Bifurcation points and bifurcated branches by an asymptotic numerical method and Padé approximants

The aim of this work is to develop a reliable and fast algorithm to compute bifurcation points and bifurcated branches. It is based upon the asymptotic numerical method (ANM) and Padé approximants. The bifurcation point is detected by analysing the poles of Padé approximants or by evaluating, along the computed solution branch, a bifurcation indicator well adapted to ANM. Several examples are presented to assess the effectiveness of the proposed method, that emanate from buckling problems of thin elastic shells. Especially problems involving large rotations are discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

A note on stress-constrained truss topology optimization

The purpose of this brief note is to demonstrate that general-purpose optimization methods and codes should not be discarded when dealing with stress-constrained truss topology optimization. By using a disaggregated formulation of the considered problem, such methods may find also “singular optima”, without using perturbation techniques like the ε-relaxed approach. Received February 19, 2002     

非对称复合材料层板在面内载荷作用下的非线性横向变形或屈曲

本文利用广义富里叶级数法对非对称复合材料层板在面内载荷作用下的非线性横向变形或屈曲问题进行了分析。文中主要研究了四边简支边界条件下,非对称层板的铺层方式和面内载荷形式对横向变形的影响。通过求解非线性控制方程得到了层板的载荷—挠度曲线或特殊情况下的后屈曲平衡曲线。计算结果表明,对于大多数非对称复合材料层板在面内载荷作用下所产生的是横向变形问题,而不是分叉屈曲问题。     

Dynamic elastic-plastic buckling phenomena in a rod due to axial impact

Dynamic elastic-plastic buckling phenomena which might develop in a rod from an axial impact loading are studied in order to identify the conditions for quasi-static behaviour. A discrete model for dynamic elastic-plastic buckling, which retains the axial and the lateral inertia forces, is proposed, and the relationship between the model parameters and the characteristics of an actual structure is given. Examples of different external loadings and boundary conditions are considered in order to clarify the influence of elastic-plastic axial wave propagation on the buckling process. The critical time for the initiation of buckling is obtained and the post-buckling behaviour of the model is analysed. Particular attention is paid to the role of the striking mass on the characteristics of the buckling process and on the development of the buckling shape. The numerical study reveals that the inertia of the striking mass affects considerably the development of the buckling shape causing different patterns of axial strain distributions at the initiation of buckling. The comparisons which are made between the model predictions and some previously published experimental data show that the buckling process is governed by the impact velocity as well as by the external loading history provided by the experimental technique.     

不规则I型和L型横截面形状薄壁杆件的横向弯曲稳定分析

根据势能驻值原理,采用转换B3样条函数模拟杆件横截面的翘曲位移场,文[8]提出了用于分析在横向荷载作用下薄壁杆件稳定问题的样条有限杆元法。方法适用于任意横截面形状和任意边界条件的薄壁杆件,考虑了杆壁中面上剪切变形的影响,能很好地描述剪力滞后现象。本文讨论了不规则I型截面简支梁和L型截面简支梁的屈曲分析,数值算例的结果表明了方法的灵活性、精确性和有效性。     

正交异性矩形薄板的稳定性分析

本文求得了正交异性矩形薄板屈曲位移函数微分方程的一般解。可用以求解任意边界矩形板的稳定问题。以两邻边简支，另两边自由的正方形板为例进行了计算。     

Buckling analysis for delaminated composites using plate bending elements based on higher‐order zig‐zag theory

A finite element based on the efficient higher‐order zig‐zag theory with multiple delaminations is developed. The bending part of the formulation is constructed from the concept of DKQ element. Unlike conventional elements, a developed element has its reference in the bottom surface which simplifies zig‐zag terms on formulation. Exact patch solutions are developed on elements which have the bottom reference system. The present element passes proper bending patch tests in the arbitrary mesh configurations in isotropic materials. Zig‐zag formulation is adopted to model laminated plates with multiple delaminations. To assess the accuracy and efficiency of the present element based on higher‐order zig‐zag theory with multiple delaminations, the linear buckling problem of laminated plates with multiple delaminations has been analysed. The results have been compared with three‐dimensional elasticity solutions. The present element works as an efficient tool for analysing the behaviour of the laminated composites with multiple delaminations. Copyright © 2002 John Wiley & Sons, Ltd.     

工字梁的抗剪极限承载力

对工字梁腹板抗剪极限承载力的研究进行总结,对各种公式与文献中的试验结果进行对比,将拉力场理论和转向应力场理论的假定与ANSYS分析揭示的腹板应力发展变化规律进行对比,指出了假定和数值分析结果的不一致。提出了翼缘对腹板转动约束的合理参数,得到精度良好的考虑翼缘约束的腹板剪切屈曲系数。利用得到的屈曲系数,考虑翼缘抗弯承载力的贡献,提出新的工字梁抗剪极限承载力的计算公式。与现有试验数据和ANSYS非线性有限元分析结果的对比,证实建议方法离散性较小,适用范围广,尤其是对于通用高厚比较大的梁,较以往方法有了较大改进。     

Some experimental findings in compression-after-impact (CAI) tests of CF/PEEK (APC-2) and conventional CF/epoxy flat plates

Compression-after-impact (CAI) tests have been conducted for quasi-isotropic thick plates with 48 plies by using the NASA method and on plates with 32 plies by using the SACMA method. Specimens are made of CF/PEEK (APC-2) and conventional CF/epoxy for the NASA plates and CF/epoxy for the SACMA plates. In the NASA CAI tests, the sequence of delamination buckling and its propagation is clearly revealed through various experimental techniques. One major technique is moiré topography, and the other is thermo-mechanical stress analysis with a high-accuracy infrared sensor. The arrest of delamination propagation just before catastrophic failure due to high fracture toughness is clearly captured by the moiré camera. This behavior provides good CAI values of CF/PEEK. The initial buckling properties of the delaminated region by the impact are then extensively discussed. Numerical predictions of initial buckling stress have been obtained by modelled geometry of the delaminated region simplified from its precise structure clarified by ultrasonic C-scanning. They agree fairly well with the experimental results. The in-plane stress distribution in the delaminated region before initial buckling is measured by an infrared stress graphic system. This compared favorably with finite element predictions. Two types of symmetric buckling modes with respect to the central plate surface, twin and single peak ones, are experimentally captured.     

钻井井架力学性能分析

钻井井架作为钻机系统设备中的关键部分,其力学性能直接关系到整套钻机系统的安全生产。文章推导了常用于分析钻井井架力学性能的理论,即线性屈曲、几何非线性和双重非线性理论。提出同时用这三种理论对钻井井架进行综合比较分析,从而合理地预见井架力学性能的方法。以A形钻井井架为例,进行了详细的分析,得到了井架的失稳形式、极限承载、破坏特征及薄弱部位,为钻井井架的设计、优化与评定提供了参考。