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。     

单轴对称截面圆弧拱平面外稳定性研究

根据变分原理推导了任意开口薄壁截面曲梁的稳定平衡方程。单轴对称截面圆弧拱在均布径向荷载(均匀受压)或两端作用大小相等、方向相反的端弯矩(均匀弯曲)作用下,平衡方程中曲率平面内的变形和曲率平面外的变形相互独立,故要么发生曲率平面内弯曲失稳,要么发生曲率平面外的弯扭失稳。给出单轴对称截面圆弧拱在这两种受力情况下平面外屈曲荷载的理论解答。通过一些无碍结果的近似使所得公式形式简洁,便于在工程中应用。最后给出了计算实例,与已有的文献进行比较,并使用通用有限元软件ANSYS 进行了模拟,分析结果与该文计算结果吻合,证明了所得公式的正确性。     

Timoshenko薄壁梁弯扭耦合振动的动态传递矩阵法

通过直接求解单对称均匀Timoshenko薄壁梁单元弯扭耦合振动的运动偏微分方程,导出了其自由振动时的动态传递矩阵,同时采用结合频率扫描法的二分法求解频率特征方程,并讨论了剪切变形和转动惯量对弯扭耦合Timoshenko薄壁梁的固有频率的影响.数值结果验证了本文方法在其适用范围内的精确性和有效性.     

Timoshenko薄壁湾弯扭耦合振动的动态传递矩阵法

通过直接求解单对称均匀Timoshenko薄壁梁单元弯扭耦合振动的运动偏微分方程,导出了其自由振动时的动态传递矩阵,同时采用结合频率扫描法的二分法求解频率特征方程,并讨论了剪切变形和转动惯量对弯扭耦合Timoshenko薄壁梁的固有频率的影响。数值结果验证了本文方法在其适用范围内的精确性和有效性。     

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。     

《薄壁Timoshenko梁弯扭耦合振动的动态有限元法》

通过直接求解单对称均匀薄壁Timoshenko梁单元弯扭耦合振动的运动微分方程,推导了其精确的动态刚度矩阵。在本文研究中考虑了弯扭耦合、翘曲刚度、转动惯量和剪切变形的影响。针对某弯扭耦合的薄壁梁算例,应用本文推导的动态刚度矩阵,采用自动Muller法和结合频率扫描法的二分法求解频率特征方程,计算了该薄壁梁的固有特性,并讨论了翘曲刚度、剪切变形和转动惯量对该弯扭耦合薄壁梁的固有频率和模态形状的影响。数值结果验证了本文方法的精确性和有效性,并指出随着模态阶次的增加,剪切变形、转动惯量和翘曲刚度对薄壁梁的固有特性的影响更加显著。     

折线形开口薄壁截面圆弧曲梁弯扭理论

现有薄壁曲梁弯扭理论缺乏严密的理论推导。本文基于薄壁构件理论的两个基本假设，精确地导出了任意折线形开口薄壁截面圆弧曲梁的翘曲位移、正应力、剪应力及其各自合力的精确表示式。为便于应用，本文也给出了槽形截面（分槽口向里和向外）曲梁和Π形截面曲梁的简化公式     

双轴对称固支圆弧拱弯扭屈曲荷载的理论解

在给出的考虑几何非线性情况下的弹性曲梁总势能的基础上,采用里兹法导出了固支圆弧拱在均匀受压和均匀受弯作用下的弯扭屈曲荷载的理论解,推导中考虑了翘曲刚度的影响。固支圆弧拱在径向均布荷载作用下,屈曲荷载随着拱圆心角的增大而逐渐减小,和简支拱不同,当圆心角为180°时,屈曲荷载并不为零。在正弯矩或负弯矩作用下,固支圆弧拱的屈曲荷载都随着拱圆心角的增大而逐渐增大。该文给出了计算实例,并与其他研究者的结果进行了比较,证明了所得公式的正确性。     

冷弯薄壁卷边槽钢梁的弹性畸变屈曲荷载简化计算公式

以既有理论研究成果为基础,结合应用广义梁理论,对冷弯薄壁卷边槽钢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。首先基于45个截面冷弯薄壁卷边槽钢梁畸变屈曲荷载的参数分析,提出了屈曲临界半波长度的近似计算公式;接着对腹板提供给翼缘板的转动约束刚度进行了分析,提出了精度较高的线性近似计算公式;依据畸变屈曲特征方程,提出了考虑翼缘自身剪切与畸变影响的修正参数的近似计算公式;利用以上结果,最后提出了冷弯薄壁卷边槽钢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。     

双轴对称固支圆弧拱弯扭屈曲何载的理论解

在给出的考虑几何非线性情况下的弹性曲梁总势能的基础上,采用里兹法导出了固支圆弧拱在均匀受压和均匀受弯作用下的弯扭屈曲荷载的理论解,推导中考虑了翘曲刚度的影响.固支圆弧拱在径向均布荷载作用下,屈曲荷载随着拱圆心角的增大而逐渐减小,和简支拱不同,当圆心角为180.时,屈曲荷载并不为零.在正弯矩或负弯矩作用下,固支圆弧拱的屈曲荷载都随着拱圆心角的增大而逐渐增大.该文给出了计算实例,并与其他研究者的结果进行了比较,证明了所得公式的正确性.     

Buckling dynamics of imperfect Elastica subject to various loading conditions

Buckling dynamics of a pinned-pinned flexible imperfect beam attached to a sliding mass is investigated using nonlinear Elastica theory. Initially straight flexible buckling beam having pinned end boundary conditions loaded at one of its end with curved imperfection is considered. Large deflection analysis of flexible beam is studied using nonlinear Elastica theory. Imperfection analysis of the flexible beam is investigated considering the imperfection as an initial curvature. The governing differential equations are expressed in terms of nonlinear functions that are typical of flexible beams, generally leading to highly implicit relationships involving elliptic integrals and functions. Dynamic simulation of the flexible beam is studied using numerical simulation procedures with various types of loading (step, ramp, and sinusoidal) assuming this member buckles in its first mode. Dynamic response of the imperfect buckling Elastica has been obtained by using numerical Runge-Kutta methods. Load deflection characteristics of flexible beams are presented in polynomial curve fits. The polynomial curve fits obtained from nonlinear inextensible exact beam theory may then be used as the nonlinear lumped system stiffness. The buckling Elastica may find applications in compliant mechanism design. The motivation behind this research is not only to present the dynamic behavior of the buckling beam considering the magnitude of the imperfection but also to provide a tool to design new types of compliant mechanisms. Original compliant mechanism designs are presented demonstrating where the buckling dynamics of imperfect Elastica or flexible curved beams might be needed in mechanism design and synthesis.     

A spatially curved‐beam element with warping and Wagner effects

This paper presents a new spatially curved‐beam element with warping and Wagner effects that can be used for the non‐linear large displacement analysis of members that are curved in space. The non‐linear behaviour of members curved in space shows that the Wagner effects are substantial in the large twist rotation analysis. Most existing finite beam element models, such as ABAQUS and ANSYS cannot predict the non‐linear large displacement response of members curved in space correctly because the Wagner effects, viz. the Wagner moment and the corresponding finite strain terms, have not been considered in these finite beam elements. As a consequence, these finite beam elements do not provide correct predictions for the out‐of‐plane buckling and postbuckling behaviour of arches as well. In this paper, the symmetric tangent stiffness matrix has been derived based on the finite rotations parameterized by the conventional displacements. The warping and Wagner effects: both the Wagner moment and the corresponding finite strain terms and their constitutive relationship, are included in the spatially curved‐beam element. Two components of the initial curvature, the initial twist and their interactions with the displacements are also considered in the spatially curved‐beam element. This ensures that the large twist rotation analysis for the members curved in space is accurate. Comparisons with existing experimental, analytical and numerical results show that the spatially curved‐beam element is accurate and efficient for the non‐linear elastic analysis of curved members, buckling and postbuckling analysis of arches, and in its ability to predict large deflections and twist rotations in more arbitrarily curved members. Copyright © 2005 John Wiley & Sons, Ltd.     

BUCKLING AND INITIAL POST-BUCKLING OF THIN-WALLED COMPOSITE BEAMS

ABSTRACT

The buckling and initial post-buckling behaviour of thin-walled composite beams is analysed in this paper. The governing equations are based on the main assumption that the displacement components in the plane perpendicular to the axial direction are of the type of rigid-body motion. The shear strain in the middle surface of the beam wall is taken into account as the shear stiffness of the composite material is low. The governing equations are solved by a perturbation method. For the case of simply supported ends, double Fourier series are used to solve the equations for perturbation terms of different orders. Then, some formulas derived by Budiansky in the notation of functional analysis are cited to calculate the initial post-buckling parameters. The experimental results of five specimens of circular open cross-section are compared with the numerical results.     

An improved model for naturally curved and twisted composite beams with closed thin-walled sections

This paper presents an improved model for naturally curved and twisted anisotropic beams with closed thin-walled cross-sections. By introducing eigenwarping functions and expanding axial displacements in series of eigenwarpings, the differential equation involving the generalized warping coordinate and the expression for eigenvalues can be derived using the principle of minimum potential energy. In the model the effects of some factors such as the initial curvature, torsion of the beams as well as torsion-related warping, transverse shear deformations and elastic coupling are incorporated. As an application, the present model is adopted to do an analysis for closed thin-walled composite box beams. Comparison with the existing experimental observation and numerical results shows that the proposed model is valid for analyzing such naturally curved and twisted beams.     

含裂纹损伤圆弧曲梁弹性屈曲的有限元网格自适应分析

该文建立圆弧形曲梁裂纹的截面损伤缺陷比拟方案,实现裂纹大小(深度)、位置、数目的模拟.引入变截面Euler-Bernoulli梁的h型有限元网格自适应分析方法,求解含裂纹损伤圆弧曲梁弹性屈曲问题,得到优化的网格和满足预设误差限的高精度屈曲荷载和屈曲模态解答.数值算例表明该算法中网格非均匀加密可适应裂纹损伤引起的屈曲模态...