剪切作用下冷弯槽钢的弹性屈曲

研究与腹板平行的纯剪切荷载作用下包含翼缘和卷边的整个槽钢截面的弹性屈曲,并给出了解决方案。采用样条有限条法(SFSM)对纯剪切作用下的薄壁槽钢进行弹性屈曲分析,以获得截面的弹性屈曲载荷(Vcr)。利用剪切屈曲载荷计算用于截面设计的腹板的剪切屈曲系数(KV)。主要变量为翼缘宽度、构件长度和卷边尺寸。边界条件为两端简支。根据分析结果绘制交互作用曲线,可作为设计指南,使得设计人员不用样条有限条法(SF-SM)软件也能够预测弹性屈曲剪切系数(KV)。给出了不同的翼缘宽度、构件长度和卷边尺寸下构件的典型屈曲模态。包括局部屈曲和翼缘屈曲,畸变屈曲和截面扭曲。     

Buckling analysis of thin-walled sections under localised loading using the semi-analytical finite strip method

Thin-walled sections under localised loading may lead to web crippling of the sections. This paper develops the Semi-Analytical Finite Strip Method (SAFSM) for thin-walled sections subject to localised loading to investigate web crippling phenomena. The method is benchmarked against analytical solutions, Finite Element Method (FEM) solutions, as well as Spline Finite Strip Method (SFSM) solutions. The paper summarises the SAFSM theory then applies it to the buckling of plates, and channel sections under localised loading. Multiple series terms in the longitudinal direction are used to compute the pre-buckling stresses in the plates and sections, and to perform the buckling analyses using these stresses. Solution convergence with increasing numbers of series terms is provided in the paper. The more localised the loading and buckling mode, the more series terms are required for accurate solutions. The loading cases of Interior One Flange (IOF) and Interior Two Flange (ITF) are investigated in this paper using simply supported boundary conditions.     

热轧花纹板钢卷外径计算模型研究

紧密度是热轧花纹板钢卷外径计算的主要参数。为提高花纹卷的外径计算精度,选择一次、二次、三次和四次勒让德多项式作为紧密度基本模式,采用基于最小二乘原理的勒让德多项式回归分解法建立了紧密度的计算模型。模型应用结果表明,该方法大幅度提高了花纹卷外径计算精度,克服了传统方法计算精度差而难以满足现场需要的缺点,是一种简捷实用的花纹卷卷外径计算方法,能够满足现场生产的需要。     

Unilateral buckling of point-restrained triangular plates

In this paper the unilateral buckling behavior of point restrained triangular plates is studied. Firstly, the energy functional of a general triangular plate with elastic foundation is calculated. The Rayleigh–Ritz method for investigating the local buckling of unilaterally restrained triangular plates is applied. The displacement functions and restraining medium are modeled as polynomials and tensionless foundation respectively. The results are obtained for different boundary conditions, aspect ratios and various in-plane compressive and shear loadings. Confirming the validity of this investigation, convergence and comparison studies are undertaken. The comparisons show the efficiency and accuracy of the presented method.     

Non-linear free vibration of elliptic sector plates by a curved triangular p-element

A curved triangular p-element is developed and applied to geometrically non-linear free vibration of isotropic elliptic sector plates. The formulation takes into account shear deformation, rotary inertia, and geometric non-linearity. The element can describe the geometry of the elliptic sector plate exactly and is therefore suitable for this type of plate. The shifted Legendre orthogonal polynomials are used as enriching hierarchic shape functions. The element stiffness and mass matrices are integrated numerically using the Gauss–Legendre quadrature. The non-linear equations of free motion are obtained using the harmonic balance method and solved iteratively by the linearized updated mode method. Numerical results for the linear and non-linear frequencies of clamped elliptic sector plates are obtained. The efficiency of the proposed p-element is demonstrated through convergence studies and comparisons with published results. The effects of the ellipse eccentricity, thickness ratio, and sector angle on the backbone curves are examined. It is shown that these parameters influence the hardening behavior.     

用三次B样条进行旋转壳有限元分析

本文成功地应用三次B样条对旋转壳进行了静力有限元分析。在本法中,壳体中面一点位移的三个分量及子午线方向的几何形状均用以三次B样条为基样条的样条函数来逼近。同一般的有限元分析相比较,本法具有多项式次数低、自由度少而连续性强、精确度高,计算速度快,内存小,方便经济等优点。     

轴心受压开口薄壁构件弹塑性屈曲荷载的统一计算方法

通过分析构件截面上应变与轴向力间的关系，以构件轴向应变为基本参数，提出了轴心受压开口薄壁构件的弹塑性屈曲荷载统一计算方法，给出了轴压构件的弯曲屈曲、扭转屈曲、弯扭屈曲等屈曲荷载的弦截法迭代格式，可应用于H形、T形、L形、十形截面等不同开口形式的轴压构件屈曲荷载计算，并可考虑具有残余应力的弹塑性本构关系。该方法以无残余应力的弹性屈曲荷载对应的轴向应变作为初始值，根据不同屈曲形式对应的非线性方程计算弦截区间点的函数值，进行弦截法迭代计算，得到弹塑性构件的临界轴向应变，进而获得屈曲荷载等信息。该方法采用的弦截法收敛速度快、计算量小、无需嵌套循环，可有效解决两端铰接轴心受压开口薄壁构件的弹塑性屈曲快速计算问题，便于工程应用。     

A full modal decomposition of thin-walled, single-branched open cross-section members via the constrained finite strip method

This paper derives a new method for fully decomposing the elastic stability solution, of a thin-walled single-branched open cross-section member, into mechanically consistent buckling classes associated with global, local, distortional, and shear and transverse extension buckling modes. The method requires a set of formal mechanical definitions for each of the buckling classes. For global and distortional buckling the definitions employed successfully by generalized beam theory are utilized herein, while for local and other (shear and transverse extension) buckling, new definitions are provided. The mechanical definitions for a given buckling class represent a series of constraint conditions on the general deformations that the thin-walled cross-section may undergo. These constraint conditions are derived as explicit constraint matrices within the context of the finite strip method, and provide the desired decomposition of the buckling deformations of the member. The decomposition is full in the sense that the union of the deformation spaces of the decomposed buckling classes is the same as the general deformation space in the original finite strip method. The resulting method is termed the constrained finite strip method (cFSM). The two primary applications for cFSM are modal decomposition and modal identification. Modal decomposition reduces the general finite strip solution to a desired set of buckling classes and performs a useful model reduction that allows the results to focus on a particular buckling class, e.g., distortional buckling. Modal identification provides a means to quantify the extent to which a given buckling class is contributing to a general buckling deformation. Application of cFSM, including graphical representation of the buckling classes, and the advantages of modal decomposition and modal identification, are provided in a series of numerical examples.     

3D Parametric Modeling of Complex Geological Structures for Geotechnical Engineering of Dam Foundation Based on T‐Splines

We propose a novel geological modeling method based on T‐splines for computer‐aided design (CAD) and building information modeling (BIM) systems of geotechnical engineering and perform original research on special T‐splines modeling strategies and the algorithm aiming at depicting structural complexity to develop and introduce the T‐splines technology into engineering geological modeling. A methodology of parametric geological modeling with T‐splines is established, where a topology‐geometry modeling strategy is adopted, the inhomogeneity, arbitrary connectivity and discontinuity of geological structures are quantified and associated with T‐spline surface elements in the topology phase. A representative parametric algorithm called IBALR is presented in the context of dam foundation geological modeling to generate an inhomogeneous local refined T‐mesh with high genus topology which can fit a complex geological layer. The proposed method is flexible and effective in improving geological representation within geotechnical engineering.     

正交各向异性板裂屈曲岩爆机制与控制对策研究

高应力硬岩板裂化破坏现象普遍存在于工程地质和采矿工程现场,而以此诱发的板裂屈曲岩爆也给深部资源的安全高效开采带来了严峻挑战。为了分析深部高应力硬岩板裂屈曲岩爆的力学机理与控制对策,对板裂化岩体建立了正交各向异性薄板力学模型,推导出双向受力条件下板裂屈曲岩爆临界荷载值;在解出弯曲形变势能的基础之上,依据能量法求得了薄板压曲状态下的挠度值。提出采用充填法的控制对策以防治板裂屈曲岩爆的发生,并推导出充填体所需的围压值。研究结果表明:(1)针对竖向层状岩体中发生的板裂屈曲岩爆现象,应对板裂化岩体建立正交各向异性薄板力学模型进行相关力学机理的研究;(2)轴向应力的增加不仅促进了板裂化破坏的形成,还加剧了板裂屈曲岩爆发生的可能性;(3)在一定范围内,板裂体在压曲作用下的水平挠度值随板厚的减小而增大,且当长高比为E_2/E_1~(1/4)时,有最大挠度值;(4)在对采空区进行充填时,较小的充填体围压值便可以有效抑制板裂屈曲岩爆的发生。     

受弯的冷弯卷边槽钢畸变屈曲强度和其相关屈曲承载力

受弯的冷弯薄壁卷边槽钢基本上有板件局部屈曲,截面畸变屈曲和构件弯扭屈曲三种屈曲模式,随后有它们之间的相关屈曲。由于畸变屈曲模式对缺陷的敏感度高,因此其屈曲后强度提高的幅度远低于局部屈曲模式。但是与局部屈曲模式相比,畸变屈曲模式抵抗破坏的能力却很强。可以用有限单元法计算受弯卷边槽钢截面的畸变屈曲强度。本文介绍了澳大利亚-新西兰标准AS/NZS4600-2005,用手算法计算受弯卷边槽钢截面的弹性畸变屈曲应力,並用直接强度法计算其相关的屈曲承载力。     

Form-finding and buckling capacity optimization of branching structures based on force density method

力密度法通常用于张拉索网结构等不需要考虑稳定性的结构体系的找形分析，但对于树状结构，由于其在竖向荷载作用下所有构件仅受到轴向压力的作用，除了找形以外还需要考虑构件稳定承载能力的问题。利用力密度法对树状结构进行找形分析的基础上，引入欧拉稳定承载力计算理论以考虑构件几何长度对稳定承载力的影响，并提出了相应的迭代算法。推导了适用于树状结构的修正迭代力密度理论计算式，通过改变每一个分枝的力密度进而达到优化分枝长度的目标。通过与已有计算结果的对比验证所提对于平面树状结构算法的可靠性，对空间树状结构进行分析验证所提算法对于复杂树状结构的适用性。算例分析表明：采用所提算法迭代100次即可得到收敛的结果，耗时5min左右；与数值逆吊法找形相比，避免了双单元法抗弯刚度不恰当而导致的计算不收敛问题。     

基于力密度法的树状结构找形及稳定承载力优化算法

力密度法通常用于张拉索网结构等不需要考虑稳定性的结构体系的找形分析,但对于树状结构,由于其在竖向荷载作用下所有构件仅受到轴向压力的作用,除了找形以外还需要考虑构件稳定承载能力的问题。利用力密度法对树状结构进行找形分析的基础上,引入欧拉稳定承载力计算理论以考虑构件几何长度对稳定承载力的影响,并提出了相应的迭代算法。推导了适用于树状结构的修正迭代力密度理论计算式,通过改变每一个分枝的力密度进而达到优化分枝长度的目标。通过与已有计算结果的对比验证所提对于平面树状结构算法的可靠性,对空间树状结构进行分析验证所提算法对于复杂树状结构的适用性。算例分析表明：采用所提算法迭代100次即可得到收敛的结果,耗时5min左右;与数值逆吊法找形相比,避免了双单元法抗弯刚度不恰当而导致的计算不收敛问题。     

基于Wieghardt地基桩基稳定性分析

基于Wieghardt地基模型,考虑剪力对桩受力的影响,采用梁的弯曲微分方程,利用梁单元间的位移、转角、弯矩和剪力协调条件,桩的整体平衡条件,建立了不计桩侧摩阻力时两端铰支完全埋入土桩的微分方程,并给出了基桩屈曲临界荷载。利用本文解答分析了地基基床系数对基桩屈曲荷载的影响。结果表明,考虑桩侧有明显土体约束计算的桩屈曲荷载明显大于没有考虑侧向约束桩的屈曲荷载,说明桩侧约束对桩的稳定性具有重要影响;并且基桩屈曲临界荷载随地基基床系数a,b增大而减小;对于细长桩,纯弯曲状态时的屈曲荷载小于考虑剪切变形时的屈曲荷载,实际计算中应采用纯弯曲变形时的屈曲荷载。     

An analytical method for the buckling analysis of cylindrical shells with non-axisymmetric thickness variations under external pressure

This article presents an analytical method for the buckling analysis of laterally pressured cylindrical shells with non-axisymmetric thickness variations. The previous results for thickness variations under external pressure are reviewed firstly. Then, a general analytical method that combines the perturbation method and Fourier series expansion is developed to derive buckling load formulas, which is in terms of thickness variation parameter up to arbitrary order. A classical non-axisymmetric thickness variation is discussed in detail by the presented analytical method. When non-axisymmetric modal thickness variation becomes axisymmetric, the buckling loads degenerate to the known results. Furthermore, the influence of circumferential modal thickness variation with mode corresponding to twice the circumferential buckling mode on the buckling of laterally pressured cylindrical shells is analytically investigated and the results show a great agreement with previous numerical ones by Gusic et al. Thus we confirm the presented method. In addition to theoretical analysis, calculations and comparisons are also performed. The general analytical method presented in the article can be utilized to determine the buckling loads of shells with general thickness variations.     

高强冷弯薄壁型钢轴压柱畸变屈曲研究

550MPa高强冷弯薄壁型钢卷边槽形截面轴压柱发生畸变屈曲时会出现三种模式（O—O,O-I,I—I）,考虑材料和几何双重非线性的有限元法对三种畸变屈曲模式的构件承载力、变形模式、畸变屈曲应力、横截面应力的分布等相关性能进行比较分析,可看出三种畸变屈曲模式诸性能存在较大不同,同时畸变屈曲与局部屈曲、整体屈曲在相关性能方面也存在不同。采用直接强度法对畸变屈曲轴压柱极限承载力进行计算,计算结果与试验结果较吻合,故在计算畸变屈曲轴压柱极限承载力时建议采用直接强度法．     

Distortional buckling of thin-web beam-columns

An approximate finite element method of analysis is developed for the distortional buckling of beam-columns. The member consists of a flexible web, to which is connected two rigid flange assemblies of arbitrary shape which remain undistorted during buckling. The method permits an economic computer analysis to be made of elastic distortional buckling of members under various conditions of loading, end support and restraint.Following studies of the convergence and accuracy of the buckling solutions, the method is used to demonstrate the effects of web distortion on the elastic buckling of lipped channel beams under moment gradient.     

A story buckling method for evaluating system buckling load of plane sway frames

With the intension of developing a simple method for system buckling analysis for engineering practice, a story buckling method for evaluating the system buckling load of a plane rigid frame is suggested. The method is developed based on the idea that at lower modes a plane sway frame buckles in story and story stiffness is getting to zero as the system getting close to the corresponding mode of buckling at that story. The stiffness of any story of a plane sway frame can be found with the stiffness without loading and then modified by a negative stiffness which represents the effect of vertical loads on the horizontal stiffness. P-Δ effect is first considered independently by letting the modified stiffness equal to zero and the system buckling load by first order analysis is obtained. To take P-δ effect into account, the buckling load from the first order analysis is modified with a modification factor and an estimation of buckling load of the whole system is obtained. Application examples are presented and the results are compared with those from FEA of the whole system. The simplicity and accuracy of the suggested method are demonstrated. The restraints of the method for application are discussed.     

钢板-砖砌体组合短柱轴心受压性能试验研究与理论分析

为了研究钢板-砖砌体组合柱中对拉螺栓间距、钢板厚度与结构胶侧向黏结力对钢板局部屈曲的影响,对6个钢板-砖砌体组合短柱试件进行轴心受压试验。结果表明,随着钢板厚度的增加、螺栓间距与钢板厚度之比的减小,钢板局部屈曲变形程度相对降低;可见屈曲荷载与极限荷载的比值为70%~85%左右;在有结构胶侧向黏结力作用下,钢板的局部屈曲发展受到一定程度的约束,使得采用应变片读数判断的钢板局部屈曲临界点与钢板发生可见屈曲变形时对应的荷载值可能存在差异。基于试验数据,通过拟合分析得到钢板发生可见屈曲变形时的钢板应力计算模型,提出轴心受压钢板-砖砌体组合柱钢板发生可见屈曲变形时的承载力计算式。通过与试验结果的对比可知,提出的计算方法可以用于指导类似构件的设计。