基于哈密顿理论的槽形梁桥剪力滞后分析

基于薄壁杆件结构双向弯曲理论,计及其剪切变形与纵向翘曲,引入纵向位移的插值函数,建立了考虑剪力滞后影响的槽形截面梁桥受弯分析的哈密顿对偶求解体系,用半离散精细积分法求该体系的高精度数值解。计算结果表明,本方法具有较高的精度和适用性,可方便地用于槽形截面梁桥的计算。     

基于哈密顿理论的薄壁结构双向弯曲分析

从能量变分原理出发,由勒让德变换引入对偶变量,导出了薄壁结构双向弯曲问题的哈密顿对偶求解体系,将薄壁结构的控制微分方程转化为哈密顿对偶方程,其系统矩阵具有辛矩阵的特性,可用精细积分法求该体系的高精度数值解。算例计算结果表明,本方法具有较高的精度和适用性,并可方便地用于变截面薄壁结构的计算。     

矩形箱梁约束扭转分析的精细积分法

在薄壁杆件结构约束扭转的一致性理论前提下,以断面的扭角φ(z),翘曲θ(z)为基本未知函数,引入相应的对偶变量,建立了矩形箱梁约束扭转问题的哈密顿对偶求解体系,导出了问题的控制方程(哈密顿正则方程)。方程中的系统矩阵具有辛矩阵的特性,能方便地通过精细积分法求出高精度数值解。该方法是哈密顿力学在薄壁杆件结构约束扭转分析中的应用,数学推导简单,且有成熟高效的数值算法,思路清晰、精度高、易于接受,对问题的求解提供了新的思路。     

弹性地基上铁摩辛柯梁的压弯问题

从哈密顿力学出发,由勒让德变换引入对偶变量,导出了弹性地基上铁摩辛柯梁压弯问题的哈密顿对偶求解体系,将梁的控制微分方程转化为哈密顿对偶方程,给出了问题的矩阵指数函数解,可用本征向量展开法求问题的解析解,也可用精细积分法求问题的高精度数值解,由于导出的系统矩阵具有辛矩阵的特性,数值计算具有良好的稳定性.     

考虑剪力滞后影响的框筒结构动力时程分析

框筒结构采用薄壁杆件模型.先从结构总势能出发,求得哈密顿对偶体系,由两端边值问题精细积分法中的区段混合能矩阵推导出结构的层单元刚度矩阵,利用有限元刚度集成法形成结构的总体刚度矩阵.采用多质点体系质量矩阵,阻尼矩阵采用瑞雷阻尼,再利用动力时程分析的精细积分法对结构进行动力时程分析,编制相应的Matlab程序.最后通过具体算例分析,将结果与文献结果进行对比,从而验证了本文方法分析动力问题的可行性.     

基于哈密顿理论的束筒结构剪力滞后分析

根据连续化原理,将超高层建筑束筒等效连续化为由各向异形板和角柱围成的等效实腹薄壁筒。计及剪切变形与纵向翘曲,引入纵向位移的分段线性插值函数,得到弯扭作用下高层建筑束筒结构的总势能,并由此得出相应的拉格朗日函数。引入对偶变量,建立考虑剪力滞后影响的束筒结构弯扭分析的哈密顿对偶求解体系,导出束筒结构弯扭作用下的哈密顿正则方程。用两端边值问题的半离散半精细积分法求该体系的高精度数值解。计算结果表明,模型的简化合理可行,具有较高的精度和实用性,为超高层建筑结构计算分析提供了一种可行的方法。     

薄壁梁桥的自振特性研究

本文在薄壁梁截面上采用线性插值函数来描述截面各点的纵向位移;基于哈密顿对偶体系,考虑薄壁梁的剪力滞后效应,导出薄壁梁自振特性的哈密顿方程;采用两端边值问题的精细积分法,确定方程的高精度数值解。     

带缀板的开口薄壁钢构件整体稳定分析

本文对开口薄壁杆件采用薄壁杆件弯扭分析的一致理论,利用线性插值函数来描述构件的纵向翘曲位移和剪力滞后的影响,将缀板的作用视作对开口杆件的弹性支承,建立了杆件整体稳定分析的计算模型,求出问题的拉格朗日函数。从而得出对整体稳定性分析时的哈密顿方程。为带缀板的开口薄壁钢构件整体稳定性研究提供了一种新的思路。     

考虑畸变的开口薄壁构件变形方程及其应用

为简化考虑截面畸变的薄壁杆件力学分析,提出一种把薄壁杆件拆分为两个较简单的部分分别分析、按需综合的方法。该文重点探讨截面畸变变形的效应分析:首先基于薄板小挠度弯曲理论,建立矩形板条的面外弯曲变形方程,然后适当简化截面畸变的变形形式和平衡条件,实现反映开口薄壁杆件畸变和扭转性能的"板件面外弯曲综合抗力体系"分析,最后与另文探讨的薄壁杆件"板件面内拉弯综合抗力体系"的分析进行综合,建立考虑截面畸变的开口薄壁杆件常微分变形方程。与目前较为常用的广义梁理论及有线条法相比,该方法无需进行截面正交分析或假定变形沿杆长的分布。为提高方法的实用性,文中还基于该变形方程,探讨了薄壁杆件单元刚度方程等矩阵位移法诸实现要件,据此编制的通用程序计算结论与基于壳单元的ANSYS软件算例结论吻合良好。     

开口薄壁杆的板件面内拉弯综合抗力体系

针对薄壁杆件力学分析较为复杂的问题，讨论了一种把开口薄壁杆的分析拆分为2个较简单部分的方法。针对薄壁中面内荷载效应的分析问题，首先在适当简化基本应力应变条件的基础上，按平面应力问题分析单肢板件面内荷载效应，然后对其进行向量综合，得到反映开口薄壁杆轴向伸缩、弯曲及翘曲性质的“板件面内拉弯综合抗力体系”及其变形方程；探讨了刚度方程的建立及其计算特点，并与经典理论进行对比。分析表明，在板件面内弯矩定义中引入板件间纵向相互作用力，可简化该体系分析过程和结论，使之具备与平面弯曲问题一致的形式。作为应用举例，推导了求解薄壁截面主轴方向、主轴惯性矩、弯心坐标、主扇性惯性矩的线性方程组，剖析了经典理论中这些截面几何特性对于计算的意义及其效率。     

Generalized beam theory—an adequate method for coupled stability problems

First-order generalized beam theory describes the behaviour of prismatic structures by ordinary uncoupled differential equations, using deformation functions for bending, torsion and distortion. In second-order theory, the differential equations are coupled by the effect of deviating forces. The basic equations for second-order generalized beam theory are outlined. Solutions for pin-ended supports are presented, demonstrating the coupling effect by modes and by loads. In the different ranges of length, the individual modes are sufficient approximations for the critical load. The application to a thin-walled bar with C-section under eccentric normal force demonstrates the quality of the single-mode compared to the exact solution.     

A theoretical analysis of the local buckling in thin-walled bars with open cross-section subjected to warping torsion

Results of a theoretical analysis of the local buckling in thin-walled bars with open cross-section subjected to warping torsion are presented. The local critical bimoment, which generates local buckling of a thin-walled bar and constitutes the limit of the applicability of the classical Vlasov theory, is defined. A method of determining local critical bimoment on the basis of critical warping stress is developed. It is shown that there are two different local critical bimoments with regard to absolute value for bars with an unsymmetrical cross-section depending on the sense of torsion load (sign of bimoment). However, for bars with bisymmetrical and monosymmetrical sections, the determined absolute values of local critical bimoments are equal to each other, irrespective of the sense of torsional load. Critical warping stresses, local critical bimoments and local buckling modes for selected cases of thin-walled bars with open cross-section are determined.     

Lateral buckling analysis of thin-walled laminated composite beams with monosymmetric sections

Lateral buckling of thin-walled composite beams with monosymmetric sections is studied. A general geometrically nonlinear model for thin-walled laminated composites with arbitrary open cross-section and general laminate stacking sequences is given by using systematic variational formulation based on the classical lamination theory. All the stress resultants concerning bar and shell forces are defined, and nonlinear strain tensor is derived. General nonlinear governing equations are given, and the lateral buckling equations are derived by linearizing the nonlinear governing equations. Based on the analytical model, a displacement-based one-dimensional finite element model is developed to formulate the problem. Numerical examples are obtained for thin-walled composite beams with monosymmetric cross-sections and angle-ply laminates. The effects of fiber orientation, location of applied load, modulus ratio, and height-to-span ratio on the lateral buckling load are investigated. The torsion parameter and a newly-defined composite monosymmetry parameter are also investigated for various cases.     

Finite element method for stability and free vibration analyses of non-prismatic thin-walled beams

In this paper, a numerical method is presented for the free vibration and stability analyses of tapered thin-walled beams with arbitrary open cross sections. The proposed method takes the flexural–torsional coupling effect of tapered thin-walled beams with arbitrary open cross sections into account. The total potential energy is derived for an elastic behavior from the strain energy, the kinetic energy and work of the loads applied on the cross section contour. Free vibration is considered in the presence of harmonic excitations. The effects of the initial stresses and load eccentricities are also considered in stability analysis. The governing equilibrium equations, motion equations and the associated boundary conditions are derived from the stationary condition. As in the presence of tapering, stiffness quantities are not constant; therefore, the power series approximation is used to solve the fourth-order differential equations. Displacement components and cross-section properties are expanded in terms of power series of a known degree. Then, the shape functions are obtained by deriving the deformation shape of tapered thin-walled member as power series form. Finally, stiffness and mass matrices are carried out by means of the principle of virtual work along the member׳s axis. In order to measure the accuracy and check the validity of this method, the natural frequencies and buckling loads of non-prismatic thin-walled beams with web and flange tapering and various boundary conditions are obtained and compared to the results of finite element analysis using Ansys software and those of other available numerical and analytical ones. It can be seen that the results of present study are in a good agreement with other available theoretical and analytical methods.     

A consistent theory for torsion of thin-walled bars

A consistent theory for torsion of thin-walled bars with cross-sections of arbitrary shape (open, closed or mixed) is developed in this paper; it is an improvement on the classical torsion theory of thin-walled bars. All the basic relations, formulas and equations are derived and proved under the consistent assumptions. A torsional stiffness matrix for thin-walled bar elements is also formulated on the basis of the consistent theory. A computer program has been written which is applicable to the practical use of torsional analysis of thin-walled bar structures with arbitrary cross-sections.     

Second-order and second-approximation theory in the statics and dynamics of thin-walled straight bars

This paper concerns the analysis of lightweight structures and especially the single bars from which they are composed. It is a further development of the general thoery derived previously by the author and allows one to analyse the single thin-walled bar exactly by the second-approximation approach in the areas of statics, dynamics, stability, dynamical stability, as well as natural or forced vibrations. The theory is valid for bars with arbitrary cross-section and any boundary conditions. It can be applied to thin-walled bars of large dimensions, such as is used in bridges, viaducts, etc., and even to high buildings stiffened by shafts treated either as single units or as groups of thin-walled bars.     

A non-linear theory for the behaviour of thin-walled sections subject to combined bending and torsion

Thin-walled steel sections are extensively used in modern building either as purlins or as sheeting rails. Comparatively little is known about the effects of position and orientation with respect to the shear centre of the loading on the stability of such sections. The governing differential equations for the non-linear elastic behaviour of thin-walled sections subject to combined bending and torsion are developed in the paper. They include the non-linear contribution resulting from the movement of the point of application of the load. This is shown to have a significant influence on the behaviour of the member when the loads are inclined to the principal axes, as in the case of an asymmetrical section subject to gravity loading. Furthermore, it is shown that load resultants which pass through the shear centre but which are inclined to the principal axes of the section do not produce pure bending. They induce torsional moments in the section which are not accounted for in traditional theories. A finite-difference method is used to solve the equations, and the validity of the theory is assessed by comparing the results with those obtained from experiment.     

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。