薄壁构件弯扭失稳的一般理论

在薄壁构件的弯扭失稳问题上近20年以来存在着传统的和较新的两种不同的理论,这两种理论的并存使得一些国家的规范和一些著作出现不一致,例如我国的(GB50017—2003)和N.S.Trahair的著作犤17犦仍然采用传统理论的结果,而(GB50018—2003)、ISO的钢结构材料标准和美国的金属结构稳定设计解说却采用较新理论的结果。作者发现被忽视的横向正应力也是影响薄壁构件稳定的重要因素。本文在考虑非线性横向应变能的基础上,导出了薄壁构件的总势能方程。从板的理论出发,全面考虑微元上各种应力以及外荷载的影响,用假想荷载法导出了薄壁构件的弯扭失稳平衡微分方程。这组平衡微分方程和本文提出能量法的是一致的,这进一步证实了本文提出理论的正确性。     

小应变下土体刚度非线性分析的试验研究

精确的试验测试显示,土体在小应变下呈非线性作用,用常规的室内试验和传统的线弹性分析方法不能真实描述土的刚度变化,只能采用原位试验和非线性分析方法来确定。基于Bolton等人提出的平面应变下不排水膨胀试验的非线性分析理论,研究了剑桥自钻式旁压试验过程中土体刚度随应变的变化规律,并与线性分析结果进行了对比。试验和分析结果表明:小应变下土体刚度具有高度的非线性,随应变的增加发生衰减,但在不同应变区间衰减程度不同;土体割线模量值大于切线模量值,其差值随应变的增加逐渐减小;传统的线性分析低估了土体弹性作用范围和强度,而采用非线性分析能确定不同应变下土的刚度参数,真实反映土的非线性作用特点。     

Analytical and experimental modelling of non-linear aeroelastic effects on prismatic bodies

This paper deals with the aeroelastic instability and non-linear post-critical behaviour of a two degree-of-freedom oscillatory system. The main goal of the study is an introduction of a realistic non-linear theoretical model making possible a detailed non-linear analysis of post-critical states of an aeroelastic system. Two component self-induced vibration of a body is described by a system of two simultaneous non-linear differential equations. The coupling of the resultant motion is due to linear and non-linear aeroelastic effects only, while the elastic forces are taken independent. Differential system is auto-parametric and represents a combination of Rayleigh or Van der Pol with Duffing types of differential equations. The qualitative analysis is based on the uplift coefficients and torsional moments as the functions of the flow velocity and structural response components. The effects of non-linearities are tested on the model where the motion of one degree of freedom is prevented. The analysis is verified experimentally by the new generation technique allowing excessive amplitudes of the oscillation.     

Bifurcation of locally buckled members

The paper presents a general bifurcation analysis of members that are locally buckled in the fundamental state. The members are assumed to be geometrically perfect in the overall sense such that bifurcation of the locally buckled member in an overall mode may occur. The analysis applies to arbitrary types of loads and support conditions. The cross-section, which may be arbitrary in shape, is assumed to be composed of flat plates. The paper derives the general variational equations expressing equilibrium of the fundamental and bifurcated states. The variational equations are applied to doubly symmetric columns and doubly symmetric beam-columns. The differential equations and boundary conditions are derived from the variational equations and solved for the fundamental and bifurcated states, thus providing the bifurcation loads of the members.     

三维块体系统非连续变形正分析模型

将非连续变形分析方法推广至三维，在一定的线性位移模式下，按最小势能原理建立三维块体非连续变形正分析模型，详细推导了荷载子矩阵，惯性子矩阵，位移约束子矩阵和接触子矩阵，给出了相应的公式和算例。     

Thin-walled cold-formed sections subjected to compressive loading

The weakening effects of local buckling on the compressive load carrying capability of thin-walled cold-formed sections is examined and discussed. Theoretical results are presented for the pin-ended support condition and a study is made of the local buckling and overall bending interaction behaviour of compression members with different cross-sectional shapes. It is shown that singly symmetric plain channel sections exhibit considerably different interactive equilibrium characteristics to those of I-sections for which the shear centre and section centroid are coincident.

The theoretical results given have been obtained through the solution of a differential equation which governs, approximately, the overall bending behaviour of a locally buckled compression member. Both local and overall imperfections are considered in the theoretical approach and it is shown that the effect of these is to reduce the ultimate compressive carrying capacity of cold-formed sections.

An experimental investigation of the behaviour of concentrically loaded pin-ended I-section struts and columns is reported and the findings from this are compared with theoretical predictions. The theoretical predictions of load-deflection equilibrium behaviour and stress variations with load are shown to be in good agreement with those obtained from test.

The provisions made in the UK Code of Practice and the American Specification pertaining to the design of cold-formed compression members are briefly outlined and compared. It is shown that with regard to I-section struts and columns the American design procedure gives, in general, more conservative estimates of collapse.     

楔形杆件结构的自主振动及弹性稳定分析

把含有小参数的二阶线性齐次方程转化为含有大参数的二阶线性齐次方程，然后求出含有大参数二阶线性齐次方程的渐近解，利用此渐近解即可求出楔形杆件结构的纵振自主频率反弹性失稳时的临界荷载。     

A beam finite element for non-linear analyses of thin-walled elements

The aim of the present paper is to investigate a theoretical and numerical model which is able to study the behaviour of thin-walled beams with open cross section in presence of large torsion. The presented model takes into account for large torsion, linear and non-linear warping currently named shortening effects, pre-buckling deformation and flexural–torsional coupling. In numerical analysis, a 3D beam with two nodes and seven degrees of freedom per node is adopted. The equilibrium equations and the material behaviour are derived in discrete form without assumption on torsion angle amplitude. Due to large torsion context, all the equilibrium equations are non-linear and highly coupled. The linear behaviour is made possible by disregarding non-linear terms. For non-linear behaviour and stability, the tangent stiffness matrix is carried out. Due to large torsion context, new matrices are present. The element is incorporated in a homemade finite element code. Newton–Raphson iterative methods are used with different control parameters. In order to prove the efficiency of the model many examples are presented in linear and non-linear behaviour with presence of bifurcations.     

Non-linear vibration of initially stressed plates with initial imperfections

Non-linear partial differential equations of vibration for isotropic plates having initial imperfection are derived. The derivation based on the classical plate theory aims to describe non-linear vibration of imperfect plates in a general state of arbitrary initial stresses. Galerkin method is used to reduce the non-linear partial differential equations to ordinary non-linear differential equations. Runge-Kutta method is used to obtain the non-linear and linear frequencies of vibration. A numerical example is presented to discuss the performances of perfect and imperfect plates. The initial stress is taken to be a combination of pure bending stress plus an extension stress in the plane of the plate. It is found that the existence of initial vibration amplitude, initial stress and geometric imperfect may result in a drastic change on the non-linear vibration behavior. The effects of various parameters on the non-linear free vibrations are discussed.     

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.     

Buckling analysis of thin-walled members with closed cross sections

In this paper, an analytical procedure for the elastic buckling problems of thin-walled members with closed cross sections by the transfer matrix method is presented. The transfer matrix is obtained from the differential equations for a plate subjected to axial load, and the extended transfer matrix for closed cross sections is derived from that for branched panels. The analytical local and overall elastic buckling loads for thin-walled members with closed cross sections can be obtained simultaneously. Furthermore, a technique to estimate the buckling mode shapes of these members is also shown. To investigate the accuracy and efficiency of this method, some numerical examples are presented.     

The geometric non-linear analysis of thin-walled structures by finite strips

The geometric non-linear analysis of prismatic thin-walled structures is presented. The theory is based on the moderately large displacement assumption, giving non-linear strain-displacement relations, but linear curvature-displacement relations. The corresponding non-linear equilibrium equations are produced by the principle of stationary potential energy using the finite strip discretisation. The equilibrium equations are solved using incremental and incremental-iterative numerical methods. Thus for the simple case of the square plate in edge compression, the self-correcting incremental method gives satisfactory results. For more complex examples of loading and structural type, a variable load incremental-iterative method is adopted. It is shown that the finite strip method used in conjunction with this method can be applied in particular to problems containing load maxima.     

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。     

型钢混凝土梁的界面滑移位移的计算与分析

研究型钢混凝土简支梁在基本荷载作用下的界面滑移。以型钢上、下翼缘为界将型钢混凝土梁截面划分成三个不同的理想弹性体,利用弹性分析理论建立一般受力情况下界面滑移的微分方程组。通过分析其受力特点,推导出型钢混凝土简支梁在纯弯矩、对称集中荷载以及均布荷载作用下的型钢上、下翼缘与混凝土之间滑移量沿梁长度方向变化的关系式,并对三种情况下滑移量的模拟曲线分析对比。为用数学方式描述复杂受力情况下型钢与混凝土之间的界面滑移提供理论依据,同时为研究型钢混凝土梁界面的粘结滑移本构关系奠定了基础。     

Elastoplastic buckling of circular annular plates under uniform in-plane loading

This paper deals with the elastoplastic buckling of a circular annular plate, with various axially symmetric boundary conditions and uniform axially symmetric in-plane radial loads on the inner and outer edge. The analysis is based on the standard linear buckling equations and the material behaviour is modelled by the small strain J₂ flow and deformation theories of plasticity where an elastic linear hardening rheological model of the material is considered. The solutions are obtained using the equilibrium approach where the governing differential equation is solved by the finite difference method which leads to the determination of eigenvalues of a homogeneous system of linear equations. Elastoplastic buckling loads for axially symmetric and asymmetric buckling shape modes with m waves in the circumferential direction are calculated and compared for both theories of plasticity. For one case, an experiment was performed and the results were compared with theoretical predictions.     

索结构找形分析的精确单元方法

索找形问题是索结构分析中所要解决的首要问题,在给定边界条件下,所施加的预张力和外部荷载通过调节索的 形状来平衡。本文研究索结构初始形状确定的精确有限单元法,对于常见的荷载形式,构造了线性和非线性两大类共5种 单元,适用于一般的索结构找形计算,并且可以给出精确的解答。本文通过将水平方向和竖直方向的平衡方程解藕,得出 了索单元的精确描述格式,并保证了索结构形状的唯一性。文中以索结构内部结点坐标作为基本未知量,以结点平衡方程 为基本方程,通过直接求解单元的平衡微分方程得到单元刚度矩阵的解析表达式。对于由线性单元组成的索结构,其基本 方程为线性,可直接求解;对于含有非线性单元的索结构,其基本方程为非线性,需通过迭代求解,文中构造了相应的 Newton法迭代格式。本文方法所需单元数目少,计算量小,所得到的解答为数值精确解。数值算例表明本法稳定可靠。     

钢筋砼T形、倒T形、工字形截面偏心受压构件的配筋计算

本文基于新的砼结构设计规范的基本假定和截面内力平衡方程,提出了在T形、倒T形、工字形截面偏心受压构件正截面强度计算时均可按矩形截面计算的“等代矩形截面法”,从而使T形,倒T形、工字形截面偏心受压构件的各种计算情况分析以及小偏心受压时遇到的中和轴相对高度ξ三次方程的近似计算方法均与矩形截面通用。在近似求解小偏心受压构件的ξ的三次方程时,以分区降阶一次逼近法为例,说明了“等代矩形截面法”的具体应用。     

考虑形心和剪心分离的变曲率箱梁弯扭分析

为考虑曲梁剪心和形心分离和曲率变化对曲线箱梁的影响，针对具有竖直对称轴的矩形断面变曲率箱梁，推导了考虑曲梁剪心和形心分离情况下的平衡方程，然后通过箱梁内任一点的位移方程和内力-位移关系得到考虑曲梁剪心和形心分离的变曲率箱梁的挠曲扭转微分方程，最后得到回旋曲线箱梁的平衡微分方程及其伽辽金求解。     

基于地基反力与沉降非线性关系的地基梁研究

基于实验测量的地基反力与地基梁沉降关系数据,分别将地基和梁之间的作用力与梁的挠度拟合成线性关系和三次多项式关系,推导出非线性弹性地基梁的有限差分法基本理论方程式,并用MATLAB软件编程解出数值解。算例计算对非线性弹性地基梁和经典线弹性Winkler地基梁的挠度、转角、剪力和弯矩结果进行了对比,结果表明二者的相对误差可达到10%~30%,因此在实际工程中应尽量考虑地基反力与沉降的非线性关系。     

Torsional analysis of thin-walled composite beams with single- and double-celled sections

The exact solutions for twist angle and fiber stresses of thin-walled composite box beams with single- and double-celled sections subjected to torsional moment are presented by introducing fourteen displacement parameters. For this, a general thin-walled composite box-beam theory including the effects of elastic couplings and restrained warping is developed based on the Vlasov’s assumptions. The equilibrium equations and the force–deformation relations are derived from the energy principle. A system of linear algebraic equations with non-symmetric matrices is constructed by introducing fourteen displacement parameters and by transforming the higher order simultaneous differential equations into first-order ones. This numerical technique determines eigenmodes corresponding to multiple zero and non-zero eigenvalues and derives exact displacement functions for displacement parameters based on the undetermined parameter method. Finally, the exact stiffness matrix is determined using the member force–deformation relations. The theory developed by this study is validated by comparing several torsional responses from the present approach with those from the finite element beam model that uses third-order Hermitian polynomials and detailed two-dimensional analysis results using the shell elements of ABAQUS for coupled composite beams with single- and double-celled sections.