国际期刊导读

正1考虑薄壁剪切变形简支薄壁柱的挠曲:基于壳模型的解析解摘要:研究简支薄壁柱的挠曲。临界力的经典计算公式大多基于梁模型。利用欧拉-伯努利梁理论,而基于剪切-变形梁理论求解的简单公式已广为人知。利用一系列平面单元模拟柱,并考虑平面内薄壁剪切变形,推导出了相应的替代公式。推导方式略有差异,得到的公式就不同。通过理论分析和数值模拟对推导出的临界力计算公式进行探讨。关键词:挠曲;薄壁构件;剪切变形;壳模型;解析解     

基于广义梁理论的薄壁构件屈曲模态有限元分析

提出基于广义梁理论(GBT)的新方法,将各向同性薄壁构件通过壳体有限元分析方法(FEA)获得的弹性屈曲模态分解成整体、畸变和局部屈曲模态。其创新之处在于仅使用GBT截面变形模态,而非构件变形模态。该方法能够单独计算各屈曲模态,更好地了解各构件的后屈曲特性和强度曲线。根据GBT的经典假设,忽略剪切应变和横向张力。通过有限元方法得到的各模态与经典GBT计算结果一致。     

对广义梁理论中的平面和空间薄壁构件的整体屈曲分析

采用广义梁理论（GBT）对平面和空间薄壁构件进行整体屈曲分析。简要概述主要概念和广义梁理论屈曲分析中所采用的程序。基于广义梁理论的梁有限元分析考虑了4种刚体变形模式,即：i）运动学模型,用于模拟连接2个或更多U型和I型构件节点的翘曲传输作用;ii）采用程序处理构件重心和剪力中心轴（横截面非双向对称）不重合的效应;iii）节点构件的定义,这些节点可提供连接构件的自由度和节点广义位移之间的联系。最后,介绍并讨论数值结果,其可能有助于基于广义梁理论的有限元公式的制定和实施。并将基于GBT分析的结果（临界屈曲载荷和模态）与ANSYS程序中壳单元和梁单元的建模分析结果进行了对比验证。     

正多边形薄壁钢管的性能研究

正多边形截面薄壁钢管用于建造输电线结构、塔、天线和桅杆结构等,该文对其变形特性进行了研究。这种类型的横截面表现出与截面边数相关的对称性,从而导致截面的平面内和平面外(翘曲)变形特性显著。研究基于广义梁理论(GBT)的特例,旨在充分分解截面变形的主要模式,从而获得分析结果,进而提取关于这类构件结构性能的详细信息。同时对几个算例进行了理论分析和数值模拟(使用GBT梁单元)。为了进行验证和对比,也给出了标准壳有限元模型的分析结果。     

基于广义梁理论的非线性材料薄壁受压构件屈曲荷载计算方法

提出适用于非线性材料的广义梁理论屈曲荷载计算方法,并对不锈钢薄壁受压构件屈曲荷载进行计算验证。通过定义材料非线性应力应变关系和瞬时弹性模量,对传统线弹性广义梁理论进行修正,建立非线性材料薄壁构件受压屈曲荷载计算方法,推导不锈钢薄板受压局部屈曲、冷弯薄壁不锈钢卷边槽形柱畸变屈曲及箱形不锈钢长柱弯曲屈曲荷载计算公式,并与既有试验数据对比。经验证,线弹性分析方法不适用于不锈钢材料;提出的修正GBT法具有较高精度,且本构关系采用变形法则结果偏于安全,可用于不锈钢等非线性金属材料薄壁构件受压屈曲荷载的确定,为研究和设计提供理论指导。     

局部封闭和开口薄壁压弯构件的弯扭屈曲

单轴对称开口薄壁压弯构件在荷载作用于对称平面内时有可能发生弯扭屈曲。在这种情况下,其临界荷载总是低于平面内弯曲失稳破坏荷载,如果在构件的开口边加上缀板,使之形成若干断续的封闭截面,则弯扭屈曲临界荷载将显著提高,并有可能使破坏模式由弯扭屈曲转化为平面内弯曲失稳。本文提出了一种计算薄壁压弯构件弯扭屈曲荷载的方法,这种方法对局部封闭和开口截面都能适用。曾经做了213根具有不同长细比、偏心距、缀板间距(或无缀板)的冷弯薄壁型钢压杆试验,其结果与理论符合较好。     

国际期刊导读

<正>基于广义梁理论的薄壁钢框架屈曲分析的最新进展摘要:介绍基于广义梁理论(GBT)研究平面和空间薄壁钢框架屈曲性能的最新研究进展。概述基于GBT屈曲分析的主要概念和相关程序,基于GBT的梁有限元分析的发展和数值模拟方法,包含以下内容:1)揭示局部、畸变和整体屈曲状态;2)计算任     

由3块板组合而成的开口截面薄壁梁的扭曲

开口截面薄壁梁经典理论计算时截面形状保持不变,可忽略,假定截面扭转引起的应力和位移对根据经典理论计算的应力和位移的影响很小,研究由3块板组合而成的有2条对称轴的开口截面薄壁梁的扭曲。根据剪切影响下开口截面薄壁梁扭转理论,假定截面扭转引起的应力和变形与剪切引起的扭转角成正比。利用壳单元,将分析结果与有限元方法进行比较。通过几个实例对两种方法进行验证。     

薄壁复合箱型梁的弯曲-扭转屈曲分析

对一轴心受压薄壁复合构件的屈曲进行研究。提出一个广义的分析模型,可用于分析轴心受压薄壁复合箱型梁的弯曲、扭转以及弯扭屈曲作用。此模型基于经典层压理论,考虑了任意层压堆积规律,结构的弯曲和扭转模式的耦合问题,如非对称以及对称和各种边界条件。采用一个基于位移的一维有限元模型来预测薄壁复合钢筋的临界荷载和随后的屈曲模式。从总势能的平稳值原则中推导出屈曲控制方程。轴心受压薄壁复合件的数值计算结果可用于估测纤维角、各向异性和边界条件对临界屈曲荷载和复合件模态的影响。     

薄壁复合箱型梁的弯曲—扭转屈曲分析

对一轴心受压薄壁复合构件的屈曲进行研究。提出一个广义的分析模型，可用于分析轴心受压薄壁复合箱型梁的弯曲、扭转以及弯扭屈曲作用。此模型基于经典层压理论，考虑了任意层压堆积规律，结构的弯曲和扭转模式的耦合问题，如非对称以及对称和各种边界条件。采用一个基于位移的一维有限元模型来预测薄壁复合钢筋的临界荷载和随后的屈曲模式。从总势能的平稳值原则中推导出屈曲控制方程。轴心受压薄壁复合件的数值计算结果可用于估测纤维角、各向异性和边界条件对临界屈曲荷载和复合件模态的影响。     

A new approach for thin-walled member analysis in the framework of GBT

A new approach is illustrated for the cross-sectional analysis to be performed in the context of the Generalised Beam Theory (GBT). The novelty relies in formulating the problem in the spirit of Kantorovich’s semi-variational method, namely using the dynamic modes of an unconstrained planar frame as in-plane deformation modes. Warping is then evaluated from the post-processing of these in-plane modes, thus reversing the strategy of the classical GBT procedure. The new procedure does not require several steps of the classical algorithm for the determination of the conventional modes, in which bending, shear and local modes are evaluated separately, and is applicable indifferently to open, partially-closed and closed sections. The efficiency and ease of use of the method are outlined by means of two examples, aimed to describe the linear–elastic behaviour of thin-walled members.     

A direct approach for the evaluation of the conventional modes within the GBT formulation

This paper proposes a new approach for the evaluation of the conventional modes, i.e. rigid, distortional, local and Bredt shear-modes, to be used in the framework of the Generalised Beam Theory (GBT) for the analysis of thin-walled members. The new method identifies a set of conventional modes in a single step cross-sectional analysis and for any type of cross-section, i.e. open, closed and partially-closed ones. The algorithm differs from that of the classical GBT, which requires a two-step evaluation procedure, consisting of an initial choice of the vector basis and its successive orthogonalization. The method is based on a definition of a new quadratic functional, whose steady condition leads to an eigenvalue problem, and directly generates the sought orthogonal basis, here found using a finite-element approach. The accuracy of the proposed method is validated by means of two numerical examples, one dealing with a lipped C-section and one with a partially-closed profile. It is shown that the conventional modes derived with the proposed approach are identical to those determined with the classical two-step procedure, thus limiting the computational effort required in their identification.     

Generalised Beam Theory (GBT) for stiffened sections

This paper presents an extension to the Generalised Beam Theory (GBT) approach to describe the response of prismatic thin-walled members stiffened by means of generic plate arrangements at different cross-sections along their length. The conventional deformation modes to be included in the GBT formulation are obtained as the dynamic modes of a planar frame, which represents the cross-section. Two numerical procedures are implemented to account for the presence of the stiffeners. One approach identifies different sets of deformation modes for the unstiffened and stiffened sections, which are then combined for the member analysis. The second procedure relies on the use of constraint equations at the stiffened locations to be included in the member analysis. For the cross-sectional analysis, a new mixed finite element is presented which incorporates the inextensibility condition usually adopted in the framework of the classical GBT, therefore simplifying the steps required for the evaluation of the conventional deformation modes. The proposed technique is applicable to open, closed and partially-closed stiffened sections. Two numerical examples are provided to highlight the ease of use of the method of analysis considering open and partially-closed sections, and their results are validated against those obtained with the commercial finite element software Abaqus.     

GBT-based buckling mode decomposition from finite element analysis of thin-walled members

This paper presents an original method based on the Generalised Beam Theory (GBT) capable to decompose the elastic buckling modes from a shell finite element analysis (FEA) of an isotropic thin-walled member, into pure buckling modes of global, distorsional or local nature. The main novelty lies in using only the GBT cross-sectional deformation modes instead of member base mode shapes. The contribution of each pure buckling mode can be calculated, allowing a better understanding of the member post-buckling behaviour and strength reserve. Following the GBT classical assumptions, the membrane shear strains and transverse extensions are neglected. The modal participations obtained from FEA are in good agreement with the values calculated via classical GBT approach.     

A generalized beam theory with shear deformation

A new formulation of the Generalized Beam Theory (GBT) that coherently accounts for shear deformation is presented in this paper. In particular, a modified formulation of the kinematics early proposed by Silvestre and Camotim for shear deformable GBT is devised. The new formulation, which preserves the general format of the original GBT for flexural modes, introduces the shear deformation along the wall thickness direction besides that along the wall midline, so guaranteeing a coherent matching between bending and shear strain components of the beam. According to the new kinematics, a reviewed form of the cross-section analysis procedure is devised, based on a unique modal decomposition for both flexural and shear modes. Much attention is posed on the mechanical interpretation of the deformation parameters in the modal space. It is shown that, in the modal space, it is possible to clearly distinguish bending deflections from deflections due to shearing strains, and to recover classical beam degrees of freedom and standard beam theories as special cases. The effectiveness of the proposed approach is illustrated on two typical benchmark problems.     

Distortional buckling modes of semi-discretized thin-walled columns

This paper presents distorting buckling solutions for semi-discretized thin-walled columns using the coupled differential equations of a generalized beam theory (GBT). In two related papers recently published by the authors a novel semi-discretization approach to GBT has been presented. The cross section is discretized and analytical solutions are sought for the variation along the beam. With this new approach the general GBT equations for identification of a full set of deformation modes corresponding to both homogeneous and non-homogenous equations are formulated and solved. Thereby giving the (complex) deformation modes of GBT which decouple the state space equations corresponding to the reduced order differential equations.In this paper the developed semi-discretization approach to generalized beam theory (GBT) is extended to include the geometrical stiffness terms, which are needed for column buckling analysis and identification of buckling modes. The extension is based on an initial stress approach by addition of the related potential energy terms. The potential energy of a single deformation mode is formulated based on a discretization of the cross section. Through variations in the potential energy and the introduction of the constraints related to beam theory this leads to a modified set of coupled homogeneous differential equations of GBT with initial stress for identification of distortional displacement modes. In this paper we seek instability solutions using these GBT initial stress equations for simply supported columns with constrained transverse displacements at the end sections and a constant axial initial stress. Based on the known boundary conditions the reduced order differential equations are solved by using the trigonometric solution functions and solving the related eigenvalue problem. This gives the buckling mode shapes and the associated eigenvalues corresponding to the bifurcation load factors. Thus the buckling modes are found directly by the analytical solution of the coupled GBT-equations without modal decomposition. Illustrative examples showing global column buckling, distortional buckling and local buckling are given and it is shown how the novel approach may be used to develop signature curves and elastic buckling curves. In order to assess the accuracy of the method some of the results are compared to results found using the commercial FE program Abaqus as well as the conventional GBT and FSM methods using the software packages GBTUL and CUFSM.     

Calculation of pure distortional elastic buckling loads of members subjected to compression via the finite element method

An analysis procedure is presented which allows to calculate pure distortional elastic buckling loads by means of the finite element method (FEM). The calculation is carried out using finite element models constrained according to uncoupled buckling deformation modes. The procedure consists of two steps: the first one is a generalised beam theory (GBT) analysis of the member cross-section, from which the constraints to apply to the finite element model are deduced; in the second step, a linear buckling analysis of the constrained FEM model is performed to determine the pure distortional loads. The proposed procedure is applied to thin-walled members with open cross-section, similar to those produced by cold-forming. The distortional loads obtained are rather accurate. They are in agreement with the loads given by GBT and the constrained finite strip method (cFSM).     

半离散法分析薄壁柱的畸变屈曲

采用广义梁理论(GBT)的耦合差分方程解决了半离散法分析薄壁柱的畸变屈曲问题。作者近期发表的两篇文章对类似GBT的新型半离散分析方法进行了阐述。对横截面进行离散分析,寻找沿梁变化的解析解。采用新方法,利用齐次和非齐次方程建立确定梁全部变形的一般GBT方程并求解,从而使GBT的(复杂)变形方程变形为可降阶的微分方程。提出的半离散方法在广义梁理论(GBT)基础上增加了用于柱的失稳分析和失稳形态识别的几何刚度因素。通过势能的变化并在梁理论中引入约束条件,对初始应力下建立的GBT齐次微分方程进行修正,以分析其变形特性。对简支梁梁端施加横向位移和轴力,建立GBT初始应力方程,通过该方程寻求失稳的解决方法。根据已知的边界条件,利用三角函数关系式和求解特征值的方法求解这些可降阶的微分方程,使得屈曲形态和相关特征值与分叉荷载因素相符。因此,无需通过模态分解,可由耦合的GBT方程直接求得屈曲形态的解析解。通过实例分析了柱的整体失稳、屈曲变形和局部纵弯失稳,以及如何将新方法用于描述特征曲线和弹性屈曲曲线。将该方法的分析结果与ABAQUS、GBTUL和CUFSM软件的分析结果进行对比,验证了该方法的正确性。     

通过有限元法计算受压构件的纯畸变弹性屈曲荷载

基于有限元法,提出一个分析方法,可以计算纯畸变弹性屈曲荷载。计算中采用的有限元模型为非耦合屈曲变形模式。具体方法分为2步:第1步,采用一般梁理论(GBT)分析构件横截面,在此可以给有限元模型施加约束条件;第2步,对受约束有限元模型进行线性屈曲分析,确定纯畸变荷载。将此法应用于开口薄壁构件和冷弯构件,得到的畸变荷载非常准确,与一般梁理论和约束有限条法(cFSM)计算的荷载值一致。