任意开口薄壁截面圆弧曲梁的通用线性理论

在曲梁精确的翘曲位移基础上,根据变分原理,提出了对任意开口薄壁截面圆弧曲梁通用的线性理论,给出平衡微分方程和相应的边界条件。定义了两个新的变量vH和qH,借助它们可以很方便地计算曲梁中的剪力和扭矩。最后就该理论在常见截面形式(工字形,槽形及无对称轴H形)水平曲梁中的应用进行说明,并与已有理论进行比较。     

考虑翘曲效应的薄壁曲梁几何非线性分析

利用UL法研究了开口薄壁曲线梁几何非线性分析问题。采用多项式插值函数表示位移场。考虑了翘曲自由度及曲率效应模拟开口薄壁曲梁的结构行为。所有位移参数定义于截面形心以便在弹性应变能中包括弯扭耦合项。利用修正的弧长法求解非线性方程,跟踪荷载位移曲线。用算例对提出的方法进行了验证,表明了薄壁曲梁的分析中翘曲变形不可忽略。     

曲梁弯扭屈曲分析

本文基于有限变形理论导出了薄壁曲梁位移和应变的一般表达式。从探讨薄壁曲梁弯扭屈曲的变形模态出发,考虑其弯矩作用平面内变形的影响,利用变分原理导出了曲梁稳定分析的基本微分方程。稳定分析表明,即使绕弱轴弯曲,曲梁也可能发生弯扭屈曲。对于曲率甚小的情况,本文把曲梁看作为具有初曲率的直梁,较精确地分析了初曲率对直梁弯扭屈曲临界弯矩的影响。此外,本文给出的闭合解与Timoshenko,Vlasov及Chai Hong Yoo等人的结果进行了比较,指出了其间差异的根源所在。     

空间结构中平面曲梁的计算

本文基于柔度法考虑了空间结构中平面等截面曲梁的弯曲、剪切、拉压和扭转变形,通过严格的数学推导,给出了计算任意曲梁的一系列公式,并在SAP 81基础上编制了曲梁程序段,给出了几个定量的计算结果。与只考虑弯曲、扭转的理论解比较,符合得很好,本文的结果可以认为是精确解。用本文给出的曲梁单元计算的结果与用多个直梁单元组成折线来近似曲梁的计算结果比较表明曲梁比直梁近似要精确得多,直梁近似往往是不能接受的。按本文公式编制的曲梁单元程序的运行表明,计算一个曲梁单元和计算一个直梁单元所需的计算机时间几乎是一样的。     

自然弯扭梁的耦合振动特性分析

以自然弯扭梁理论为基础对具有一般横截面形状空间曲梁的耦合振动特性进行了研究。 在该梁的运动控制方程中,位移函数和广义翘曲坐标均被定义在形心轴上,且在分析中包括了转动惯量、横向剪切变形以及和扭转有关的翘曲对振动的影响。通过对数学计算软件MATHEMATICA的精确运用可以得到该梁振型的解析表达式,精确的固有频率则可用搜索的方法来确定。为了证明理论的有效性,对两端固支椭圆截面曲梁的固有频率和振型进行了求解,并把数值计算结果同使用PATRAN梁单元的有限元结果进行了比较。     

考虑自平衡条件槽形曲梁的静力学特性分析

考虑了剪滞翘曲应力自平衡条件、剪力滞后、剪切变形和翘曲扭转等因素的影响,以最小势能原理为基础,建立了薄壁槽形曲梁的弹性控制微分方程和自然边界条件,获得了弯、扭、翘和剪滞效应相耦合广义位移的闭合解。算例中,分析了不同荷载形式、曲梁半径R、宽跨比等因素对曲线槽形梁力学特性的影响。该文解析法更好揭示了曲线槽形梁的力学特性以及各参数之间的内在关系,所得公式是对曲梁剪滞理论的发展。     

薄壁曲梁的横向弯曲稳定分析

根据势能驻值原理,从曲梁的变形几何方程出发,采用转换B3样条函数模拟薄壁杆件横截面的纵向位移场,得到含非线性应变的薄壁曲梁的能量方程,采用样条有限杆元法求解薄壁曲梁的横向弯曲稳定问题。方法很好地描述了薄壁曲梁的翘曲位移和剪滞效应,为分析薄壁曲梁弯扭问题提供了一种有效的方法。数值算例表明本方法的前处理简单、收敛速度快,精度高。     

自然弯扭梁的耦合振动分析

以空间曲梁理论为基础对具有一般横截面形状自然弯扭梁的耦合振动特性进行了研究,分析中包括了转动惯量、横向剪切变形以及和扭转有关的翘曲对振动的影响.通过对数学计算软件MATHEMATICA的精确运用可以得到该梁振型的解析表达式,精确的固有频率则可用搜索的方法来确定.为了证明理论的有效性,对两端固支椭圆截面曲梁的固有频率和振型进行了求解,并把数值计算结果同PATRAN梁单元的有限元结果进行了比较.     

冷弯薄壁卷边Z形钢梁的弹性畸变屈曲荷载

该文以既有理论研究成果为基础,结合应用广义梁理论,对两端简支的冷弯薄壁卷边Z形钢梁在绕截面强轴弯矩作用下的弹性畸变屈曲荷载进行了深入细致的分析。通过对45个截面的参数分析,将原先适用于冷弯薄壁卷边槽钢梁的参数计算公式推广应用于Z形钢梁,并根据Z形钢截面的几何特性对相应参数进行了重新推导和修改。利用以上结果,最后提出了冷弯薄壁卷边Z形钢梁在绕强轴弯矩作用下的弹性畸变屈曲荷载简化计算公式。简化公式具有足够的精度、便于手算、实用性强,可供工程设计人员和各国冷弯薄壁型钢设计规范修订相应内容时参考采用。     

曲梁缓冲器的大变形及变形能的椭圆函数解EI北大核心CSCD

金属曲梁结构在发生大变形情况下仍然具有良好的回弹性能,可以用作承受重复冲击系统的冲击能量吸收装置。针对由固支圆形曲梁组成的缓冲器,推导了基于半径和截面角的固支曲梁的大变形平衡方程。给出了端部压力及平板压力作用下曲梁的截面角、位形及变形能的Jacobi椭圆函数解,详细分析了简支圆形曲梁缓冲器的大变形特性及能量吸收特性。结果表明:曲梁缓冲器具有明显的非线性大变形特性和良好的缓冲吸能特性,其缓冲系数曲线有明显的极小值点;缓冲系数的极小值取决于曲梁材料、曲率半径及初始安装角度,与其数量无关。     

Exact static element stiffness matrices of non‐symmetric thin‐walled curved beams

An evaluation procedure of exact static stiffness matrices for curved beams with non‐symmetric thin‐walled cross section are rigorously presented for the static analysis. Higher‐order differential equations for a uniform curved beam element are first transformed into a set of the first‐order simultaneous ordinary differential equations by introducing 14 displacement parameters where displacement modes corresponding to zero eigenvalues are suitably taken into account. This numerical technique is then accomplished via a generalized linear eigenvalue problem with non‐symmetric matrices. Next, the displacement functions of displacement parameters are exactly calculated by determining general solutions of simultaneous non‐homogeneous differential equations. Finally an exact stiffness matrix is evaluated using force–deformation relationships. In order to demonstrate the validity and effectiveness of this method, displacements and normal stresses of cantilever thin‐walled curved beams subjected to tip loads are evaluated and compared with those by thin‐walled curved beam elements as well as shell elements. Copyright © 2004 John Wiley & Sons, Ltd.     

A one‐dimensional theory of thin‐walled curved rectangular box beams under torsion and out‐of‐plane bending

A new five degree‐of‐freedom one‐dimensional theory is proposed for the analysis of thin‐walled curved rectangular box beams subjected to torsion and out‐of‐plane bending. In addition to the usual three degrees of freedom used for solid curved beams, two additional degrees corresponding to warping and distortion are included in the present theory. The coupling between the deformations corresponding to five degrees of freedom due to the curvature of the beam is carefully treated in the present work. The superior behaviour of the present beam theory is verified through numerical examples. Copyright © 2001 John Wiley & Sons, Ltd.     

复合材料薄壁梁力学特性分析

综述了人们在建立研究复合材料薄壁梁力学特性的非线性梁理论及分析结构剖面特性,确立结构算子参数等方面所做的工作以及这些研究工作的特点。同时,结合作者的工作,介绍了近年来各国学者在复合材料薄壁梁力学特性研究上的进展。      

Topology optimization of thin‐walled box beam structures based on the higher‐order beam theory

The investigation aims to formulate ground‐structure based topology optimization approach by using a higher‐order beam theory suitable for thin‐walled box beam structures. While earlier studies use the Timoshenko or Euler beams to form a ground‐structure, they are not suitable for a structure consisting of thin‐walled closed beams. The higher‐order beam theory takes into an additional account sectional deformations of a thin‐walled box beam such as warping and distortion. Therefore, a method to connect ground beams at a joint and a technique to represent different joint connectivity states should be investigated for streamlined topology optimization. Several numerical case studies involving different loading and boundary conditions are considered to show the effectiveness of employing a higher‐order beam theory for the ground‐structure based topology optimization of thin‐walled box beam structures. Through the numerical results, this work shows significant difference between optimized beam layouts based on the Timoshenko beam theory and those based on a more accurate higher‐order beam theory for a structure consisting of thin‐walled box beams. Copyright © 2015 John Wiley & Sons, Ltd.     

One‐dimensional analysis of thin‐walled closed beams having general cross‐sections

This paper presents a new one‐dimensional theory for static and dynamic analysis of thin‐walled closed beams with general cross‐sections. Existing one‐dimensional approaches are useful only for beams with special cross‐sections. Coupled deformations of torsion, warping and distortion are considered in the present work and a new approach to determine sectional warping and distortion shapes is proposed. One‐dimensional C⁰ beam elements based on the present theory are employed for numerical analysis. The effectiveness of the present theory is demonstrated in the analysis of thin‐walled beams having pillar sections of automobiles and excavators. Copyright © 2000 John Wiley & Sons, Ltd.     

Study of warping torsion of thin‐walled beams with open cross‐section using macro‐elements

Thin‐walled beams with open cross‐section under torsion or complex load are studied based on the hypotheses of the classical theory (Vlasov). Different from previous techniques presented in the literature, the concept of a strip‐plate is introduced. This concept is used to accurately model the effect of bending induced by torsion and to define an alternate finite element called macro‐element. The macro‐elements are shown to model more accurately the thin‐walled beams under warping torsion or complex load therefore giving better results than the classical theory. Copyright © 1999 John Wiley & Sons, Ltd.     

Buckling of core wall structures coupled with connecting beams

A rational and accurate numerical analysis is presented for the buckling of core walls coupled with connecting beams by using spline finite member element method (SFMEM) in which the effects of torsion, warping and, especially, the shearing strains in the middle surface of the walls are taken into account. The core wall structure is discretized and modelled as an equivalent thin‐walled closed section, while the connecting beams between openings are replacement by an equivalent shear diaphragm of thickness. The numerical method combines the advantages of B₃‐spline, the finite member element method and Vlasov's thin‐walled bar theory. The simplicity and accuracy of the proposed scheme are demonstrated by a numerical example. Copyright © 2005 John Wiley & Sons, Ltd.     

A rational elasto‐plastic spatially curved thin‐walled beam element

Torsion is one of the primary actions in members curved in space, and so an accurate spatially curved‐beam element needs to be able to predict the elasto‐plastic torsional behaviour of such members correctly. However, there are two major difficulties in most existing finite thin‐walled beam elements, such as in ABAQUS and ANSYS, which may lead to incorrect predictions of the elasto‐plastic behaviour of members curved in space. Firstly, the integration sample point scheme cannot capture the shear strain and stress information resulting from uniform torsion. Secondly, the higher‐order twists are ignored which leads to loss of the significant effects of Wagner moments on the large twist torsional behaviour. In addition, the initial geometric imperfections and residual stresses are significant for the elasto‐plastic behaviour of members curved in space. Many existing finite thin‐walled beam element models do not provide facilities to deal with initial geometric imperfections. Although ABAQUS and ANSYS have facilities for the input of residual stresses as initial stresses, they cannot describe the complicated distribution patterns of residual stresses in thin‐walled members. Furthermore, external loads and elastic restraints may be applied remote from shear centres or centroids. The effects of the load (and restraint) positions are important, but are not considered in many beam elements. This paper presents an elasto‐plastic spatially curved element with arbitrary thin‐walled cross‐sections that can correctly capture the uniform shear strain and stress information for integration, and includes initial geometric imperfections, residual stresses and the effects of the load and restraint positions. The element also includes elastic restraints and supports, which have to be modelled separately as spring elements in some other finite thin‐walled beam elements. Comparisons with existing experimental and analytical results show that the elasto‐plastic spatially curved‐beam element is accurate and efficient. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Higher‐order beam analysis of box beams connected at angled joints subject to out‐of‐plane bending and torsion

The difficulty in the analysis of thin‐walled beams by a beam theory comes from slowly decaying end effects associated with warping and distortion. However, a beam theory without considering such effects yields inaccurate solutions especially near beam ends. Numerical analysis using a higher‐order beam theory capable of representing such effects is now available, but the analysis of a series of box beams connected by angled joints still remains an unsolved problem because of the lack of a matching condition at the joint. The objectives of this investigation are to develop a field‐variable‐matching technique at an angled joint through a higher‐order beam theory and to implement it in the finite element formulation. Thin‐walled box beams in consideration are assumed to be subject to out‐of‐plane bending and torsion. Thus, the minimization of three‐dimensional displacement mismatch is used to relate the field variables at a joint intersection. The minimization condition turns out to represent coupling effects of different deformation kinematics such as torsion, bending, distortion and warping. Point‐wise displacement matching is not possible with a higher‐order beam theory. The validity of the proposed technique was verified by a finite element analysis using two‐node higher‐order beam elements applied to some benchmark problems. Copyright © 2008 John Wiley & Sons, Ltd.