无背索斜拉桥稳定分析的能量法

无背索斜拉桥在理想的成桥状态下,面内失稳模态为主梁屈曲。将主梁简化成弹性地基梁计算模型,选用正弦级数作位移函数,运用能量方法,提出了主梁屈曲临界荷载的计算公式。结合该类桥梁的结构布置特点,用简洁的连续函数描述主梁轴压力和拉索弹性支承刚度的变化,同时用简单的线形折减系数反映斜塔变形对拉索弹性支承刚度的影响。最后以长沙市洪山大桥为例,用该方法计算了其成桥状态屈曲临界荷载,其结果与有限元解对比具有很好的精度。     

ACCURATE CALCULATION OF ELASTIC BUCKLING LOADS FOR SPACE FRAMES BUILT UP OF UNIFORM BEAMS WITH OPEN THIN-WALLED CROSS-SECTION

A so-called exact static stiffness matrix for a uniform beam element with open thin-walled cross-section carrying an axial compressive load is derived. This stiffness matrix is useful in an accurate calculation of bifurcation loads and corresponding buckling modes of space frames built up of such beam elements. One may also calculate displacements and sectional forces caused by external joint loads taking into account the second-order effect of the axial beam loads. The exact stiffness matrix is derived by use of the general solution to a set of three coupled differential equations. This means that no preselected shape functions need be introduced and that discretization errors are avoided. The differential equations model coupled Euler–Bernoulli bending in the two principal planes and Saint-Venant/Vlasov torsion and warping with respect to the shear centre axis. No cross-sectional symmetries are assumed. Numerical examples are given. One application will be to loaded pallet racks. The ‘effective length’ for a rack column is calculated.     

Efficient laminated composite beam element subjected to variable axial force for coupled stability analysis

A numerically efficient laminated composite beam element subjected to a variable axial force is presented for a coupled stability analysis. The analytical technique is used to present the thin-walled laminated composite beam theory considering the transverse shear and the restrained warping-induced shear deformation based on an orthogonal Cartesian coordinate system. The elastic strain energy and the potential energy due to the variable axial force are introduced. The equilibrium equations are derived from the energy principle, and explicit expressions for the displacement parameters are presented using the power series expansions of displacement components. Finally, the member stiffness matrix is determined using the force–displacement relations. In order to verify accuracy and efficiency of the beam element developed in this study, numerical results are presented and compared with results from other researchers and the finite beam element results, and the detailed finite shell element analysis results using ABAQUS; especially, the influence of variable axial forces, the fiber orientation, and boundary conditions on the buckling behavior of the laminated composite beams is parametrically investigated.     

液化场地中Timoshenko桩自由振动与屈曲的精确数值解

基于单桩的Timoshenko梁模型和桩-土相互作用的Winkler模型,建立考虑轴力效应的具有分布参数的Timoshenko梁模型微分控制方程,确定对应的齐次方程的通解,并以此作为有限单元的基函数。推导得精确形函数矩阵,建立分布参数Timoshenko梁的精确有限单元,根据拉格朗日方程得到有限元离散方程和单元刚度矩阵、几何刚度矩阵和一致质量矩阵。应用建立的精确Timoshenko梁单元于分层液化土中单桩-土-结构系统的自由振动与屈曲模态分析,通过与对应解析解以及常规有限元解的对比,表明精确Timoshenko桩基础单元的可靠性与较常规有限元法的优势。     

Spatial stability and free vibration of shear flexible thin-walled elastic beams. I: Analytical approach

An improved formulation for spatial stability and free vibration analysis of thin-walled elastic beams is presented by applying Hellinger–Reissner principle and introducing Vlasov's assumption. It includes shear deformation effects due to flexural shear and restrained warping stress, rotary inertia effects and bendirsg–torsional coupling effects due to unsymmetric cross sections. Closed-form solutions for determining flexural–torsional buckling loads and natural frequencies of unsymmetric simply supported beam-columns subjected to eccentric axial force are newiy derived and also, the tangent stiffness matrix and stability functions for symmetric thin-walled beam elements subjected to axial force are presented. In a companion paper,²⁶ these analytic solutions are compared with the finite element solutions according to the increase of shear deformation effects.     

线弹性土壤中埋设悬跨管道的屈曲分析

建立了两端埋设在线弹性土壤中的悬跨管道的屈曲方程。利用细长梁小挠度理论,建立了含有轴向压力的悬跨段和埋设段管道的弯曲控制方程。基于埋设段管道的刚度和变形特性,建立了符合悬跨段管道实际情况的边界条件。导出了悬跨段管道对称屈曲和反对称屈曲的屈曲载荷方程,通过数值求解给出了不同土壤刚度系数条件下悬跨段管道屈曲载荷。研究表明:悬跨段管道的屈曲载荷系数依赖于土壤刚度系数,简支梁模型只在特定的土壤刚度系数下适用于悬跨管道;在土壤刚度系数很大时,两端固支梁模型才能反映悬跨管道的屈曲特性。建议采用该方法进行埋设悬跨管道的屈曲分析。     

钢管混凝土结构材料非线性的一种有限元分析方法

为了更简单地考虑梁单元的材料非线性受力性能,把断面广义力和广义应变的概念运用于单元分析中,将单元的弹塑性刚度矩阵分离为弹性刚度矩阵和塑性刚度矩阵。这样,梁单元的变形可以由弹性变形和塑性变形简单地迭加,结构内力可通过弹性应变能的斜率(弹性刚度矩阵)与位移的乘积求得,从而在增量-迭代计算时可较准确且较快地计算出结构变形后的不平衡力。应用这一计算方法,推导了基于纤维模型的三维梁单元的钢管混凝土结构的有限元基本公式,并将其植入能考虑几何非线性的三维梁单元非线性计算程序NL_Beam3D中以计算结构的双重非线性问题。算例分析表明该方法和程序能较准确地反映钢管混凝土结构的双重非线性特性。     

高强钢框架-屈曲约束支撑体系抗震性能研究

针对高强钢结构在抗震设计中存在的结构延性差、刚度小的问题,提出了高强钢框架-屈曲约束支撑结构.为研究此类结构的抗震性能,对2个足尺单榀单跨单层试件进行了拟静力加载试验,观测了结构在水平往复荷载下变形特征与破坏模式,分析了结构及构件滞回曲线特征,探讨了试件强度退化、刚度退化、塑性变形、耗能能力以及钢框架和屈曲约束支撑的承...     

Instability of laminated composite thin-walled open-section beams

Instability of thin-walled open-section laminated composite beams is studied using the finite element method. A two-noded, 8 df per node thin-walled open-section laminated composite beam finite element has been used. The displacements of the element reference axis are expressed in terms of one-dimensional first order Hermite interpolation polynomials, and line member assumptions are invoked in formulation of the elastic stiffness matrix and geometric stiffness matrix. The nonlinear expressions for the strains occurring in thin-walled open-section beams, when subjected to axial, flexural and torsional loads, are incorporated in a general instability analysis. Several problems for which continuum solutions (exact/approximate) are possible have been solved in order to evaluate the performance of finite element. Next its applicability is demonstrated by predicting the buckling loads for the following problems of laminated composites: (i) two layer (45°/−45°) composite Z section cantilever beam and (ii) three layer (0°/45°/0°) composite Z section cantilever beam.     

任意截面预应力混凝土细长柱的非线性分析

提出了轴力和双向弯曲作用下任意截面混凝土和预应力混凝土细长柱的非线性有限元计算模型。分析时既考虑了由单元变形和轴力二次矩引起的几何非线性效应,也考虑了由材料非线性应力应变关系和截面刚度矩阵引起的材料非线性效应。推导了非线性全过程分析的标准有限元公式,得到的单元刚度矩阵可分割成三个子矩阵,分别反映了材料非线性、材料非线性和单元大位移的耦合、轴力二次矩等三种不同的非线性作用效应。计算分析结果和试验结果吻合较好。     

Super convergent shear deformable finite elements for stability analysis of composite beams

The super convergent finite beam elements are newly presented for the spatially coupled stability analysis of composite beams. For this, the theoretical model applicable to the thin-walled laminated composite I-beams subjected to the axial force is developed. The present element includes the transverse shear and the warping induced shear deformation by using the first-order shear deformation beam theory. The stability equations and force–displacement relationships are derived from the principle of minimum total potential energy. The explicit expressions for the seven displacement parameters are then presented by applying the power series expansions of displacement components to simultaneous ordinary differential equations. Finally, the element stiffness matrix is determined using the force–displacement relationships. In order to demonstrate the accuracy and the superiority of the beam element developed by this study, the numerical solutions are presented and compared with the results obtained from other researchers, the isoparametric beam elements based on the Lagrangian interpolation polynomial, and the detailed three-dimensional analysis results using the shell elements of ABAQUS. The effects of shear deformation, boundary condition, fiber angle change, and modulus ratios on buckling loads are investigated in the analysis.     

Effects of approximations in analyses of beams of open thin‐walled cross‐section—part I: Flexural–torsional stability

In formulating a finite element model for the flexural–torsional stability and 3‐D non‐linear analyses of thin‐walled beams, a rotation matrix is usually used to obtain the non‐linear strain–displacement relationships. Because of the coupling between displacements, twist rotations and their derivatives, the components of the rotation matrix are both lengthy and complicated. To facilitate the formulation, approximations have been used to simplify the rotation matrix. A simplified small rotation matrix is often used in the formulation of finite element models for the flexural–torsional stability analysis of thin‐walled beams of open cross‐section. However, the approximations in the small rotation matrix may lead to the loss of some significant terms in the stability stiffness matrix. Without these terms, a finite element line model may predict the incorrect flexural–torsional buckling load of a beam. This paper investigates the effects of approximations in the elastic flexural–torsional stability analysis of thin‐walled beams, while a companion paper investigates the effects of approximations in the 3‐D non‐linear analysis. It is found that a finite element line model based on a small rotation matrix may predict incorrect elastic flexural–torsional buckling loads of beams. To perform a correct flexural–torsional stability analysis of thin‐walled beams, modification of the model is needed, or a finite element model based on a second‐order rotation matrix can be used. Copyright © 2001 John Wiley & Sons, Ltd.     

基于弹性基础梁理论的复合材料薄壁圆柱壳屈曲承载力模型

提出一种复合材料薄壁圆柱壳轴压局部屈曲承载力计算模型。在梁弯曲变形平截面假定和小变形假定的基础上,提出复合材料层合梁抗弯刚度的计算方法;根据轴压下圆柱壳的几何对称性及受力对称性,将圆柱壳局部屈曲问题转化为轴向和环向壳带的弯曲变形问题。依据薄壳稳定理论,建立弹性基础上纵向壳带局部屈曲模型,得到了复合材料圆柱壳屈曲承载力解析公式。理论计算公式与经验工程计算公式相比,具有形式上的相似性,且得到的计算系数可直接求出,而非经验范围选取。对三种铺层的复合材料薄壁圆柱壳进行了轴压试验,结合文献试验数据对比,试验结果与理论预测值基本一致,满足工程精度要求,验证了模型的正确性。     

埋设悬跨海底管道的屈曲分析

考虑海床刚度,研究了埋设悬跨海底管道在热膨胀引起的轴向压力下的屈曲问题。传统方法是将悬跨管道简化为两端简支或者两端固支梁来处理。基于欧拉-伯努利梁理论,考虑线弹性海床刚度和轴向压力,建立并求解了埋设段管道和悬跨段管道在自重作用下的四阶常微分方程,获得了两段管道的静挠度和内力的解析公式。通过对静挠度的特性分析,给出了埋设管道段和悬跨管道段的稳定性判断准则。     

一种新的集成非线性杆件单元刚度矩阵的方法

对于非线性杆件单元,本文提出一种新的简便有效的集成单元刚度矩阵的算法。该方法直接从结构力学中的位移法的概念出发,通过解析积分或数值积分求解积分算子,由积分算子线性组合,能快速求解考虑弯、剪、扭、轴压等各种非线形刚度的杆件单元的刚度矩阵。该方法具有广泛的普适性,能适用于所有多项式、插值多项式、解析式、离散点描述的变刚度、变截面直杆的单元刚度矩阵集成计算。文中通过求解线性直杆单元刚度矩阵验证了该方法的正确性。     

复合材料加筋圆拱壳的失稳特性分析

本文应用增量形式的拉格朗日列式法对其有纵横加筋的迭层圆拱壳在均布载荷作用下的稳定性进行了非线性有限元分析。文中应用Sander 壳体理论及横向剪切的影响, 推导了矩形壳元及与该壳元变形相协调的直梁元和曲梁元的切线刚度矩阵。编制了FORTRAN 计算程序。计算并分析了加筋拱壳的局部及整体失稳过程。      

The geometric stiffness of thick shell triangular finite elements for large rotations

This paper is concerned with the development of the geometric stiffness matrix of thick shell finite elements for geometrically nonlinear analysis of the Newton type. A linear shell element that is comprised of the constant stress triangular membrane element and the triangular discrete Kirchhoff Mindlin theory (DKMT) plate element is ‘upgraded’ to become a geometrically nonlinear thick shell finite element. Perturbation methods are used to derive the geometric stiffness matrix from the gradient, in global coordinates, of the nodal force vector when stresses are kept fixed. The present approach follows earlier works associated with trusses, space frames and thin shells. It has the advantage of explicitness and clear physical insight. A special procedure, tailored to triangular elements is used to isolate pure rotations to enable stress recovery via linear elastic constitutive relations. Several examples are solved. The results compare well with those available in the literature. Copyright © 2005 John Wiley & Sons, Ltd.     

基于弯曲刚度最大分层临界载荷的层压板局部屈曲预测

提出了一种预测含特定分层损伤层压板发生局部屈曲时整体应变的方法。认为含分层子板的局部屈曲载荷由其弯曲刚度最大的分层决定, 因而含有相同最大弯曲刚度分层的不同子板具有相同的屈曲载荷。在已知弯曲刚度最大分层的屈曲载荷的情况下, 根据层压板的轴向刚度公式, 计算出发生局部屈曲时弯曲刚度最大的分层与完好的基板分别承受的载荷, 即得到总载荷, 进而得到层压板的整体应变。用ABAQUS有限元分析软件建立含分层损伤的层压板模型, 使用准静态加载进行了多种分层深度和分层位置下的局部屈曲仿真, 所得局部屈曲载荷符合上述推论。用所提方法预测发生局部屈曲时的整体应变, 结果与有限元结果吻合较好, 此方法可用于建立分层参数识别的参照样本库。     

不同截面梁构件的刚度和稳定性优化设计

本文运用有限元分析与优化设计软件JIFEX，对五种常用截面梁结构的尺寸和形状进行了抗剪、抗弯、抗扭的刚度优化设计和在轴力、剪力作用下的结构稳定性优化设计。通过对优化设计的计算结果分析，得到了对工程设计有意义的若干结论。然后通过飞机结构中一种波形梁构件的优化，进一步讨论了波形梁的波数对结构稳定性和刚度的影响。     

含损伤复合材料AGS 板的屈曲特性

采用有限元数值模拟方法, 研究了蒙皮内含分层损伤复合材料格栅加筋板结构(AGS) 的稳定性问题。对蒙皮和肋骨分别采用基于Mindlin 一阶剪切理论的复合材料层合板单元和层合梁单元来模拟, 推导了相应的有限元列式, 并通过坐标变换, 利用蒙皮与肋骨的几何连续条件, 形成了AGS 的单元刚度阵和几何刚度阵, 建立了含损伤AGS 稳定性分析的有限元控制方程。通过典型算例, 研究了压缩载荷作用下, 分层形状、分层大小、分层深度、肋骨的高度和宽度、布置方式等因素对AGS 的稳定性特征的影响。数值结果表明, 含分层损伤的AGS 具有十分复杂的屈曲性态。屈曲临界力和屈曲模式与分层面积、分层形状、分层深度、肋骨的高度和宽度、布置方式和位置均密切相关。