索结构找形分析的精确单元方法

索找形问题是索结构分析中所要解决的首要问题,在给定边界条件下,所施加的预张力和外部荷载通过调节索的 形状来平衡。本文研究索结构初始形状确定的精确有限单元法,对于常见的荷载形式,构造了线性和非线性两大类共5种 单元,适用于一般的索结构找形计算,并且可以给出精确的解答。本文通过将水平方向和竖直方向的平衡方程解藕,得出 了索单元的精确描述格式,并保证了索结构形状的唯一性。文中以索结构内部结点坐标作为基本未知量,以结点平衡方程 为基本方程,通过直接求解单元的平衡微分方程得到单元刚度矩阵的解析表达式。对于由线性单元组成的索结构,其基本 方程为线性,可直接求解;对于含有非线性单元的索结构,其基本方程为非线性,需通过迭代求解,文中构造了相应的 Newton法迭代格式。本文方法所需单元数目少,计算量小,所得到的解答为数值精确解。数值算例表明本法稳定可靠。     

高层混凝土框架核心筒-木盒混合结构抗震性能研究

提出了一种以混凝土框架-核心筒结构为“主结构”,每层主结构间内嵌3层装配式轻型木结构为“子结构”的装配式高层建筑结构体系。该混合结构体系实现了建筑使用功能多样化,结构体系集成化,建筑材料绿色化,建造施工装配化的特点。着重研究了体系中主结构与子结构间的连接,根据连接的特点和强弱,提出了3种不同的结构模型：1）重力模型,其特点是主结构与子结构在侧向不连接或弱连接,不考虑子结构对整体结构抗侧刚度的贡献;2）刚度模型,主子结构间采用螺栓有效连接;3）隔震模型,其子结构底面与主结构采用隔震支座连接。采用有限元软件SAP2000对3种具有不同受力特点的模型结构进行抗震性能分析研究。结果表明：重力模型主结构受力安全合理;刚度模型中子结构对整体结构抗侧刚度的贡献可达6%~35%;隔震模型中隔震子结构可明显降低整体结构的地震反应。与建筑功能相同的混凝土框架核心筒结构相比,混凝土框架核心筒-木盒结构自重可减轻25%,地震作用可减小30%,有利于在地震设防区应用。     

Large deflection analysis of beams,pipes, or poles

This paper describes an efficient algorithm for the analysis of flexible beams, pipes or poles. The algorithm has been applied to a wide variety of offshore systems in which flexible pipes or hoses are commonly used. The method can be used to study either a complete line-like flexible structure or to develop the properties of a ‘long flexible beam element’ which can be combined with other types of elements or substructures to model complex structural systems.     

超高龙门吊安装塔架结构系统的非线性静力分析

大型龙门吊安装塔架系统是应用于重型龙门吊安装过程中的一种索杆混合结构体系。在水平力作用下 ,体系非线性效应显著。为了比较全面的解决大型龙门吊安装塔架的非线性静力问题 ,文中给出了龙门吊安装塔架静力分析的经典力学法和非线性有限元法。前者首先建立了轴压悬臂柱的平衡微分方程 ,再联立纤绳方程 ,求解了柱顶位移和纤绳内力 ;后者通过一种非线性直线单元 ,建立了混合体系的增量平衡方程。最后分别用两种分析方法验算了体系横风、纵向顺风 ,两种工况 ,并比较了二者的柱顶位移和纤绳张力。结果表明 ,两种方法都是可靠的     

Instability of variable-arc-length elastica subjected to end moment

This article presents the instability of a variable-arc-length elastica where one end is attached on the hinged joint and the other end is placed on the sleeve support. The friction is also introduced at the sleeve end. At the hinged end, the concentrated moment is applied to turn the elastica around the joint. The system of governing differential equations is obtained from equilibrium equations, constitutive equation and nonlinear geometric relations. To extract the behaviour of this problem, the system of differential equations needs to be integrated from one end to the other and satisfied boundary conditions. In this problem, we utilise the Runge–Kutta scheme as an integration tool and the shooting method plays a vital role to compute the results. The results are interpreted by using the load-deflection diagram where the stiffness of the system can be observed. From the results, it can be found that there are two equilibrium points for a given end moment that is less than its critical value. This results from the non-monotonic load-deflection curves. There is a limit load point (buckling load) for each value of frictional coefficient. Beyond the buckling load, the elastica can lose its stability. Moreover, we discovered that, with presence of the friction (i.e. dry friction), the elastica shows more stable behaviour than its counterpart without friction since the buckling load increases when the frictional coefficient increases.     

Seismic response of multi-storey buildings including foundation interaction and P-Δ effects

This paper presents a method of seismic analysis of multi-storey buildings when both soil-structure interaction and P-Δ effects have been taken into account. The additional overturning moment at each storey due to P-Δ effects is replaced by two fictitious horizontal forces acting in opposite directions at the upper and lower ends of each storey. Then, the governing equation for each floor is developed in which these fictitious horizontal forces are incorporated along with seismic inertia forces. Considering the footing as a rigid disc resting on the surface of an elastic half-space, two equations expressing the equilibrium of the building as a whole in translation and rotation complete the set of equations in terms of floor displacements and two rigid body base displacements. Recognizing that the superstructure alone admits classical normal modes, floor governing equations are uncoupled and substituted into the remaining equations, which results in two coupled integro-differential equations in terms of two rigid body displacements. These two equations can be solved using numerical procedures. The method is applied to two unbraced steel buildings and numerical results are presented for different foundation soil conditions. The influence due to P-Δ effects and soil-structure interactions on the responses of these buildings is discussed.     

两个弯剪型抗侧力体系的线性相互作用

本文对两个弯剪型抗侧力结构在水平荷载作用下的共同工作进行了分析。推导了基本微分方程并得到了水平均布荷载下的解析解。算例表明,一个结构的抗弯刚度参与另一个结构共同工作的能力受到自身抗剪刚度的影响;反之,一个结构的抗剪刚度参与另一个结构共同作用的能力也受到自身抗弯刚度的影响。本文还提出了一个简单的、利用两个弯剪型子结构作为独立结构在水平力作用下的挠度,构造双重弯剪型结构在相同水平力作用下水平挠度的方法,对比表明,这种构造出来的挠度与精确解挠度非常接近。通过这种构造模型,对双重弯剪型结构之间的相互作用可以获得非常直观的了解和理解,本文建议了一个串联一并联电路来帮助理解双重抗侧力结构之间的共同作用。     

Natural frequencies for flexural and torsional vibrations of beams on Pasternak foundation

This paper studies the free vibrations of prismatic beams resting on Pasternak foundation. Special attention is given to the consideration of the bending–twist deformations of the beams. The governing differential equations of the motion are derived by imposing the dynamic equilibrium of a Timoshenko beam element. Differential equations are solved numerically using the combination of the Runge–Kutta and Regula–Falsi methods. The results of some cases are presented, and are analyzed to highlight the effects of the end constraint, rotatory and torsional inertias, aspect ratio, thickness ratio, beam stiffness, and foundation stiffness on the natural frequencies of the beams. The natural frequencies of the present model are validated by comparing to those from model tests.     

A GRAPH-THEORETIC MODEL FOR FINITE ELEMENTS WITH SIDE VARIABLES

Most finite elements have variables associated with corner nodes. However, families of equilibrium and hybrid elements exist that have connections on sides, or interfaces, and retain the corner nodes only to describe the geometry. The aim of this paper is to combine concepts from finite elements and graph-theory so that models composed of such elements can be rigorously derived. Two tree graphs are introduced to each element to represent two distinct types of generalized through (forces and moments) and across (translations and rotations) variables. These variables are termed basic and higher-order and are associated with element properties in the form of mukiterminal representations. The terminal equations couple the variables from the two graphs, and are based on weak integral forms, although discrete versions based on graph-theoretic models are also possible. The variables satisfy vertex and circuit laws for each system graph as built up from connected elements, along with driver edges that represent specified loads and displacements. Graph-theory issues are invoked to obtain independent equations for stiffness and flexibility methods of analysis.     

传播矩阵法

本法适用于杆件体系结构的分析。系根据子结构间内力或形变的传播和平衡条件,建立了以传播系数为元素的矩阵。具有方程组写出更为直接、解算全过程有物理性、并可使矩阵阶数大为降低等特点。所采用的传播系数和载常数,部分来自各种力或形变的传播法,但为了简明划(?)和适用,本文简要地作了新的表达和补充。这足将以往的传播法与现今所流行的矩阵法进行了结合,以期对结构的程序设计有所裨益。此外还介绍了按此法推导出的一套规律化的内力计算公式。     

Non-linear in-plane stability analysis of FG circular shallow arches under uniform radial pressure

In this paper, non-linear stability behavior of functionally graded (FG) circular shallow arches subjected to a uniform radial pressure is investigated by an analytical method. For this purpose, the classical single layer assumption is used to approximate the displacement field through the arch. Donnell׳s non-linear model for shallow shells is employed to derive the strain–displacement relations. The material properties vary smoothly through the thickness of the arch according to a power-law distribution. The governing equilibrium equations and the complete set of boundary conditions are extracted employing the principle of virtual displacements and variational calculus. Because of considerable pre-buckling deformations of shallow arches, the stability analysis is accomplished considering the pre-buckling deformations. The non-linear equilibrium paths are presented for two symmetric types of boundary conditions. Results show the influences of properties dispersion, geometrical characteristics, and boundary conditions on the stability behavior of the FG circular shallow arches. Also, the results of the paper are compared with the known data in literature.     

An improved continuous medium technique for structural frame analysis

This paper presents an improved constitutive equation of frame in the context of continuous medium technique. This improved constitutive equation, which is a consistent formulation of column global bending, is applicable to a complete class of frameworks including the ideal shear frame panel, for which the beams are assumed to be rigid, and the associated column system, for which the rigidity of beams is negligible. Global buckling and second‐order effects of the frame structure are discussed. The main results can be extended to other types of lateral stiffening elements as built‐up columns. A worked example is presented in order to compare the main results with those obtained by the classic matrix method. Copyright © 2007 John Wiley & Sons, Ltd.     

Strain-based finite element for the natural frequencies of cylindrical shells

The free-vibration natural frequencies of complete cylindrical shells, having different end conditions, and cylindrical panels have been investigated. The finite element method is used in which a strain-based cylindrical shell element is employed. This element satisfies the exact representation of rigid-body modes of displacements and all components of strains are assumed to be independent insofar as it is allowed by the compatibility equations. The element has only external degrees of freedom, five at each corner node, to avoid difficulties associated with higher-order elements. The stiffness and mass matrices are obtained using numerical integrations by the deployment of Gauss-Legendre quadrature points.     

大型复杂结构健康精准体检方法

精确的安全检测与诊断评估是保证结构安全与长寿命服役的基础。为此,提出大型复杂结构的健康精准体检方法。建立了区域子结构与整体结构特征参数的定量关系式,推导区域子结构灵敏度计算方程,提出基于灵敏度分析的复杂结构损伤关键区域确定方法。提出了关键区域内部混凝土探伤的压电智能精准探测方法,通过压电阻抗的统计指标长距离、高精度表征混凝土内部损伤状况;建立关键区域内部钢结构磁电智能精准探伤方法,推导C形开环电流空间域磁场的聚集和调控方程,并在此基础上研发了开环式电磁磁化装置。基于子结构有限元模型修正的损伤识别方法,依据关键区域精准损伤精确诊断评估整体结构安全状态。研究结果表明：该健康体检方法精准探测结构内部微损伤,仅需关键区域损伤即可精确诊断评估结构安全性能,全寿命周期记录并动态评估大型结构各时期安全状况,为大型复杂结构安全诊断评估提供可靠的技术支撑。     

Behavior and resistance of beam-column structural elements

Most of the structural elements in a steel structure are subjected to bending moment and axial force simultaneously. In some elements, one of the two components is relatively small compared to the other. Yet, the smaller component cannot be ignored due to the interactive behavior of the two components. Therefore, it is not adequate to design the beam-column element as a beam or a column by ignoring one of the two load components even if the ignored component is relatively small.Most of the design codes use empirical interaction equations that are based on semi-experimental semi-analytical results. Most of the design formulae adopted by the design codes do not explicitly account for the geometrical imperfection.This research aims at investigating the buckling behavior of steel beam-column elements for the sake of developing an analytical model to calculate their ultimate resistance under axial compression and bending moment. The analytical model will be based on Perry-type formulation, and it will account for the effect of initial imperfection. The model will be validated by comparing its results with those obtained by the Finite Element Non-Linear Elasto-Plastic analysis using ANSYS 5.4 program.Finally, a simple but rational design method based on the model, will be introduced. This method can be applied using a simple mathematical expression or charts and tables. The results of the developed design method will be compared with the design method of the international codes of practice for design of steel structures. On light of these comparisons, design recommendations are introduced.     

高层建筑结构非线性地震反应分析的竖向空间子结构法

对原竖向空间子结构法进行了改进,使竖向空间子结构的划分更趋简单,便于计算机进行前处理,自动形成结构力学分析的原始数据;子结构内部能处理各种复杂平、立面情况,避免了因子结构划分过细导致的计算工作量的增加;减少了边界节点总数;子结构间无需连接单元,结构分析仅有统一的竖向空间子结构模式,便于计算机编程,本文作者采用FORTRAN语言编制了相应的结构非线性地震反应分析程序,并进行算例分析。分析结果表明,竖向空间子结构法特别适合于多塔联体结构的非线性动力分析。     

轮辐式交叉索结构构形研究及其预应力态分析

以传统轮辐式索结构为基础,提出一类轮辐式交叉索结构,该类结构由双层外环压梁、双层内环拉索、内环撑杆、径向交叉布置的径向承重索、径向稳定索及它们之间的联系索杆组成。采用径向索交叉布置的新形式可减小结构层高度,改善结构整体抗扭刚度,同时形成的“空间谷脊效应”便于屋面组织排水。根据内环撑杆布置方式的不同,轮辐式交叉索结构又可分为竖撑杆型和人字撑杆型两种不同构形的轮辐式交叉索结构。基于节点平衡方程,对提出的两种轮辐式交叉索结构进行预应力态分析,推导出轮辐式交叉索结构预应力态内力的计算公式。此外还将轮辐式交叉索结构的预应力态受力特性与传统轮辐式索结构进行对比,并考虑不同内环结构高度、内外环几何中心高差等几何参数下结构的自应力分布情况。结果表明,轮辐式交叉索结构具有结构高度低、结构刚度大、受力合理等特点,在大型体育场等建筑中有很好的工程应用前景。     

An adaptive numerical scheme based on the Craig–Bampton method for the dynamic analysis of tall buildings

A new numerical scheme is proposed to perform a nonlinear dynamic analysis for tall buildings. The structural components (beams and columns) of tall buildings gradually enter the inelastic phase under strong seismic excitation. Because the distribution of nonlinear components is initially unknown due to the randomness of earthquake inputs, a group of linear and nonlinear substructures are automatically figured out during the time‐history analysis of a structure. Then a modified Craig–Bampton method is proposed to condense the DOFs of the linear substructures in modal coordinates at each time step while keeping the governing equation of the nonlinear substructure in physical coordinates. The dominant modes of the linear substructures are selected to capture the main dynamic characteristics of the structure. The time step integration analysis is used to solve the governing equation of the structures in hybrid coordinates. A 20‐story building is employed as the numerical simulation test to validate the feasibility and effectiveness of the proposed numerical scheme. This scheme provides a new method for the nonlinear dynamic analysis of tall buildings with acceptable simulation accuracy and high computational efficiency.     

Nonlinear Analysis of Structural Frame Systems by the State-Space Approach

This article presents the formulation and solution of the equations of motion for distributed parameter nonlinear structural systems in state space. The essence of the state-space approach (SSA) is to formulate the behavior of nonlinear structural elements by differential equations involving a set of variables that describe the state of each element and to solve them in time simultaneously with the global equations of motion. The global second-order differential equations of dynamic equilibrium are reduced to first-order systems by using the generalized displacements and velocities of nodal degrees of freedom as global state variables. In this framework, the existence of a global stiffness matrix and its update in nonlinear behavior, a cornerstone of the conventional analysis procedures, become unnecessary as means of representing the nodal restoring forces. The proposed formulation overcomes the limitations on the use of state-space models for both static and dynamic systems with quasi-static degrees of freedom. The differential algebraic equations (DAE) of the system are integrated by special methods that have become available in recent years. The nonlinear behavior of structural elements is formulated using a flexibility-based beam macro element with spread plasticity developed in the framework of state-space solutions. The macro-element formulation is based on force-interpolation functions and an intrinsic time constitutive macro model. The integrated system including multiple elements is assembled, and a numerical example is used to illustrate the response of a simple structure subjected to quasi-static and dynamic-type excitations. The results offer convincing evidence of the potential of performing nonlinear frame analyses using the state-space approach as an alternative to conventional methods.     

建筑结构混合试验平台HyTest开发研究

拟动力试验是一种重要的结构抗震联机试验方法,近年来出现了网络化、有限元化和实时化的趋势,形成了混合试验方法。鉴于混合试验分支多样,涉及数值分析、加载设备与控制等多个学科,为了方便试验的实施与技术的发展,迫切需要使用混合试验平台。为此开发了建筑结构混合试验平台HyTest,能够实现全结构拟动力试验、传统子结构拟动力试验、本地及分布式的基于静力子结构的混合试验和基于动力子结构的P2P混合试验。试验平台采用MTS二次开发编程库VB-COM连接试验控制系统,还可以调用有限元软件OpenSEES和ABAQUS进行数值子结构的分析。为了开展分布式的混合试验,该平台采用Socket通讯机制实现子结构间的数据传输,并采用带中转服务器的通讯模式,解决不同局域网之间的数据传输问题。利用该平台完成了6自由度单层单跨钢框架混合试验,验证了该试验平台的有效性。