Nonlinear analysis of thin walled bars of open cross-section

Energy equations governing the goemetrically nonlinear behaviour of thin walled bars of open cross-section when subjected to axial, flexural and torsional displacements, are derived. The equations are based on the assumption of small displacements and linear elastic material behaviour. Shear deformations due to nonuniform bending, and distortion of the cross-section are not included in the analysis. Solutions of the governing nonlinear equations are obtained by the finite element method, making use of linearised mid-increment stiffness matrices. The results of the geometrically nonlinear analysis are combined with an approximate failure criterion to predict the failure loads of I beams having initial imperfections. The predicted failure loads are compared, and show satisfactory agreement, with existing experimental results.     

Second order strains and instability of thin walled bars of open cross-section

Complete expressions for the strains, including second order terms, occurring in thin walled bars of open cross-section are derived. Shear deformation due to non-uniform bending and distortion of the cross-section are not considered in the present theory. The correctness of the expressions is verified by incorporating them in a general instability analysis based on energy considerations.     

薄壁杆系考虑节点柔度特征的计算模型及其应用

在有限元梁理论中节点完全刚性的假设和实际薄壁杆系节点局部变形的出现产生矛盾,不得不考虑薄壁杆系节 点刚度特征对结构分析结果的影响。该问题引起国内外研究者的重视。针对上述问题,提出一个能够考虑薄壁杆系节 点刚度特征的计算模型。该模型的优点在于它包括了用壳单元离散的节点超单元和梁单元共同构成薄壁杆系计算模 型。在一次计算中能提供节点设计所需要的节点细部应力分布特征,同时也提供梁截面设计所需要的截面内力。     

Large deflection analysis of a thin walled channel section cantilever beam

For a special application the large deflection behaviour of thin walled channel section beams made of thin sheet steel has been investigated. The experiments consisted of cantilever bending tests with the beam loaded through the shear centre and through the centroid. When loaded through the shear centre the beam buckling took place in the compression flange at the root of the cantilever. When loaded through the centroid however, it was noted that the compression flange buckled at a fixed distance from the fixed end. The general theory of thin walled beams developed by Vlasov was applied to the problem and indicated that the maximum compression stress at the edge of the flange would be at some distance from the fixed end. The value of the maximum compression stress obtained by the general linear theory was small and its position did not coincide with the experimental position. The Vlasov analysis has been modified to include the increase in the twisting moment due to the lateral deformation of the beam along its length. Good agreement between the modified theory and experiment both for the position of the maximum compressive stress and for the twist of the cantilever at three points along its length.

Because of the very low torsional stiffness of thin walled channel sections, the small deflection theory is only applicable for small bending loads applied through the centroid and the modified theory should be used for practical loading cases.     

十字弹性机构精度性能的研究

分析了在加载条件下十字弹性机构功能方向和非功能方向的精度性能,以及结构参数对精度性能的影响。给出了特殊条件下十字弹性机构的优化设计方法。     

当量长度法确定变截面压杆临界弯曲载荷

以机械传动中常见的变载面压杆为例,根据临界弯曲载荷相等的条件,推导出了变截面压杆在轴向压力作用下所对应的当量长度的计算公式。从而可利用材料力学中求解等截面均质压杆临界弯曲载荷的欧拉公式,求出各种不同支承形式变截面压杆折临界弯曲载荷。     

薄壁方钢管冷弯机构设计

介绍薄壁方钢管的冷弯机构及其原理,并提出冷弯工艺的难点及解决方法,以及该冷弯机构的应用范围。     

Parametric studies on buckling loads and critical speeds of microdrill bits

Transverse bending vibrations of the spinning microdrill bit subjected to a compressive axial load are developed based on the Timoshenko beam theory. The system equations of motion are discretized into the form of time-dependent ordinary differential equations by the finite element method. Two types of eigenvalue problems are formulated and utilized to study the effects of the drill helix angle, flute length and diameter on the buckling load and critical speed of microdrill bits with different supported ends. Equivalent formulae similar to those of untwisted Euler beams are established to predict critical buckling loads and critical speeds for microdrills and provide results with sufficient accuracy. The effect of rotational speed on the buckling load, and the influence of thrust force on critical speed are also investigated. A Galef-type equation associated with critical speed, thrust force and buckling load is formulated.     

For the problem of measurement of the displacements of magnetorheological transformer of the shock loads by wave methods

The problems of evaluating errors when measuring the displacements of magnetorheological transformers by ultrasonic wave methods have been considered, in which the throttle channels were replaced by the cylindrical gap between two coaxial cylinders [1]. The cylinder gap, as well as the volumes of main and compensation chambers have been filled with magnetorheological fluid. Under the action of the shock loads, the measurement of displacements by wave methods is associated with a number of features that have been considered in this article and the evaluation of the measurement errors is implemented.     

变截面柔性铰链变形分析计算方法

柔性铰链的几何结构对其性能有着直接的影响。文中分析了变截面柔性铰链的变形特性,给出了变截面柔性铰链的特征厚度比和等效截面厚度的概念。定义了平均截面厚度的修正系数,通过算例给出了不同特征厚度比对应的修正系数值,以此对变截面柔性铰链的平均截面厚度进行修正得到等效截面厚度,进而采用伪刚体模型法分析变截面柔性铰链的变形。实例计算结果表明,经过修正计算得到的变形结果与有限元法的分析结果具有很好的一致性,表明了修正系数的合理性。     

Nonlinear forced vibrations and static deformations of 3D beams with rectangular cross section: The influence of warping, shear deformation and longitudinal displacements

The geometrically nonlinear vibrations of beams with rectangular cross section, which may experience longitudinal, torsional and bending deformations, in any plane, are investigated by the p-version finite element method. Two main models are used: one of them is based on Bernoulli-Euler theory for beam bending and the other is based on Timoshenko theory; both models assume that the cross section rotates as a rigid body and is free to warp in longitudinal direction, as in Saint-Venants’s theory for torsion. The geometrical nonlinearity is taken into account by considering Green’s strain tensor and the importance of the longitudinal displacements of quadratic order, which are most often neglected in the strain-displacement relation, is here examined. Generalized Hooke’s law is used and the equation of motion is derived by the principle of virtual work. The importance of the warping function is analysed for different rectangular cross sections, and it is shown that its consideration can be fundamental to obtain correct results. Then, it is shown that the linearization of the trigonometric functions related with the twist angle, which is usually applied in the displacement field in models based on Saint-Venant’s hypothesis, should be done in the strain-displacement relations. Comparisons of the models for 3D beams based on Bernoulli-Euler’s and Timoshenko’s theories is presented. It is shown that if the rotations along the transverse axes are directly approximated by the respective derivatives of the transverse displacement functions, as is assumed in the model presented here that is based on Bernoulli-Euler’s theory, the additional shear stresses that appear when the bending and torsion motions are coupled, lead to wrong results. Finally, taking into account accuracy and simplicity, a model is chosen and employed to investigate the nonlinear forced vibrations of beams using direct integration of the equations of motion in the time domain. Examples of bending-torsion couplings due to the nonlinear terms are presented in dynamical problems.     

车削薄壁零件的弹性夹具设计

根据薄壁零件难于加工和容易变形的特点，设计了一种利用径向夹紧适合于小批量生产的车削夹具。该夹具以零件的内孔定位，加工薄壁外圆，结构简单，制造容易，操作方便，夹紧可靠，定位精度高。经在生产实践中使用后证明，该夹具既能保证工件加工精度和产品质量，又提高了生产效率，取得了良好的应用效果。     

铝合金薄壁零件数控加工夹具问题探讨

以铝合金薄壁零件数控加工夹具使用为例,介绍了薄壁零件在数控机床铣削加工过程中的装夹方法.在实际生产过程中,对夹具进行了优化改良,有效减少了工件的装夹时间和定位时间,提高了加工效率和加工精度.满足了月产20万件的批量生产要求,使产品的工艺性、经济性得到显著提高.     

聚甲基丙烯酸甲酯薄膜的弹性模量测量研究

高聚物材料由于其易热变形、常温下状态稳定且不易被破坏等优点,是新型的存储技术———基于扫描探针显微术(SPM)的热机械超高密度信息存储技术的理想存储介质材料,存储介质的力学特性是影响热机械形成的数据斑形貌的重要因素。实验使用纳米压痕法对270nm厚聚甲基丙烯酸甲酯(PMMA)薄膜的弹性模量进行测试,采用两次保载过程,有效地消除了材料的黏性对测试结果的影响。同时研究了基底效应的影响,通过引入与深度相关的影响因子估算基底的影响,得到PMMA薄膜在常温下的弹性模量为6.5GPa。     

轴用弹性挡圈临界转速计算分析

介绍了轴用弹性挡圈使用原理及范围,分析了挡圈临界转速失效机理,建立了单一旋转离心力作用下挡圈受力模型,通过微积分对挡圈模型进行受力分析,给出了在离心力作用下,轴用弹性挡圈临界转速推导方法及计算公式。结合某型号推土机变速箱使用案例,对推导公式进行了验证,为设计及相关问题原因分析提供参考。     

连续变截面横梁回弹特性及控制

连续变截面板各处厚度不同,冲压成形后的回弹特性与等厚板有很大差异,如何减小回弹并使各处回弹趋于平衡成为连续变截面板应用中的重要问题。利用大型通用有限元软件ANSYS及其参数化设计语言APDL,通过编程建立横梁的变截面有限元模型;利用ANSYS/LS-DAYNA对连续变截面横梁和等厚板冲压卸载后的回弹进行了数值模拟,模拟结果分析表明:变截面板的回弹规律与等厚板的回弹规律有很大不同;最后利用分块压边圈技术,使横梁的回弹量趋于平衡,同时使整体回弹量下降。     

Influence of loads on the stress-strain state of aluminum-oxide ceramic cutting plates

The influence of point and distributed loads on the stress-strain state of aluminum-oxide ceramic cutting plates is investigated. The nonlinear properties of aluminum oxide and gray iron are taken into account.     

Natural frequencies of Euler-Bernoulli beam with open cracks on elastic foundations

A study of the natural vibrations of beam resting on elastic foundation with finite number of transverse open cracks is presented. Frequency equations are derived for beams with different end restraints. Euler-Bernoulli beam on Winkler foundation and Euler-Bernoulli beam on Pasternak foundation are investigated. The cracks are modeled by massless substitute spring. The effects of the crack location, size and its number and the foundation constants, on the natural frequencies of the beam, are investigated.     

On the lateral instability of a thin beam under periodic bending loads

The lateral instability of a thin beam under periodic bending loads was investigated. Physical evidences of the instability were observed previously by experiments. But an analytical study has not been reported. The object of this study is to demonstrate the nature and existence of dynamic lateral instability. The harmonic balance method is applied to bifurcation modes which result from the stability change of torsional mode of a beam and then compared with numerical simulations. It is found, in a certain frequency range, that a small bending load results in the lateral instability when damping is small. Inha University     

Experimental and theoretical studies on buckling of thin spherical shells under axial loads

In this paper we present experiments, simulation as well as analysis of the collapse behaviour of thin spherical shells under quasi-static loading. Various aluminium spherical shells with variation in geometrical parameters were manufactured by spinning. Experiments were performed on these shells in a universal testing machine and their load–compression histories were obtained on the machine chart recorder. Three-dimensional numerical simulations were carried out for all the specimens tested under quasi-static loading using ANSYS^®. All the stages of collapse of the shell including non-symmetrical lobe formation were simulated. Material, geometric and contact nonlinearities were incorporated in the analysis. The stress–strain curves of standard samples made from the material were used as input. Piecewise linearity was taken in the plastic region of the material curve. Results thus obtained compared with the experiments well.An analysis was also carried out to study the behaviour of shells under axial compression based on the formation of rolling and stationary plastic hinges. These hinges were also simulated numerically and results match the experiments well.