THE COMPUTATIONAL METHOD FOR STABILITY OF TRUSSES WITH SMALL DEFORMATION

基于桁架结构稳定性计算的经典理论,分析了利用特征值理论开展桁架结构屈曲分析的计算方法,以及利用欧拉临界载荷屈曲理论,采取杆件撤除的静力求解确定桁架结构稳定临界载荷的计算方法. 通过理论研究和相关算例分析,论证了利用特征值理论和临界载荷屈曲理论相结合的方法,判断小变形桁架结构的失稳模态,求解桁架结构稳定临界载荷的确定性.     

井筒内受压杆管后屈曲能量法分析与实验研究

目前不少理论力学教材都涉及刚体平面运动动力学方程的教学内容,但有些教材在叙述上有许多值得商榷之处.对这一重要的基本概念,本文提出作者的思考,供理论力学教学的教师与学过此内容的学生讨论.     

Tensile and compressive buckling of plates weakened by cracks

Plates are susceptible to buckling under compression when the thickness dimension becomes sufficiently small. Such mode of structure failure can prevail even if the plates were extended in tension. Wribkling of stretched thin sheets is a commonly observed phenomenon that leads to complex deflection patterns, particularly in regions close to crack-like imperfections. Predictions of the buckled displacement modes for plates weakened by cracks will be made on the basis of a theory formulated by application of variational calculus. Finite element method is used such that defects of other shapes can also be analyzed. Various buckled displacement modes of a center-cracked plate are determined and displayed graphically. The critical buckling loads are found to decrease with increasing crack size. Moreover, local wrinkling of the plate surface becomes less pronounced for the higher buckling modes. The method of solution applies equally well to plates that are initially curved.     

条带式太阳帆的结构动力学分析

依靠光压推进,太阳帆被认为是最可行的星际探测航天器,太阳帆结构总体方案主要有两类:桅杆式和旋转式,其中,帆膜被分割成窄条的条带式太阳帆在桅杆式太阳帆中具有较为理想的结构效率,如何准确计算条带式太阳帆的结构动力学特性值得研究.本文对条带式太阳帆结构的振动特性和结构稳定性进行研究,将太阳帆看作是由若干个桅杆-膜带组件依次连接而成的整体结构,桅杆-膜带组件由4根桅杆段和4条薄膜条带组成,分段轴压作用下的桅杆与薄膜条带耦合振动.考虑帆面薄膜条带与支撑桅杆之间的耦合振动,采用分布传递函数法建立了的条带式太阳帆的结构动力学模型,推导了条带式太阳帆结构自由振动和失稳载荷的求解方法.研究表明:条带式太阳帆构型有利于提高太阳帆结构的整体刚度和结构稳定性,随着帆面薄膜条带数目的增加,太阳帆结构的振动频率和失稳载荷增大;随着帆面薄膜预应力的增大,太阳帆结构振动的基频减小,稳定性变差;随着支撑桅杆刚度的提高,太阳帆结构整体的振动频率和失稳载荷增大.本文建立的解析求解方法具有求解效率快和精度高的特点,为条带式太阳帆的结构设计和姿态控制提供了有力的分析工具.      

A dynamic method for measuring the critical loads of elastic flat plates

A dynamic method is described for determining the linear buckling loads of elastic, perfectly flat, rectangular plates. The proposed method does not require the application of in-plane loads; it requires only vibrational excitation of the plate. The buckling load is determined from the measured normal modes of vibration. The method is applicable to isotropic as well as anisotropic plates with any type of edge support. The accuracy of the dynamic method was evaluated by tests in which buckling loads of aluminum and graphite fiber-reinforced-epoxy composite plates were determined both by the dynamic method and by imposing static in-plane loads on the plates. The results of the dynamic and static tests agree closely. A. Segall (on leave from RAFAEL, Israel)     

夹层梁总体屈曲及皱曲的有限元计算

皱曲是夹层结构的一种短波屈曲模式,通常发生于夹心较厚或夹心刚度较低的情况。由于模型规模的限制,在常规有限元建模时通常将夹层板模拟为二维板单元,这种方法忽略了面板和夹心在厚度方向上的相互作用,无法计算出皱曲模式。针对上述问题,本文首先介绍了一个计算夹层结构总体屈曲和皱曲的统一理论,并将此理论的计算结果作为理论解。为了同时...     

THE TRANSVERSE NONLINEAR FREE VIBRATION AND THE BUCKLING OF A COMPRESSIVE BAR ON AN ELASTIC FOUNDATION

基于Hamilton 原理,运用假设时间模态法,得到了弹性基础上压杆的横向非线性自由振动与屈曲的位移型常微分控制方程. 考虑一端固定另一端可移简支边界条件,采用打靶法得到了结构第一至第三阶结构频率与一阶屈曲载荷的数值结果. 结果表明：随轴心压力增加,结构频率减小;随弹性基础刚度增加,结构频率与屈曲载荷均增加;弹性基础刚度对结构频率的影响随振型阶数增加在减小;在小振幅的情形下,不同振型对一阶屈曲载荷的影响很小.     

Studies of nonlinear deformation and stability of noncircular cylindrical shells in transverse bending

The variational finite element method in displacements is used to solve the problem of geometrically nonlinear deformation and stability of cylindrical shells with a noncircular contour of the cross-section. Quadrangle finite elements of shells of natural curvature are used. In the approximations of element displacements, the displacements of elements as solids are explicitly separated. The variational Lagrange principle is used to obtain a nonlinear system of algebraic equations for the unknown nodal finite elements. The system is solved by the method of successive loadings and by the Newton-Kantorovich linearization method. The linear system is solved by the Crout method. The critical loads are determined in the process of solving the nonlinear problem by using the Sylvester stability criterion. An algorithm and a computer program are developed to study the problem numerically. The nonlinear deformation and stability of shells with oval and elliptic cross-sections are investigated in a broad range of variation of the elongation and ellipticity parameters. The shell critical loads and buckling modes are determined. The influence of the deformation nonlinearity, elongation, and ellipticity of the shell on the critical loads is examined.     

局部径向载荷作用下外压薄壁圆筒稳定性分析

为简化真空塔器外挂件支撑区局部失稳分析,提炼出局部径向载荷作用下外压薄壁圆筒稳定性计算模型. 以易拉罐为薄壁圆筒试件,对不同外压下试件的局部径向临界载荷进行了测试. 利用有限元法对各实验模型进行了特征值屈曲分析,结果与实验数据能较好地吻合. 采用正交设计及参数化计算,得到了各结构参数及外压下的局部径向临界载荷经验公式. 实例计算表明,所得经验公式稍有保守,可用于真空塔器外挂件支撑件区的局部稳定性分析.     

GPU-BASED DISCRETE ELEMENT MODELLING OF INTERACTION BETWEEN SEA ICE AND JACK-UP PLATFORM STRUCTURE

在海冰与自升式海洋平台结构的相互作用过程中,冰载荷是影响平台结构振动响应和疲劳寿命的重要因素. 采用具有粘接-破碎效应的离散元模型,可对海冰与自升式海洋平台结构作用中的海冰破碎特征及相应冰载荷进行数值分析. 针对自升式海洋平台的多桩腿结构特性及其冰载荷离散元分析的大规模计算需求,建立了基于GPU 的并行算法并开发了相应的计算程序. 为实现离散元分析的高效计算,采用网格排序方法创建单元邻居列表,以快速确定海冰单元间及其与平台结构间的接触模式和作用力. 此外,还发展了球体单元与圆柱形结构在不同接触形式下的计算模型. 为检验该离散元模型的有效性,对渤海锥体海洋平台结构的作用过程进行了计算,并与现场实测冰力数据进行了对比验证. 在此基础上对多桩腿自升式平台结构的冰载荷进行了离散元分析,获得了海冰的破坏特性,确定了不同桩腿上的冰力时程. 该模型可进一步应用于不同类型海洋结构的冰载荷分析,为冰区海洋平台的结构设计和现役平台结构的疲劳分析提供参考依据.     

NODAL DISPLACEMENT ACCURACY OF ONE-DIMENSIONAL FINITE ELEMENTS

研究高次杆单元和梁单元的节点位移精度问题.首先求出一端固支均匀杆和悬臂梁在任意次多项式形式分布载荷作用下的位移精确解,然后用二次杆单元、五次欧拉梁单元和三次铁木辛柯梁单元求得了节点位移.通过比较有限元解与精确解以及利用静力凝聚方法,发现一次以上杆单元、三次以上欧拉梁单元以及三次以上铁木辛柯梁单元都可以给出精确的端点位移.     

基于弧长法的受压球壳稳定性分析

对受压球壳进行特征值屈曲分析,得到了前6阶屈曲模态及线性屈曲临界载荷;采用弧长法进行非线性有限元分析,对理想球壳施加初始扰动,通过2次扰动值折半的方法求得引起结构屈曲的最小扰动值,追踪到了屈曲分支点和全过程载荷-位移路线。基于前6阶屈曲模态位移,在受压球壳中分别引入2.5mm和1mm两种缺陷值,分析缺陷对球壳屈曲特性的影响。结果表明:取壳厚的0.5%即0.05mm时,得最小扰动值,近似模型与完善结构极值载荷的差值为0.93%;球壳是缺陷敏感性结构,缺陷的幅值和分布都对其极限载荷有影响,缺陷幅值与厚度比为0.1时,缺陷球壳承载力相对理想结构下降了约11%,缺陷幅值与厚度比为0.25时,承载力相对下降了约30%,说明提高球壳稳定性需要提高球壳加工精度。     

Torsional buckling of spherical shells under circumferential shear loads

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光滑节点插值法:计算固有频率下界值的新方法

将光滑节点插值法用于悬臂梁的静力学,并首次用于旋转柔性梁的频率分析. 采用梯度光滑技术,用线性插值形函数描述梁的位移场,求解4 阶微分方程. 在静力学分析中,将该方法所得梁中各点位移与假设模态法、有限元法及解析解的结果对比,可知该方法虽用简单的线性插值形函数描述梁的位移场,但精度却很高. 进一步研究表明,采用模态高于9 阶的假设模态法会使刚度阵条件数变差,导致结果发散. 在频率分析中,与有限元法、假设模态法和解析解对比,表明该方法一个重要特性:能提供固有频率的下界值,而有限元法和假设模态法只能提供固有频率的上界值,说明该方法结合有限元法在处理无解析解的问题时可以从上下界最大程度的逼近真实解,提高精度. 光滑节点插值法具有形函数结构简单、独立变量少且能提供固有频率下界值的特性,因此,具有较高的推广及应用价值.      

STUDY ON AMPLIFICATION FACTOR OF FLEXURAL BUCKLING CRITICAL LOAD OF AXIAL COMPRESSION BARS1)

为了建立一般条件下轴压构件屈曲临界载荷的计算理论,首先对轴心受压构件发生屈曲时的总势能方程进行了推导,然后采用Rayleigh-Ritz法并基于势能驻值原理得到了4种不同端部约束条件下轴压构件的屈曲临界载荷,对比欧拉临界载荷,给出了临界载荷放大系数 的计算式,全面考虑了构件长细比、压缩变形、剪切变形以及截面形状系数对临界载荷的影响,推导的计算式可用于较小长细比轴压构件发生屈曲时临界载荷的计算.圆截面和双轴对称工字形截面轴压构件屈曲临界载荷的分析表明构件长细比是影响放大系数的主导因素。     

复合材料多墙盒段弯扭耦合下的屈曲和后屈曲

针对复合材料典型多墙盒段，采用试验和有限元分析相结合的方法，研究了弯扭耦合载荷作用下的稳定性、承载能力及损伤起始、扩展情况．试验采用数字图像相关(Digital Image Correlation, DIC)测量方法捕捉试验件屈曲模态的变化过程，通过载荷-应变曲线获得屈曲和后屈曲破坏载荷．数值仿真基于ABAQUS/Explicit模块，采用Hashin准则结合刚度降的VUSDFLD子程序模拟复合材料的屈曲和后屈曲行为．研究结果表明，多墙盒段在弯扭载荷组合作用下发生屈曲时，扭矩会改变屈曲模态的分布形式和对称性，屈曲鼓包依然保持波峰、波谷交替出现；多墙盒段后屈曲阶段历程较长，屈曲模态由一阶向高阶逐渐发展，直到结构发生过大变形，彻底破坏而失去承载能力．     

薄壁加筋肋圆柱壳稳定性分析的参数化研究

针对在轴向载荷作用下的正置、正交网格形式的薄壁加筋肋圆柱壳结构，利用有限元程序，对薄壁加筋肋圆柱壳稳定性分析进行了参数化研究，得到了进行结构优化设计的准则，对于给定的设计载荷，当结构参数位于某一个局部失稳与整体失稳的临界区域时，结构的重量最轻。提出了基于有限元分析进行结构优化设计的策略，利用优化策略，获得了一薄壁加筋肋圆柱壳结构的优化设计结果，同时给出了粘合刚度简化模型与有限元计算结果的比较。     

Secondary buckling of a flat plate under uniaxial compression: Part 2. Analysis of clamped plate by F.E.M. and comparison with experiments

In Part 1, a theoretical analysis was used to study the secondary buckling of a simply supported plate. In Part 2, a clamped plate is analysed by the finite element method. The stability criterion for a non-linear post-buckling equilibrium state is evaluated by the sign of the determinant of the stiffness matrix. It should be noted that the secondary buckling loads of clamped plates are unexpectedly smaller than those of simply supported plates and are only one and a half times the primary buckling loads. In previous analyses, only a quarter segment of the plate was considered by assuming a stable equilibrium state with symmetrical mode. However, instability can also be predicted by considering the unsymmetrical mode over the whole plate. Results of experimental analysis of secondary instability of clamped square plates under uniaxial compression agreed with the numerical results.     

Non-linear in-plane buckling of rotationally restrained shallow arches under a central concentrated load

This paper investigates the non-linear in-plane buckling of pin-ended shallow circular arches with elastic end rotational restraints under a central concentrated load. A virtual work method is used to establish both the non-linear equilibrium equations and the buckling equilibrium equations. Analytical solutions for the non-linear in-plane symmetric snap-through and antisymmetric bifurcation buckling loads are obtained. It is found that the effects of the stiffness of the end rotational restraints on the buckling loads, and on the buckling and postbuckling behaviour of arches, are significant. The buckling loads increase with an increase of the stiffness of the rotational restraints. The values of the arch slenderness that delineate its snap-through and bifurcation buckling modes, and that define the conditions of buckling and of no buckling for the arch, increase with an increase of the stiffness of the rotational end restraints.     

Exact solution and stability of postbuckling configurations of beams

We present an exact solution for the postbuckling configurations of beams with fixed–fixed, fixed–hinged, and hinged–hinged boundary conditions. We take into account the geometric nonlinearity arising from midplane stretching, and as a result, the governing equation exhibits a cubic nonlinearity. We solve the nonlinear buckling problem and obtain a closed-form solution for the postbuckling configurations in terms of the applied axial load. The critical buckling loads and their associated mode shapes, which are the only outcome of solving the linear buckling problem, are obtained as a byproduct. We investigate the dynamic stability of the obtained postbuckling configurations and find out that the first buckled shape is a stable equilibrium position for all boundary conditions. However, we find out that buckled configurations beyond the first buckling mode are unstable equilibrium positions. We present the natural frequencies of the lowest vibration modes around each of the first three buckled configurations. The results show that many internal resonances might be activated among the vibration modes around the same as well as different buckled configurations. We present preliminary results of the dynamic response of a fixed–fixed beam in the case of a one-to-one internal resonance between the first vibration mode around the first buckled configuration and the first vibration mode around the second buckled configuration.