Geometrically nonlinear numerical procedure for Saint-Venant's problem for a symmetrical elastic shell with a closed contour and circular axis

An original numerical procedure of treating Saint-Venant's problem for toroidal-like shells under pressure and bending moment is suggested. Its peculiarity consists in that the loading and displacement parameters are separated into two groups: the first one describes the ring-like transverse deformation of the shell cross section, while the second the beam-like axial deformation of the latter. One of them is considered separately in the sequential iteration procedure while the other is reckoned to be known. After each step of calculation, the parameters considered to be known are made more exact.A lot of the well-known problems widely presented in the literature are considered. Among them are: (1) Karman's problem, which explains the ovalization of the cross section and the enlarged flexibility of a pipe bend as compared to a straight pipe under bending; (2) the so-called pressure reduction effect when the internal pressure prevents ovalization, which is a demonstration of the influence of the geometrical nonlinearity even at small displacements; (3) Brazier's effect, which deals with nonlinearly enlarged ovalization of an initially straight elastic pipe with an increase in the bending moment.The main advantage of the method is that it allows analyzing a toroidal shell of arbitrary cross section with a variable wall thickness. As an example, a toroidal shell with two long symmetrical axial cracks is considered, where cracks are modeled as the jumps of the contour angular displacement whose values are related to the crack depth.     

轴向压缩下不加劲T型/Y型管节点性能的研究

使用有限元分析软件ABAQUS对轴向压缩载荷下T型和Y型管节点的失效模式﹑极限强度和具体性能进行研究。不加劲管节点的性能可从用于试验的管节点的数据库中提取。在数值分析中,使用修正弧长法可准确地模拟节点的性能,并有助于研究其真正的失效模式。通过数值分析发现,失效模式包括弦构件的局部弯曲、椭圆化变形、弦的塑性破坏。通过数值模拟得出的结果显示:节点表面的临界面积与椭圆化变形﹑变形量和应力有关。此外,对数值分析所预测出的极限强度与已有的试验结果进行了比较和验证。尽管已对管节点进行了大量的研究,但多集中于对极限强度和应力集中系数的估算上而不是对节点性能的具体研究,而此研究是一个全面解释轴向压缩下节点性能的具体研究。在已有的文献资料中很难看到这样深入又详细的节点研究。     

Two-step seismic limit state design procedure based on non-linear LRFD and dynamic response analyses

Recently, the limit state design (LSD) or performance-based design have got popularity in the field of building design in Japan as well as in other countries. In the two design methods the structural reliability theory plays an essential role in setting design criteria as well as demonstrating the target reliability level to society. However, the conventional load and resistance factor design (LRFD) has been basically formulated supposing that safety checking is done on the basis of linear assumption of member forces and displacement. Therefore, when applying the LRFD for seismic design, for more accurate treatment of the non-linearity, a new procedure has to be explored especially for the ultimate limit state. Although several procedures for the structural reliability evaluation, treating non-linear displacement responses, have been proposed, they require complex procedures that may not be used in the practical design process. Accordingly, for applying it to a seismic LSD format based on the probabilistic concept, it is essential to manage two important requirements at the same time, accuracy and simplicity of procedure. In the present study, a new design format using the following two-step procedure is proposed to maintain both accuracy and simplicity; (1) a non-linear LRFD formulation, and (2) a formulation based on non-linear dynamic response analysis. Also, two design examples are presented.     

预应力空间结构基于索力-位移观测值的预应力施工方案决策

针对预应力空间结构设计要求为目标位移的情况,研究结构实际状态与理论分析模型存在较大差异时预应力施工方案的决策分析方法。以索力、位移递推公式为基础,建立了仿真预应力施工过程的递推系统,该系统包含四类参数:结构初始状态、张拉力方案、索力与位移影响矩阵、张拉完成后的结构状态。利用施工过程中的索力-位移观测数据可计算出系统状态参数影响矩阵,然后基于递推系统的并行计算,提出了基于索力-位移观测值的预应力施工方案决策方法。利用矩阵分析软件MATLAB,编制了递推系统及决策方法的实现程序,并结合有限元分析软件ANSYS对工程算例进行了模拟分析。结果表明:利用本文方法可求得下一次循环补拉完成时达到设计要求位移状态的张拉控制力方案,从而保证预应力施工达到设计要求。     

不平衡堆载作用下邻近结构桩的侧向受力机制

为了分析结构桩在邻近堆载作用下的受力特性,以条状梯形分布堆载为代表,基于布西奈斯克弹性理论解得出堆载作用下地基附加侧压力表达式,并据此通过对局部塑性变形理论模型的改进,推导得出桩前土体侧移作用下桩身实际附加荷载,同时考虑土体可能发生绕桩流动的极限状态,结合绕桩极限模型给出桩身被动荷载的合理确定方法;在此基础上,考虑地基土体塑性屈服和桩顶结构荷载的影响,基于三参数Winkler弹性地基梁模型,建立桩身自由段、被动受荷段和主动作用段的微分方程,并通过桩身离散与矩阵传递法给出结构桩被动受力特性的半解析解。实测结果、文献理论解与该解答的对比分析,验证了本文计算方法的可靠性。     

Cellular buckling in I-section struts

An analytical model that describes the interactive buckling of a thin-walled I-section strut under pure compression based on variational principles is presented. A formulation combining the Rayleigh–Ritz method and continuous displacement functions is used to derive a system of differential and integral equilibrium equations for the structural component. Numerical continuation reveals progressive cellular buckling (or snaking) arising from the nonlinear interaction between the weakly stable global buckling mode and the strongly stable local buckling mode. The resulting behaviour is highly unstable and when the model is extended to include geometric imperfections it compares excellently with some recently published experiments.     

Non-linear thermoelastic analysis of steel arch members subjected to fire

This paper addresses the non-linear thermoelastic behaviour of steel arches acted on by a sustained uniformly distributed load, when subjected to elevated temperatures as caused by fire. The steel arch is restrained at its two ends by elastic translational springs in both the horizontal and vertical directions, as well as by counterpart elastic rotational springs, which simulate a generic semi-rigid connection, or restraint by other members in a frame, or when the arch acts as a large-span roofing element supported and restrained by columns. The study is restricted to the thermoelastic structural response of the steel material and therefore the high-temperature effects of catenary action and yielding are not considered; however the important effect of the second order term in the strain–displacement relationship is included. In order to model structural response of an elastically supported steel arch under thermal loading, an alternative geometric formulation is needed since the tangential and radial deflections and rotations as well as the axial compressive force in the member are substantial at the early stage of the fire. The formulation presented in this paper takes into account the degradation of the stiffness of the steel arch prior to yielding at elevated temperatures and it is argued that there are many situations for which analyses of a real fire situation in the thermoelastic range are valid. It is shown that the proposed model agrees well with independent solutions obtained using finite element analyses. The proposed model has significant potential for use in the analysis of restrained steel arches subjected to uniformly distributed load at elevated temperatures, such as large-span roofs and can provide a foundation for codified procedures in design.     

Response of flexible structures in random seas

A general stochastic formulation which addresses the relative motion effects of flexible structures in a random seaway is presented. The formulation utilizes a least-squares cubic polynomial approximation to the nonlinear drag force contribution. This influences the process of developing the stochastic equations of motion in two ways. First, by introducing higher order moments in the covariance form of the equations. Through the use of Gaussian closure these moments are replaced by equivalent expressions involving only second order moments. Secondly, the cubic drag force approximation results in the appearance of a three-fold convolution of the velocity spectrum in the final form of the spectral equations. Although, an iterative solution technique is required to solve the resulting spectral equations, this formulation provides the engineer with a means to directly evaluate the structural displacement spectrum at selected elevations. Once the response spectra are known extremal response behaviour can be predicted. A single-degree-of-freedom model of a monotower platform and a multi-degree-of-freedom model of a marine riser are used to illustrate the influence of the various approximations on the response predictions. Issues addressed include the impact on the viscous damping in the structural model as a result of first and third order approximations to the viscous drag force and the need to include higher modes for very flexible structures.     

平面钢管桁架拱平面外稳定试验研究与有限元分析

对2个跨度为10 m的圆弧形平面圆钢管桁架拱模型进行全跨均布荷载作用下的静力试验研究,分析了平面钢管桁架拱的平面外稳定承载力。引入平面外转动弹簧单元、水平位移弹簧单元,建立弹簧-杆系有限元模型,对试验模型进行非线性有限元分析。试验和有限元分析结果表明：下弦杆无平面外支撑的平面钢管桁架拱,在极限状态时,受压上、下弦杆发生侧向弯曲失稳,并引起整体平面外弯曲失稳破坏;圆钢管相贯节点的平面外转动刚度对试验模型的平面外稳定承载力影响显著。弹簧-杆系有限元分析结果与试验结果较为吻合,可为同类型结构的平面外稳定分析、设计提供参考。     

Structural optimization of thin-walled tubular trusses using a virtual strain energy density approach

The present paper deals with the weight minimization of tubular trusses subjected to multiple loads under size, stress and buckling constraints. The applied optimization procedure is based on a virtual strain energy density approach developed by the first two authors, already tested in plane and space truss structures. The key point of the method is the activation of at least one of the imposed displacement constraints. In case where such limitations are absent, a dummy displacement constraint is introduced instead, which iteratively sustains corrections until convergence is achieved within the desirable tolerance. The efficiency and practicability of the proposed method was tested in typical cases of tubular truss structures. For reasons of comparison, the same cases were also optimized using Sequential Quadratic Programming (SQP), which is a powerful mathematical programming optimization method. The results revealed that the proposed method performs very well in terms of convergence, of required number of iterations and of optimum tracing, while the value of the introduced dummy displacement constraint has insignificant effect on the optimization procedure.     

乙烯生产钢塔架地震响应分析

采用有限元法和求解特征方程法分别对某乙烯生产钢塔架进行动力特性分析,得到结构的基本频率,通过比较发现两者的计算结果较接近,从而验证采用有限元软件建立的模型的正确性。进而,采用有限元软件对乙烯生产钢塔架进行两个方向的地震响应分析,同时研究有重力和阻尼对结构地震响应的影响。结果表明:①结构侧移刚度小的方向,结构的响应较大,但各层的层间弹性位移转角最大值都满足《建筑抗震设计规范》给定的限值;②重力会增大结构的位移响应,但是对结构的速度及加速度响应没有影响;③阻尼会大幅度降低结构的位移、速度、加速度响应,因此,增大结构的阻尼对结构抗震十分有利。     

Generic nonlinear modelling of restrained steel beams at elevated temperatures

This paper presents a novel numerical method to describe the nonlinear behaviour of a restrained steel beam at elevated temperatures, which is based on a non-discretisation semi-analytical formulation of a generic steel cross-section with elastic and plastic parts. The model incorporates moderately large displacement effects as well as material nonlinearity to assess the performance of steel beams exposed to thermal loading in a compartment fire, and it considers the yielding and development of catenary action affects with an increase in the temperature. The effects of the thermal gradient along the length of the beam are considered in the formulation, in which the cross-section is subjected to an arbitrary thermal profile. Degradation of the stiffness and yield strength with increasing temperature is simulated using empirical retention functions given elsewhere, and the technique is shown to be part of the class of boundary value problems in engineering mechanics. The generic technique developed in the paper is shown to agree with solutions given by ABAQUS finite element modelling, and it provides a computationally superior formulation to that of commercial finite element packages, and provides a formulation which may be used as a platform for structural design and evaluation.     

基岩地震谱与地震动位移输入的土–结构相互作用(SSI)计算模型改进

 对基岩地震动输入的适用性和SSI计算模型的合理性进行研究。首先,借鉴已有基岩地震谱表达式,采用数值方法修正高频段过滤函数,得到适用于我国目标场地的基岩地震谱;然后,分析当前位移输入的SSI计算模型,指出所存在的因单元尺寸划分逐步精细而导致的不收敛问题,推广无质量刚性元(massless rigid element,MRE)法解决这一问题,并给出MRE、结构系统和黏弹性人工边界三者间连接示意图;最后,基于上述工作和随机振动理论生成基岩地震动位移输入谱,对一算例进行分析,结果表明采用MRE法解决SSI计算模型的可行性。研究工作可为土–结构共同作用相关问题的研究提供参考。     

钢管混凝土斜交网格结构性能分析

以广州西塔为工程背景,建立了圆筒钢管混凝土斜交网格结构模型,分析了斜柱倾角对结构周期、侧移、竖向刚度和内外筒的弯矩和剪力分配的影响,探讨了核心筒剪力墙厚度对结构性能的影响。结果表明:高宽比大于5的圆筒斜交网格结构的最优斜交角度介于68°～78°;随着斜柱倾角的减小,结构抗侧刚度下降,下部楼层刚度突变明显;随着核心筒墙厚的增加,结构自振周期略有增大,内外筒的基底剪力与弯矩分配更加合理。     

General analysis and application to redundant arches under static loading

The aim of this paper is to define an exact formulation of a curved beam finite element for static analysis. The basic equations are combined in the coupled fundamental system in terms of radial displacement v, tangential displacement u and rotation ϕ. An original procedure for solving the fundamental system of equations is used. A finite element formulation based on shape functions that satisfy the homogeneous form of the fundamental system of differential equations is developed. The effects of bending moment, axial extension and transverse shear are taken into account. The exact elastic solution renders the element obtained free of shear and membrane locking.An efficient numerical procedure is presented for determining the pressure curve in the case of circular arches under static loading and arbitrary bonding conditions. The solution obtained is applicable to the analysis of both thin and thick curved beams.Several examples of arches with various loading and boundary conditions are investigated to illustrate the validity and the accuracy of the method. Finally, the effect of the arch rise on the structural response is pointed out.     

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.     

考虑翘曲变形的复合材料叠合梁几何非线性的有限元分析

提出了一个用于复合材料叠合梁结构分析的有限元模型,梁结构具有几何非线性性能,包括扭转翘曲变形。采用一个考虑了改进拉格朗日法和广义位移控制法的公式对结构的变形进行计算。采用二次等参有限单元对梁横截面进行离散化,以确定梁的弯扭特性。利用两结点的Hermitean三维有限梁元对结构进行离散化,其中每结点具有7个自由度。运用数个实例,分析了层的取向对结构性能的影响。     

附加限位装置对钢管混凝土拱桥的减震效果

以某钢管混凝土拱桥为工程背景,在动力特性和反应谱分析结果的基础上,分析其在地震荷载作用下主桥伸缩缝处采用限位装置后的结构地震响应。研究结果表明,附加限位装置能显著减小伸缩缝处相邻桥面系的相对位移,提高结构的抗震安全性。     

pushover分析方法及其在方钢管混凝土框架结构中的应用

简介了pushover分析方法,采用ETABS结构分析软件对一榀单跨两层方钢管混凝土框架结构进行了pushover分析。计算结果与试验结果的对比表明,pushover分析能够确定结构的破坏机制,判断结构最先破坏的薄弱环节,pushover分析得到的基底剪力-顶点位移曲线与试验结果较吻合,P-△效应对pushover分析影响较大。     

Fuzzy‐Valued Intensity Measures for Near‐Fault Pulse‐Like Ground Motions

Two fuzzy‐valued (FV) structure‐specific intensity measures (IMs), one based on squared spectral velocity and the other on inelastic spectral displacement, are presented to characterize near‐fault pulse‐like ground motions for performance‐based seismic design and assessment of concrete frame structures. The first IM is designed through fuzzying structural fundamental period to account for the period shift effect due to stiffness degradation, whereas the second IM is developed to take into account higher mode contribution in high‐rise buildings by employing a fuzzy combination of the first two or three modes for the lateral loading pattern in pushover analysis. A benchmark study of three example reinforced concrete frame structures shows that for moderate‐ to medium‐period structures, both of the proposed IMs improve prediction accuracy in comparison with the existing IMs. For short‐period structures, the FV inelastic spectral displacement is the best.