Flexibility of shafts with abrupt changes of section

The calculation of deflections of shafts by simple bending theory can incur errors if it is applied where the shafts are stepped with large and abrupt changes of section. Following an experimental check, the finite element displacement method was used for an investigation into the flexural properties of such shafts, particular attention being paid to the relationship between the step geometry and the centre line deflection curves.It is shown that centre line deflections of a stepped shaft may be calculated by using simple bending theory in conjunction with an appropriate equivalent variable second moment of area for sections of shaft in the region of the step. Graphical data on the equivalent second moment of area is provided for a wide range of step length/basic shaft diameter and step diameter/basic shaft diameter ratios.     

Photoelastic approach to the determination of the flexural rigidity of rectangular beams with abrupt changes of section

In some previous work finite element analysis was used to determine distributions of flexural rigidity in beams with abrupt changes in section by calculating the variation in the curvature of the beam centre-line. An alternative experimental treatment of the same problem is described herein, the centre-line curvature being derived from photoelastic data.     

矩形截面径向阵列式柔性支承的设计

介绍了一种能提供精密有限转动的柔性支承。在有限弹性变形范围内,采用组合变形理论给出了扭转刚度、最大正应力和最大剪应力计算公式。分析了主要结构尺寸参数对扭转刚度系数的影响,进行了算例设计计算,并对算例进行了有限元验证。结果表明,给出的解析计算公式可用于矩形截面径向阵列式柔性支承的指导性设计;对于扭转刚度系数有更高精度要求的应用,结合计算公式,采用有限元计算可获得满意的精度。     

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.     

Bending collapse of rectangular and square section tubes

The bending collapse behaviour of rectangular and square section tubes is studied theoretically and experimentally. A limit analysis technique was employed and a set of formulae relating the hinge moment and associated angle of rotation was derived. The theoretical predictions were verified by comparison with 56 quasi-static bending tests on 27 different sections having aspect ratios ( ) varying between 3.0 and 0.33 and with width to wall thickness ratios ( ) between 128 and 9.14. Very good agreement was found between the theoretical predictions and experimental results for the whole range of sections.     

钻井封隔器用矩形截面弹簧的设计与校核

根据钻井封隔器的功能和尺寸要求,设计了矩形截面弹簧。根据矩形截面弹簧的结构特点,采用等效并联组合弹簧的方法对矩形截面弹簧进行了理论计算,并推导出轴向刚度的计算方法。运用Solid Works进行三维实体建模,并用ABAQUS进行有限元分析,获得了矩形截面弹簧的轴向刚度,通过与理论计算结果比较,证明了理论计算方法的合理性。通过有限元分析进行强度校核,结果表明矩形截面弹簧满足设计要求,为此类弹簧的设计提供了参考。     

An investigation of the collapse of thin-walled rectangular beams in biaxial bending

Two different thin-walled closed sections, one square and one rectangular were tested in biaxial bending using displacement controlled cantilever bending tests.Two different constraint conditions were used, the first kept the deflection axis fixed and left the direction of the load axis free. The second kept the load axis direction fixed and allowed the beam to deflect freely.Each configuration was repeated at 15° axis intervals and was performed twice to assure repeatability. This gave a total of 42 cantilever bending tests.The results are used to compare the beam behaviour in the transition and collapse stages between the two constraint conditions. The behaviour is also contrasted with thick-walled theory predictions, since this is the only currently available reference.     

Inelastic behaviour of rectangular beams subjected to steady axial load and cyclic bending

Analytical and numerical solutions are given for the inelastic behaviour of a rectangular cross-section beam, subjected to a steady axial load and cyclic, fully reversed load-controlled bending. Elastic-perfectly plastic, linear isotropic and kinematic materials are examined and solutions for the strain accumulation and cyclic reverse plastic strains obtained. Also the effect of introducing a creep dwell period into the cycle is considered.     

A technology to improve formability for rectangular cross section component hydroforming

In order to overcome difficulties in non-uniform thickness distribution and cracking failure during rectangular tube quasi-static hydroforming, a new forming technology, named as electromagnetically assisted hydroforming, is put forward. Both experiment and finite element method were conducted to investigate corner deformability and deformation pattern and its effect mechanisms. Results indicate that both corner deformability and thickness distribution are improved greatly under electromagnetic-assisted hydroforming. The reason is that deformation behavior changed after electromagnetic force application. As electromagnetic force is applied, tine petal cross sections are periodically produced and flattened. Thus, petal-like preform continues to generate and play a useful role in corner filling. Such deformation pattern overcomes friction holding back defect and results in stress state going over from tensile stress to compressive stress, which helps to avoid cracking failure and greatly improve thickness uniformity. At the same time, it also contributes to improve surface quality and decrease forming pressure simultaneously.     

在设计中钢筋混凝土矩形截面梁高度的确定

建筑设计中常用到钢筋混凝土矩形梁，通过公式的推导确定梁高的简捷算法。     

Dynamic analysis of bending–torsion coupled composite beams using the Flexibility Influence Function Method

In this work the dynamic behaviour of symmetrical laminated beams was studied, taking into account the effect of bending–torsion coupling by a one-dimensional model. This model includes the influence of the shear force and rotatory inertia. To solve the equations of motion, the Flexibility Influence Function Method (FIFM) was used. The dynamic displacements (deflection, bending rotation, and torsional rotation) were calculated for a beam in which the deflection and torsional rotation were restricted at its both ends, allowing the bending rotation. The accuracy of this method was determined by using a Three-Dimensional Finite Element Method (FEM3D) model to compare the dynamic displacements. The need was shown to incorporate coupling in the one-dimensional model in order to calculate the dynamic deflection and bending rotation of a composite beam.     

FCC-BCC phase transformation in rectangular beams subjected to plastic straining at cryogenic temperatures

FCC metals and alloys are frequently used in cryogenic applications, nearly down to the temperature of absolute zero, because of their excellent physical and mechanical properties including ductility. These materials, often characterized by the low stacking fault energy (LSFE), undergo at low temperatures three distinct phenomena: dynamic strain ageing (DSA), plastic strain induced transformation from the parent phase (γ) to the secondary phase (α^′) and evolution of microdamage. The FCC-BCC phase transformation results from metastability of LSFE metals and alloys at very low temperatures. The phase transformation process leads to creation of two-phase continuum where the parent phase coexists with the inclusions of secondary phase. Such heterogeneous material structure induces strong strain hardening related to two distinct mechanisms: interaction of dislocations with the inclusions and increase of tangent stiffness as a result of mixture of two phases, each characterized by different parameters. The strain hardening model is based on micromechanics considerations (first mechanism) and on the Hill concept (1965) including the Mori-Tanaka (1973) homogenization scheme (second mechanism). Identification of parameters of the constitutive model is based on the available experimental data. The model is used to describe phase transformation in rectangular beams subjected to elastic-plastic bending at cryogenic temperatures. Several examples of rectangular beams with FCC-BCC phase transformation induced functionally graded (FGM) microstructure are presented.     

A consistent approach to linear stability of thin-walled beams of open section

This paper presents a stability criterion for thin-walled beams of curvilinear section, based on the positive definiteness of the second variation of the potential energy. The internal stresses are derived according to a shell model which incorporates the kinematic restraints of thin-walled beams. In addition to the classical terms of the potential energy, the geometric effects of an applied torque, as well as flexural-extensional and torsional-extensional coupling terms, are accounted for.     

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。     

Transmission loss prediction on SIDO and DISO expansion-chamber mufflers with rectangular section by using the collocation approach

This paper presents the acoustical performance prediction on single-inlet/double-outlet (SIDO) and double-inlet/single-outlet (DISO) expansion-chamber mufflers with rectangular section. Expressions for the transmission loss (TL) of this kind of mufflers are formulated by using the collocation approach. Numerical results of TL are compared with the plane wave theory to show up the higher-order mode effects. Furthermore, the finite element method (FEM) is also employed again to verify its accuracy in view of these configurations of muffler.     

高柔韧性的革命性现场成型密封剂产品

经济危机始终可加速变革并促进创造与创新。在这方面,乐泰5188的开发便是一个完美的范例。乐泰5188是汉高密封剂产品系列中的最新产品,与先前的其他产品不同,乐泰5188能够涂覆形成较薄的薄膜,同时仍具有较强的柔韧性,从而在密封件之间形成一个既有良好密封性而又坚固的连接,并且满足多种工业部门飞速变化的技术要求。目前,这一产品正引入亚太区市场。     

含界面相复合材料的柔度预报

界面相对复合材料的力学行为有很大影响.考虑夹杂与界面相的联合作用,建立由夹杂、界面相、基体和有效介质组成的四相模型.首先根据有效自相容法推导出夹杂与界面相内的局部应力场,进而得到复合材料有效柔度的隐性形式,再利用Taylor级数展开得到复合材料的柔度张量的显性表达式,复合材料的柔度张量与夹杂和界面相的体积含量、夹杂形状和分布形式有关.     

Calculation of the three-dimensional magnetic field produced by a circular DC-carrying coil of rectangular cross section

Expressions used for computer calculations of magnetic fields via a combined analytic and digital method are presented. Examples of the accuracy of such calculations are given.     

Flexibility and types of changes in FMSs: A timed petri-nets assessment of machine flexibility

This paper discusses the flexibility concept in the light of the production-systems capabilities needed to cope with changes occurring at different time horizons. Two basic flexibility components emerge: set-up (in time units) and variety (operations and transfer). The paper further describes a timed Petri-nets approach to machine-flexibility evaluation (set-up and operations variety). A timed Petrinets decomposition technique is used to derive measures of flexible machines' performance under changes that a flexible system has to cope with, such as failures, changeover interruptions, fluctuations in demand, and re-routing.