital simulation proving the existence of chaotic motion.

Buckling Load Evaluation Method for Single Layer Cylindrical Lattice Shells

A rational design evaluation procedure is investigated for the elastic overall buckling load carrying capacity of single layer cylindrical lattice shell roof structures. The nature of the imperfection sensitivity of these structures is for the first time reviewed in this paper. This allows the development of the reduced stiffness buckling analytical concept for the lattice shells based upon the introduction of a simple lower bound estimation equation through the use of the so-called continuum shell analogy theory. The linear and nonlinear buckling loads found from conventional finite element analyses are compared with the present estimations. Finally, the elastic-plastic load carrying capacity estimation method through the use of the present elastic lower bound criteria is also proposed.

Optimization for Maximum Nonlinear Buckling Load and Topics on Imperfection of Latticed Shells

The present paper represents comparison of continuum shells and latticed shells with qualitative analysis. For shells, the mechanical characteristics in the two perpendicular directions are continuous and related to each other, and any change in thickness will result in change in stiffness in any direction. In latticed shells, members are discrete and stiffnesses in two mutually perpendicular directions are discontinuous and independent of each other. Therefore, sensitivity of geometrical imperfection for buckling of latticed shells should be different from that of continuum shells. The author proposes a shape optimization method for maximum buckling load of a latticed shell. A single layer latticed dome is taken as a numerical example, and the results show that the buckling load parameter for full area loading case increases 32.75% compared to that of its initial shape. Furthermore, the numerical example demonstrates that an optimum latticed shell with maximum buckling load, unlike an optimum continuum shell, may not be sensitive to its geometrical imperfection.

Non-uniform thermal behavior of single-layer spherical reticulated shell structures considering time-variant environmental factors: analysis and design

Contrary to conventional design methods that assume uniform and slow temperature changes tied to atmospheric conditions,single-layer spherical reticulated shells undergo significant non-uniform and time-variant temperature variations due to dynamic environmental coupling.These differences can affect structural performance and pose safety risks.Here,a systematic numerical method was developed and applied to simulate long-term temperature variations in such a structure under real environmental conditions,revealing its non-uniform distribution characteristics and time-variant regularity.A simplified design method for non-uniform thermal loads,accounting for time-variant environmental factors,was theoretically derived and validated through experiments and simulations.The maximum deviation and mean error rate between calculated and tested results were 6.1℃ and 3.7%,respectively.Calculated temperature fields aligned with simulated ones,with deviations under 6.0℃.Using the design method,non-uniform thermal effects of the structure are analyzed.Maximum member stress and nodal displacement under non-uniform thermal loads reached 119.3 MPa and 19.7 mm,representing increases of 167.5%and 169.9%,respectively,compared to uniform thermal loads.The impacts of healing construction time on non-uniform thermal effects were evaluated,resulting in construction recommendations.The methodologies and conclusions presented here can serve as valuable references for the thermal design,construction,and control of single-layer spherical reticulated shells or similar structures.

A new neural-network-based method for structural damage identification in single-layer reticulated shells

Single-layer reticulated shells(SLRSs)find widespread application in the roofs of crucial public structures,such as gymnasiums and exhibition center.In this paper,a new neural-network-based method for structural damage identification in SLRSs is proposed.First,a damage vector index,NDL,that is related only to the damage localization,is proposed for SLRSs,and a damage data set is constructed from NDL data.On the basis of visualization of the NDL damage data set,the structural damaged region locations are identified using convolutional neural networks(CNNs).By cross-dividing the damaged region locations and using parallel CNNs for each regional location,the damaged region locations can be quickly and efficiently identified and the undamaged region locations can be eliminated.Second,a damage vector index,DS,that is related to the damage location and damage degree,is proposed for SLRSs.Based on the damaged region identified previously,a fully connected neural network(FCNN)is constructed to identify the location and damage degree of members.The effectiveness and reliability of the proposed method are verified by considering a numerical case of a spherical SLRS.The calculation results showed that the proposed method can quickly eliminate candidate locations of potential damaged region locations and precisely determine the location and damage degree of members.

Random fractal-based computational design of an ice-ray (IR) lattice shell structure

Chinese ice-ray (IR) lattices, known for their intricate and visually fascinating random patterns as decorative elements in traditional 18th-century Chinese window design, exhibit underlying stiffness as latticed window fences. Such unique patterns represent a new morphology within the family of stochastic lattices. However, the latent structural potential within the random patterns of ice-ray lattices remains largely unexplored, particularly in the context of lattice shell design. This study systematically studies the geometric qualities of ice-ray lattice patterns and develops an algorithm to model these patterns for ice-ray lattice shell design. Subsequently, it assesses the structural feasibility and effectiveness of these lattice shells in comparison to conventional gridshells. The practicality of constructing random lattice shells using digital fabrication tools is also explored. Employing fractal geometry as a foundational framework, this research not only offers insights into the potential of ice-ray lattices for innovative lattice shell design but also introduces a new structural morphology to the field, expanding the possibilities of incorporating stochastic patterns in lattice shell design. Ultimately, it opens up new opportunities for innovative lattice shell designs, emphasizing the potential of stochastic patterns in structural applications.

利用负刚度磁流变阻尼器的单层球面网壳三维隔震研究

网壳结构三维隔震是备受关注的研究热点之一。已有的研究聚焦于被动型三维隔震装置,其在竖向的性能参数无法实时调控。为解决这一问题,将负刚度磁流变阻尼器(magnetorheological negative stiffness dampers,MRNSDs)与预压弹簧装置(prepressed spring devices,PSDs)并联,形成一种可调节阻尼力的竖向隔震装置(MRDNSD-PSD)。面向延长受控结构竖向自振周期的目标,建立了MRNSD的控制策略及其实施方法,利用其模拟了该控制装置的滞回响应。以某周边支承单层球面网壳作为研究对象,将含有MRNSD-PSD的半主动三维隔震系统、两种不同的被动三维隔震系统分别用于提升该结构的抗震性能。通过数模模拟,对上述受控和无控结构进行了地震响应分析。数值结果表明,三种隔震系统均可有效降低结构地震响应,但半主动隔震系统较被动型隔震系统能够提供更优的竖向加速度和竖向位移控制效果。

点阵夹芯圆柱壳自由振动分析的波有限元方法

针对点阵夹芯圆柱壳的自由振动分析发展了波有限元法.首先基于自由波的传播规律,建立了点阵夹芯圆柱壳胞元的二维波有限元控制方程,相比于全尺寸有限元模型,显著缩减了控制方程的自由度规模;其次,基于Neumann级数推导了约束动刚度矩阵求逆的显式表达式,不仅可以提高计算效率,而且使得固有频率从控制方程中分离出来,从而将点阵夹芯圆柱壳的固有频率求解转化为单个胞元自由度规模的二次特征值问题;最后,根据结构振动模态与自由波的关系,给出了圆柱壳轴向和周向的波传播参数的表达式,进而求得点阵夹芯圆柱壳的固有频率和模态.数值算例考虑了多种边界条件下的点阵夹芯圆柱壳自由振动问题,验证了该方法的正确性和高效性.

不同布索方案下预应力双层柱面网壳结构稳定性分析

在双层柱面网壳结构中引入预应力拉索,不仅能增大结构跨度,还能提高大跨度结构的安全性、稳定性。钢结构建筑的稳定性能是钢结构设计的关键因素。文中以大跨度双层柱面网壳结构为例,采用有限元法,选取四种对结构受力有利的布索形式,结合矢跨比、跨度、厚度等因素,对所选结构模型进行稳定性分析。

基于位移-速度输入法结构多点激励FPS支座隔震效果研究

受行波效应、相干效应、场地效应的影响,大跨度结构的多点激励地震反应分析非常复杂,且考虑多点激励下对大跨空间网格结构隔震性能的影响是结构工程抗震方向中有重大意义的研究课题。以单层圆柱面大跨度空间网架结构为研究对象,基于直接位移法,应用SAP2000有限元软件建立了多点激励动力反应时程分析模型,进行结构在地震动一致激励和多点激励作用下的动力反应分析计算。结果表明:水平地震动多点激励效应对大跨度空间结构的影响十分显著,需采取使用多点激励输入方式。不设置隔震支座时,多点激励下,支撑柱弯矩与剪力随波速的减小而明显增加,柱顶位移变小,中柱轴力略微上升。基础隔震时,各支撑柱柱顶内力与位移的分配较无隔震时存在差异。边柱的弯矩、剪力及轴力均小于中柱的相应值,但柱顶位移增加明显。柱弯矩减震效率保持在45%~75%,柱剪力减震效率保持在60%~85%;柱顶隔震时,能得到比基础隔震更高的隔震效率,且柱弯矩隔震效率高达90%左右,柱剪力隔震效率保持在85%~90%。柱顶位移显著减小,柱轴力比基础隔震时略有增加。

某单层椭圆抛物面网壳结构荷载试验

网壳结构杆件和节点几何尺寸的偏差以及曲面的偏离对网壳的内力、整体稳定性影响较大。而在既有网壳结构安全鉴定过程中发现质量偏差时,承载力计算应考虑这些偏差情况,但标准并未给出具体方法,文章以某单层椭圆抛物面网壳结构荷载试验为背景,通过荷载试验检验某单层椭圆抛物面网壳结构存在质量偏差的同时,增加额外吊挂荷载情况下结构的承载能力,并为提高结构承载力复核模型的准确性提供依据。

单层球面网壳设计研究

单层网壳结构的特点是结构的刚度和位移为非线性关系,非线性稳定分析事关结构工程安全。结合某单层球面网壳玻璃采光顶结构设计,重点介绍网壳结构几何非线性、材料非线性稳定分析、受力复杂的关键节点有限元分析、节点细部设计。分析表明,非线性稳定分析及关键节点有限元分析可确保工程设计安全可靠,所用方法可供同类工程设计参考。

基于有限质点法的单层柱面网壳冲击作用下动态响应

为了探究单层柱面网壳结构受冲击作用下的动态响应,验证有限质点法模拟网壳结构冲击动态响应的准确性,建立了7个冲击工况的有限质点法模型,采用以对称罚函数为基础的双球碰撞模型为冲击模型,根据能量守恒定律确定冲击模型中碰撞刚度系数,引入Cowper-Symonds本构模型,获取结构动力响应,并将模拟结果与试验结果对比。结果表明:1)有限质点法得到的冲击力时程变化曲线与试验结果相近;2)由于未考虑结构损伤因素,有限质点法所得节点位移略小于试验值,但所获得的结构失稳动量与试验一致;3)冲击产生的网壳应变能更易沿着网壳斜杆传递,同时冲击区杆件,刚度较大区域如支座附近的杆件为结构的主要受力构件。有限质点法可以较为准确的判断单层柱面网壳结构受冲击作用的动态响应,可为提高相关结构抗冲击性能提供理论依据。

含初始转角的隔震支座在双层柱面网壳结构中的隔震性能

为了研究大跨度空间结构中存在支座转动问题,通过含初始转角的橡胶隔震支座的双层柱面网壳结构研究了水平方向上结构水平地震反应。结合通过实验得出的经验公式对橡胶隔震支座水平性能进行修正,并通过SAP2000应用动力时程分析法,在考虑下部支承结构的情况,对含初始转角的橡胶隔震支座进行了参数分析。结果表明:水平地震作用下,较小转角的隔震支座的支座底部剪力峰值与加速度峰值会下降;随着转角增加,柱顶加速度峰值、隔震支座底部剪力峰值等迅速增加;而跨高比大的网壳结构会放大初始转角对结构的影响,加大结构整体的加速度峰值和结构柱的位移峰值,但限制上层网壳结构的位移峰值。因此在考虑初始转角的情况下,若需要限制网壳结构加速度或位移,设计时需要将网壳结构跨高比的放大效应纳入考虑范围。

某网壳结构分析与设计

某地上连体结构位于四个地块交汇处,采用单层双曲抛物面网壳+预应力拉索杂交的结构形式,网壳下方有栈桥与其形成一体。介绍了该网壳的概况、结构传力体系、设计标准和荷载,以及网壳的承载力、变形,结果表明杆件承载力和变形满足规范要求;介绍了网壳的整体稳定分析,包含几何非线性稳定和几何双非线性稳定分析,结果表明网壳的稳定承载力满足规范要求。此外,还介绍了该工程复杂相贯节点的有限元分析,该项目风洞试验及风荷载取值方法。