Elastica buckling analysis of a simple frame

Summary A nonlinear stability analysis based on an analytical approach of elastic type is performed for the first time on a simple two-bar frame. In order to obtain an exact determination of its buckling and postbuckling behavior the effect of compressibility of the bar centroidal axis is taken into account. This effect implies very slight increase in the buckling load which can be safely ignored. Moreover, it is found that even in the most extreme cases of geometry and stiffness, the critical buckling displacements are of negligibly small magnitude contrary to existing results obtained by the nonlinear kinematic stability analysis. The two foregoing findings enable us to replace the limit point by a bifurcation point. Such a simplification, being correct in an asymptotic sense, allows the application of a stability analysis of frames by considering their bars as incompressible.A variety of numerical results shows the degree of accuracy and the range of applicability of the aforementioned nonlinear kinematic stability analysis by comparing it with the exact method of stability analysis proposed herein.With 2 Figures     

The effect of interaction of loadings and geometry imperfection on the buckling state of frames

In this paper the effect of the interaction of two loadings, and of the deviation from right angle on the buckling mechanism of a rectangular two-bar frame is discussed. Using a nonlinear stability analysis it is found that there is a critical value of the ratio of the two loadings, as well as of the deviation from right angle, for which the physical equilibrium path and the physically unacceptable complementary path meet each other at an asymmetric bifurcation point. At this point, the response of the frame changes from an elastic limit point instability to a stable equilibrium path associated with inelastic buckling. The analysis is supplemented by a variety of numerical results obtained by an efficient and reliable simplified nonlinear stability analysis applied for the first time to a non-rectangular frame.     

大长细比抛物线形钢管混凝土无铰拱平面内稳定性能研究

为研究圆拱结构几何非线性内力和位移计算以及平面内稳定分析问题,基于圆拱几何非线性静力分析模型,构造了解析位移形函数,进而利用能量法和势能变分原理,构造了解析型几何非线性圆拱单元,给出了单元列式;同时将该文模型通过理论退化,得到了不考虑轴向变形的无压缩圆拱模型,进一步得到了解析型无压缩几何非线性圆拱单元,并将此单元应用于圆拱的平面内稳定分析。研究结果表明：采用本单元模型进行平面内分岔失稳分析得到的失稳临界荷载系数与经典Timoshenko模型、Dinnik模型及静力法模型计算结果一致,相对误差为0%;平面内分岔失稳的临界荷载与平面内极值点失稳的临界荷载一致。该文单元具有解析型、高精确性以及良好的适用性,可用于任意工况下圆拱结构几何非线性位移、内力和平面内稳定分析。     

解析型几何非线性圆拱单元

为研究圆拱结构几何非线性内力和位移计算以及平面内稳定分析问题,基于圆拱几何非线性静力分析模型,构造了解析位移形函数,进而利用能量法和势能变分原理,构造了解析型几何非线性圆拱单元,给出了单元列式;同时将该文模型通过理论退化,得到了不考虑轴向变形的无压缩圆拱模型,进一步得到了解析型无压缩几何非线性圆拱单元,并将此单元应用于...     

The effect of interaction of loadings on the change of buckling response of framed structures

Summary In this investigation the effect of two loadings interaction and right angle deviation on the response of a rectangular two-bar frame is thoroughly discussed. It is found that there is a critical value of the two loadings ratio as well as of the right angle deviation for which the physical equilibrium path and the physically unacceptable complementary path meet each other at an asymmetric bifurcation point. This state constitutes the boundary between stability and instability, since the response of the frame changes from snapthrough buckling to a stable equilibrium path.Moreover, a very efficient and simple to use stability analysis, employed for the first time at a non-rectangular frame, gives reliable results compared to those of the nonlinear kinematic stability analysis.With 5 Figures     

Representative static load models for transient stability analysis: development and examination

Load representation has a significant impact on power system analysis and control results. Currently, static load models are still popular in power industry for transient stability analysis. Dynamic load models are recommended in both industry and academia for possible improvement in analysis accuracy. The accuracy of using static (nonlinear) load models with suitably identified parameters for transient stability analysis is examined. Numerical studies conducted using on-line measurement data indicate that static load models, as compared with induction motor load models, are acceptable for modelling real power behaviours during disturbances and hence are adequate for transient stability analysis. Using multiple sets of on-line measurements, representative model parameters of five static nonlinear load models are derived and their performance in modelling dynamic behaviours of both real and reactive powers is compared. A method is presented to determine a representative set of parameters of static (nonlinear) load models for each loading condition     

变截面门式刚架结构的非线性性能

本文论述了变截面有限梁元几何非线性分析方法;研究了变截面刚架的几何非线性影响;通过非线性屈曲分析考察了屋面均布荷载对刚架柱稳定的影响;计算结果表明,刚架在屋面均布荷载作用下所产生的横梁轴力和弯曲变形对其侧向屈曲荷载的影响不能忽视。     

远场地震作用下钢管混凝土组合框架的地震反应分析

为研究在远场地震动作用下钢管混凝土组合框架的反应,设计了某10层钢管混凝土组合框架,从PEER强震记录数据库中选取了28条远场(距离大于10km)强震地震动记录作为输入地震波,按美国地质勘探局(USGS)对场地类别分类方法将其分为A、B、C、D四类,基于OpenSees建立了非线性纤维梁柱单元的理论模型,对其进行了设防烈度为8度时多遇和罕遇地震作用下弹塑性时程分析,计算结果同时与Pushover分析结果进行了对比。结果表明:虽然不同地震动作用下钢管混凝土组合框架结构反应的离散性较大,但该类结构在不同场地类别下的反应仍具有一定规律性。与Pushover分析结果对比表明,对于该文中规则框架倒三角侧力分布模式比均布侧力更接近于钢管混凝土组合框架在地震作用下的地震力分布,可用在钢管混凝土框架结构的抗震分析中。     

空间框架结构非线性分析的简化数值方法

钢筋混凝土框架结构正常使用期间是带裂缝工作的,合理的分析方法应考虑因开裂引起的非线性.在杆系结构有限元基础上,根据构件截面广义应力-应变关系,提出了空间框架结构非线性分析的简化数值方法--网格-等效截面法.该方法能考虑材料非线性,混凝土开裂导致构件有效刚度降低,混凝土徐变和加载历程等影响因素.给出了相应的实施步骤,并采用通用有限元软件ANSYS部分功能,自编主体计算程序的混合编程方法编制了程序.通过考题,程序编制方法正确,计算精度满足工程要求.最后,采用程序对荷载和温度作用下某超长框架结构进行了计算.     

移动荷载作用下结构损伤的近似熵分析

当移动荷载接近或远离结构损伤部位时,结构的振动响应的幅值和非线性特征会发生变化,可以从中提取有关结构损伤的信息;近似熵可以表达一个时间序列的复杂性和内在模式。用移动荷载作用于结构上,对其振动响应数据进行近似熵计算,提取其非线性特征值,进而用神经网络进行结构损伤模式识别。通过一个移动荷载作用下简支梁的计算实例考察了这一方法的有效性。移动荷载的作用,使得损伤造成的结构非线性特征更加显著;研究、计算与实测案例表明近似熵能够有效地表征信号的非线性程度,而且对噪声干扰的敏感度低,可以作为神经网络模式识别的特征向量。     

穿芯高强螺栓-端板节点方钢管混凝土框架抗震性能数值分析

为研究采用穿芯高强螺栓-端板节点的方钢管混凝土框架的抗震性能,基于一榀两层两跨方钢管混凝土框架的拟静力试验研究结果,利用有限元软件ABAQUS对试验试件进行了非线性数值分析。研究框架的破坏机制、延性、耗能能力及节点性能。在峰值荷载前,数值分析结果与试验结果吻合较好。对轴压比、节点端板厚度、加劲肋厚度以及高强螺栓预拉力等因素进行了分析。结果表明,框架滞回曲线饱满,具有良好的延性和耗能能力,节点在加载过程中未产生塑性变形。当框架柱的轴压比较小时,可形成理想的梁铰破坏机制。增大端板厚度和设置梁端加劲肋可提高结构的刚度与承载力,使框架刚度的退化趋于平缓。高强螺栓预拉力对框架性能无显著影响。     

任意分布轴力作用下框架柱弹性稳定的实用解法

该文根据等效负刚度相等的原则,建立了框架柱中力与柱顶力之间的等效关系,推导了等效力系数的计算公式。通过该系数,可以将柱中力折算到柱顶,直接通过规范查取计算长度系数验算框架的整体稳定,而不需要重新对计算长度系数进行折算。进一步提出了等效力法,该方法可以很好的解决框架变多次轴力问题,具有很好的精度,满足工程应用的要求。对于变轴力非对称框架,用等效力法推导了考虑柱间支援作用之后的计算长度系数计算公式,并通过算例进行了验证。研究结果表明:等效力法具有很好的精度和准确性,可供工程设计及理论计算使用。     

无侧移变轴力框架柱稳定性的等效力法

该文根据无侧移压杆的屈曲形态提出了以轴力对压杆跨中抗侧刚度的削弱来表征轴力负刚度的力学模型,并利用该模型阐释了无侧移框架计算长度系数的力学意义。在该模型的基础上,根据等效负刚度相等的原则,建立了无侧移框架柱中力与柱顶力之间的等效关系,推导了等效力系数的计算公式。通过该系数,可以将柱中力折算到柱顶,并直接通过规范查取计算长度系数验算框架柱的整体稳定,而不需要重新对计算长度系数进行折算。进一步提出了等效力法,该方法可以很好的解决无侧移框架柱的变多次轴力问题,具有很好的精度。算例计算结果表明：等效力法具有很好的精度和准确性,可供工程设计及理论计算使用。     

船体开孔薄板面内剪切屈曲特性研究

船体板材不可避免地存在不同形式的开孔,开孔破坏了结构的连续性,对结构的强度、稳定性具有重要影响,因此研究船体板开孔结构的屈曲特性对保证船舶安全十分重要。在面内载荷作用下,通过画框型剪切夹具、3D全场变形测量-分析系统等对两种不同形式的船体开孔薄板进行剪切屈曲试验,获得了圆形开孔板和方形开孔板的临界屈曲载荷、全场位移/应变信息和拉力-伸长率曲线等;考虑试验夹具的影响,基于Abaqus对不同形式的开孔板进行数值仿真,通过对开孔板进行特征值屈曲分析和非线性屈曲分析,获得了两种不同形式船用开孔薄板的屈曲、后屈曲力学响应信息。通过数值仿真与试验结果的对比研究,验证了数值仿真方法的有效性、准确性。在此基础上,重点剖析载荷-伸长率关系、典型时刻板面全场位移、临界屈曲载荷以及开孔边缘的应力分布响应特征,明确了面积等效情况下圆孔和倒圆角方孔对方形薄板剪切稳定性的影响。为船用薄板面内剪切稳定性的试验和仿真研究以及大型船体结构的设计优化、力学性能评估等提供有益参考。     

基于无单元Galerkin法的软土区高承台超长嵌岩基桩屈曲分析

为探讨洞庭湖软土区桥梁工程常用高承台超长嵌岩灌注桩的屈曲稳定性,将其视为第二类稳定问题,引入新型无单元Galerkin数值分析法,考虑桩-土共同工作中的非变形协调与非线性等因素,给出了基于非线性弹性-理想塑性模型的桩土接触分析非线性迭代算法及基于弧长法的桩身屈曲分析无单元Galerkin法,并开发出相应的计算程序。最后,结合某大桥一试桩现场载荷试验结果进行了应用,对比分析表明:基于桩身屈曲分析无单元Galerkin法获得的桩顶荷载-沉降曲线与实测曲线吻合较好,桩身失稳临界荷载与实测极限荷载的相对误差为5.6%,远优于按第一类问题的线性与非线性增量屈曲分析结果(其相对误差分别达37.0%和15.4%)。     

SPATIAL STABILITY ANALYSIS OF THIN-WALLED SPACE FRAMES

A clearly consistent finite element formulation for spatial stability analysis of thin-walled space frames is presented by applying linearized virtual work principle and introducing Vlasov's assumption. The improved displacement field for unsymmetric thin-walled cross-sections is introduced based on inclusion of second-order terms of finite rotations, and the potential energy corresponding to the semitangential moments is consistently derived. In the present formulation, displacement parameters of axial and bending deformations are defined at the centroid axis and parameters of lateral and torsional deformations at the shear centre axis, and all bending-torsional coupling effects due to unsymmetric cross-sections are taken into account. For finite element analysis, cubic Hermitian polynomials for the flexural beam with four types of end conditions are utilized as shape functions of Hermitian space frame element. Also, load correction stiffness matrices for off-axis point loadings are derived based on the second-order rotation terms. Finite element solutions for the spatial buckling analysis of thin-walled space frames are compared with available solutions and other researcher's results.     

样条有限点法分析板的大挠度问题

样条有限点法已成功地应用于板的线性分析。本文用样条有限点法求解几何非线性平板,以位移u、u和W作为基本未知量,采用三次B样条插值函数与梁函数级数的乘积作为位移试函数,从最小势能原理出发建立基本方程,推导了非线性切线刚度矩阵,用改进的Newton-Raphson方法求解非线性方程组,最后给出了算例,其结果与一些已有的成果进行了比较,表明该方法分析板壳结构的非线性问题是十分有效的。     

Effectiveness of linear bifurcation analysis for predicting the nonlinear stability limits of structures

As an effort to predict effectively the actual collapse load of a structure, a series of numerical studies on the stability of shell structures are made. The difference in formulation between the two types of linear buckling loads, the classical and the fully linearized, is first demonstrated. Their correlations with respect to the actual stability limit of the structure are compared, and finally the two types of critical load approximations are obtained at various stages of a nonlinear analysis to study the pattern of convergence to the actual collapse load. It is found that the fully linearized buckling analysis, when combined with nonlinear analysis, can serve as a useful tool for prediction of the stability limit of a structure. While for most types of structures the approximation is within engineering accuracy, the rate of convergence of the extrapolated critical load also gives some insight to the accuracy of the approximation.     

钢管混凝土框架柱计算长度研究

钢管混凝土框架柱计算长度是合理正确计算其承载力的重要参数,是进行钢管混凝土结构内力分析和设计必不可少的参数,因缺乏系统研究,现行钢管混凝土框架柱计算长度暂参照钢框架柱取值,由于两种结构体系受力特性的差异会导致结果不合理。该文基于ABAQUS软件,通过合理选取钢管混凝土框架的稳定简化模型,同时考虑几何非线性和材料非线性的影响对框架体系进行非线性屈曲分析,从而求解有侧移和无侧移钢管混凝土框架柱计算长度。在此基础上通过大量参数分析,分别得到了有侧移和无侧移钢管混凝土框架柱计算长度系数表,并回归了简化计算公式。为比较不同方法计算结果的差异,选取某四层四跨钢管混凝土框架典型算例进行比较,结果表明：该文考虑初始缺陷和非线性行为所得到的计算长度系数取值方法比现行按采用钢框架柱计算方法的结果偏大,无侧移框架柱变化范围为0.97%~4.05%,有侧移框架柱变化范围为9.95%~27.17%,可见材性差异及初始缺陷对计算长度系数影响较大,不可忽视。     

Reliability analysis of nonlinear laminated composite plate structures

A procedure for the reliability analysis of laminated composite plate structures subjected to large deflections under random static loads is presented. The nonlinear analysis of laminated composite plate structures is achieved via a corotational total Lagrangian finite element formulation which is based on the von Karman assumption and first order shear deformation theory. This formulation is applicable for the nonlinear analysis of plate structures with large rotations but moderate deformation and thus accurate enough to predict the behavior of the structures at the point of failure. The reliability assessment of laminated composite plate structures with random strength subjected to random loads is approached by the determination of limit state surfaces in load space. The limit space surfaces are obtained by performing a series of first ply failure analyses following different load paths in load space using the proposed nonlinear structural analysis technique and an appropriate failure criterion. A numerical technique is then proposed to evaluate the reliability of the plate structures. Examples of the reliability analyses of laminated plates with different layer orientations subject to random loads are given for illustration.