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。     

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。     

扭转作用下有缺陷柱形壳的屈曲和后屈曲性能

分析扭转作用下有缺陷柱形壳的屈曲和后屈曲性能。基于Karman-Donnell-Type非线性微分方程建立计算公式,采用壳屈曲的边界层理论进行分析,以获得能严格满足边界条件的解决方案。采用奇摄动技术,以确定屈曲载荷和后屈曲平衡路径。数值结果显示,目前的理论能对柱形壳的后屈曲性能进行较好评估。同时分析了几何参数对柱形壳的屈曲和后屈曲性能的影响。证实了扭转作用下柱形壳的后屈曲平衡路径并不稳定,并且相对更短的壳体具有更高的后屈曲平衡能力。最后,指出初始缺陷对柱形壳屈曲和后屈曲性能的影响。对具有初始横向挠曲的有缺陷壳体的分析结果显示：即便是非常小的缺陷,也确实会减少屈曲承载力,并使得后屈曲稳定性变差。扭转作用下柱形壳的屈曲和后屈曲性能显示出明显的缺陷敏感性。此外,如果缺陷更大,那么带来的影响也随之会变得更大。     

轴向冲击下柱形壳局部和整体动力屈曲

对轴向受压冲击荷载下,柱形壳局部和整体屈曲进行研究。引进哈密尔顿系统,通过哈密尔顿二元方程,采用4对对偶变量,对系统中的基础问题进行数学描述,并归纳为临界荷载的特征值和特征解问题。通过各自的阶数对屈曲模式进行描述,将其分为两类:短波或局部屈曲以及长波或整体屈曲,得到解析与数值的解决方案并给出了一些规则。     

面内受压大跨度混凝土板自由振动

文章基于经典薄板理论,利用Hamilton原理推导面内受压大跨度混凝土板自由振动的控制微分方程并进行无量纲化。采用一种半解析方法—微分变换法(DTM)将无量纲控制微分方程及边界条件变换为等价的代数方程,得到含有无量纲固有频率和屈曲载荷的特征方程。数值给出了不同边界条件下无量纲压力强度、载荷参数、长宽比对大跨度混凝土板无量纲固有频率的影响,可为大跨度混凝土板设计提供及现场施工提供参考。     

基于Koiter理论的板片空间结构缺陷敏感性研究

目前对板片空间结构缺陷的研究主要集中在数值分析方面,尝试基于Koiter理论进行近似解析方法的研究。通过把板片空间结构的网架或网壳部分连续化为板或壳,将板片空间结构简化为双层板或双层壳。再分别对完善的双层板和双层壳进行大挠度方程求解,研究完善结构的初始后屈曲性能。在求解大挠度方程时,省略了边界条件中的耦合项,从而能够应用伽辽金法求解。最后基于Koiter理论,得出板型板片空间结构对缺陷不敏感,而扁壳型板片空间结构对缺陷敏感的结论。     

薄壁组合箱梁的自由振动

研究薄壁叠加组合梁的自由振动。建立了适用于薄壁组合箱梁截面动力性能的一般分析模型。该模型基于古典叠加理论，考虑任意层压板叠合次序情况下弯曲和扭转的耦合，也就是非对称和对称以及各种边界条件。对薄壁组合梁，建立基于位移的一维有限元模型以预测自振频率和相应的振型，并由Hamilton原理派生出运动方程；考虑薄壁组合梁纤维角度、模数比、振动频率的边界条件以及组合形式的影响，得出计算结果。     

轴压组合叠合梁自由振动的动态刚度分析

采用动态刚度分析方法,对自由振动和轴压组合叠合梁的屈曲性能进行研究。在公式中考虑了轴力、泊松效应、轴向变形、剪切变形和转动惯量的影响。通过直接求解轴压组合叠合梁自由振动的控制微分方程,建立严格的动态刚度矩阵,并用该矩阵对已有文献中其他组合梁进行计算比较,证明了动态刚度矩阵的适应性。同时,论证了轴力和边界条件对自然频率、屈曲荷载和叠合梁模式的影响。     

开孔冷弯型钢柱的试验研究

分析研究了开孔冷弯型钢柱的弹性屈曲和试验响应间的关系。对24个腹板开孔和不开孔的短柱和柱进行了压力试验。利用壳单元建模,对每一个构件都进行了有限元屈曲分析,从而可以获取边界条件、局部开孔、扭曲和整体弹性屈曲反应对构件的影响。腹板上的开孔,可能影响构件局部和扭转屈曲的半波长度,同时可能会导致临界弹性屈曲荷载的改变。从试验结果分析可知,尽管在某些试验中出现了延性下降等现象,但总体而言,腹板开孔对试验构件的极限强度影响很小;同时发现,在局部和扭转屈曲中,弹性屈曲也与荷载-位移曲线有关。试验中对柱子采用摩擦轴承的边界条件,其中柱端磨平且直接由钢板传力。尽管构件的延性等问题还需要更进一步研究,但这种边界条件对于评估短柱和普通柱屈曲性能是有效的,而且还可以缩短试验构件的准备时间。     

中厚功能梯度环扇形板的热屈曲分析

对中厚功能梯度环扇形板进行热屈曲分析。利用一阶剪切变形板理论推导出平衡及稳定方程。这些方程为5次耦合偏微分方程。经过分析,可简化为4次方程。在已知边界条件下求解,得出屈曲临界温度。环扇形板为径向简支,环向自由。研究了在均匀与沿厚度梯度升温两种热荷载作用下,功能梯度环扇形板的热屈曲分析。详细讨论了边界条件、幂律指数、板厚、环形和扇形角对功能梯度环扇形板屈曲临界温度的影响。     

Dynamic torsional buckling of cylindrical shells in Hamiltonian system

By considering the effect of stress waves in a Hamiltonian system, this paper treats dynamic buckling of an elastic cylindrical shell which is subjected to an impact torsional load. A symplectic analytical approach is employed to convert the fundamental equations to the Hamiltonian canonical equations in dual variables. In a symplectic space, the critical torsion and buckling mode are reduced to solving the symplectic eigenvalue and eigensolution, respectively. The primary influence factors, such as the impact time, boundary conditions and thickness, are discussed in detail through some numerical examples. It is found that boundary conditions have limited influence except free boundary condition in the context of the scope in this paper. The localization of dynamic buckling patterns can be observed at the free end of the shell. The new analytical and numerical results serve as guidelines for safer designs of shell structures.     

Critical state of an axially compressed cylindrical panel with three edges simply supported and one edge free

The subject of the paper is a circular cylindrical panel with three edges simply supported and one edge free. The structure is axially compressed by a load uniformly distributed at both ends. The system of stability equations of shallow cylindrical shell was solved, assuming the deflection function and the force function—the Airy function which were formulated with respect to the boundary conditions. The system of stability equations was reduced to one regular differential equation of eighth degree. The results of numerical investigations (FEM) and buckling models are presented in the figures. The results of analytical and numerical investigation are compared in the paper.     

Dynamic effects on buckling and energy absorption of cylindrical shells under axial impact

The crushing behaviour of aluminium and steel cylindrical shells, when subjected to an axial impact, is examined using a numerical simulation. The influence of the material properties, shell geometry, boundary conditions and loading techniques on the energy absorbed and the buckling shapes is explored. Various shell response characteristics, such as the peak load, fold lengths, axial compression and energy absorption are studied. An examination is also made of the influence of filtering on the accuracy of data obtained usually in dynamic tests.     

Benchmark symplectic solutions for bending of corner-supported rectangular thin plates

This work presents the first ever analytical solutions for bending of a rectangular, thin plate supported only at its four corners. This breakthrough analysis employs a new symplectic elasticity approach that extends beyond the limitation of the classical plate bending methods such as Timoshenko's method, Navier method, Levy method and the polynomial approximation analysis of Lee and Ballesteros (Int J Mech Sci 1960;2:206). The classical methods are, in fact, special cases of this symplectic approach in the real eigenvalue regime for wavenumber with at least one pair of opposite sides of plates simply supported. For plate problems that do not fall into this category, the classical methods fail to yield any analytical solutions, but the symplectic approach does because in these cases the plate bending problems enter the complex eigenvalue regime for wavenumber. Another distinctive feature of this new approach is its necessity to pose an eigenvalue problem even for plate bending. In short, this innovative approach establishes the relationship between eigenvalue problem and bending. The novelty of this approach lies in the use of the Hamiltonian principle in a symplectic geometry space to derive a Hamiltonian system and a full state vector. The free boundaries with corner supports are dealt with using the variational principle. Analytical bending modes are then derived by expansion of eigenfunctions. The solutions are compared with other known (approximate) results and numerical finite element solutions but some of the results are not in agreement. Because the analytical bending moment and shear force solutions thus derived fulfill all natural and geometric boundary conditions, it leaves ample room for authentication of the benchmarks in the future. In addition, the twisting moment at the corners satisfies the condition for static bending equilibrium, in which the finite element solutions fail.     

网格圆柱扁壳的稳定性

本文用将网格壳转化为连续壳的方法建立了网格圆柱扁亮屋盖的稳定平衡微分方程,所得的方程是属于异性圆柱扁壳的方程,并用方法求得简支边界条件的网格圆柱扁壳的临界荷载计算公式。     

Buckling of intermediate ring supported cylindrical shells under axial compression

This paper is concerned with the elastic buckling of axially compressed, circular cylindrical shells with intermediate ring supports. The simple Timoshenko thin shell theory and the more sophisticated Flügge thin shell theory have been adopted in the modeling of the cylindrical shells. We used these two representative theories to examine the sensitivity of the buckling solutions to the different degree of approximations made in shell theories. By dividing the shell into segments at the locations of the ring supports, the state-space technique is employed to derive the solutions for each shell segment and the domain decomposition method utilized to impose the equilibrium and compatibility conditions at the interfaces of the shell segments. First-known exact buckling factors are obtained for cylindrical shells of one and multiple intermediate ring supports and various combinations of boundary conditions. Comparison studies are carried out against benchmark solutions and independent numerical results from ANSYS and p-Ritz analyses. The influence of the locations of the ring supports on the buckling behaviour of the shells is examined.     

Dynamic buckling of fiber composite shells under impulsive axial compression

The paper deals with dynamic buckling due to impulsive loading of thin-walled carbon fiber reinforced plastics (CFRP) shell structures under axial compression. The approach adopted is based on the equations of motion, which are numerically solved using a finite element code (ABAQUS/Explicit) and using numerical models validated by experimental static buckling tests. To study the influence of the load duration, the time history of impulsive loading is varied and the corresponding dynamic buckling loads are related to the quasi-static buckling loads. To analyse the sensitivity to geometric imperfections, the initial geometric imperfections, measured experimentally on the internal surface of real shells, are introduced in the numerical models. It is shown numerically that the initial geometric imperfections as well as the duration of the loading period have a great influence on the dynamic buckling of the shells. For short time duration, the dynamic buckling loads are larger than the static ones. By increasing the load duration, the dynamic buckling loads decrease quickly and get significantly smaller than the static loads. Since the common practice is to assume that dynamic bucking loads are higher than the static ones, which means that static design is safe, careful design is recommended. Indeed, taking the static buckling load as the design point for dynamic problems might be misleading.     

Elastic buckling analysis of ring-stiffened cylindrical shells under general pressure loading via the Ritz method

This paper presents the Ritz method for the elastic buckling analysis of shells with ring-stiffeners under general pressure loading. The stiffeners may be of any cross-sectional shape and arbitrarily distributed along the shell length. Using polynomial functions multiplied by boundary equations raised to appropriate powers as the Ritz functions, the method can accommodate any combination of end conditions. As far as it is known, the Ritz method has not been automated in this way for the buckling of ring-stiffened shells. By formulating in a nondimensional form, generic buckling solutions for shells with various end conditions, stiffener distributions and under various pressure distributions, were presented. These new buckling solutions should serve as useful reference sources for checking the validity and accuracy of other numerical methods and software for buckling of cylindrical shells. This paper also shows that the appropriate distribution of ring stiffeners can lead to a significant increase in the buckling capacity over that of a stiffened shell with evenly spaced and identical ring stiffeners.     

Elastic buckling of an axially compressed cylindrical panel with three edges simply supported and one edge free

The paper is devoted to a circular cylindrical panel with three edges simply supported and one edge free. This panel is axially compressed by a load uniformly distributed at both ends. The Donnell equations for linear buckling of shells are assumed and the adequate boundary conditions are defined. The deflection function and the force function–the Airy function are formulated with respect to the boundary conditions. The Donnell equations are reduced to a generalized eigenvalue problem with the use of Galerkin method. The results of numerical investigation are presented in figures.