钢筋混凝土板弯曲问题的各向同性化域外奇点解法

本文提出了求解钢筋混凝土板弯曲问题的各向同性化域外奇点法。引入简单的坐标变换，将该问题转化成相应的各向同性板的弯曲问题，利用后者的简单格林函数，按域外奇点法求解。算例表明，这种方法简单，计算时间短，精度高。     

弹性力学的样条边界元法

本文对弹性力学问题提出一个样条边界元法。文中用三次B样条函数来逼近边界未知量,并且利用域外奇点法建立了样条边界元法的计算格式。这种计算格式十分简单,容易在微机或小机上实现。利用域外奇点法建立起来的计算格式,完全可以避免奇异积分。计算结果表明,样条边界元法是一个经济有效的计算方法。     

弹性地基中厚板的拟薄板域外奇点法分析

本文从简化的Reissner 理论出发，将中厚板问题模拟成薄板问题，导出类似于求解弹性地基上薄板问题的边界积分方程。本文利用域外奇点法提出的方法适用于弹性地基上的任意边界，任意荷载的薄板，中厚板的弯曲问题。该方法简单，易于编程序，能方便的应用于工程计算中。     

转炉用变截面自平衡式扭力杆扭转变形的理论计算

扭力杆通过弹性扭转变形储备能量的大小对氧气顶吹转炉大型设备工作的可靠性有着重要影响,研究其扭转变形成为关键的技术问题之一。该文基于圆柱弹性扭转初等理论,推导了由等截面圆杆、变截面锥杆和过渡圆角三部分共同组成的自平衡式扭力杆的扭转变形的理论计算公式,并以150t转炉用自平衡式扭力杆为例,对其正确性采用有限元方法进行了验证,两种方法的计算结果吻合。该自平衡式扭力杆的实际应用也表明该文两种研究方法都是可行的,但是解析法比有限元法简单方便,更适合工程设计人员直接使用。     

无奇点边界元法分析板的稳定

根据板的稳定问题控制微分方程，利用无奇点边界元法（域外奇点法）离散比，导出稳定特征方程，从而求出临界荷载因子。经编程计算例题，效果良好。     

轴对称横观各向同性土体中桩的扭转振动响应研究

基于单相弹性土体的运动方程以及横观各向同性材料的本构关系,研究了轴对称条件下端承桩在横观各向同性土体中的耦合扭转振动响应问题.在柱坐标下推导得到横观各向同性土体受谐和扭转荷载作用的动力控制方程,并采用分离变量法求得了土体扭转振动位移形式解.依据桩土接触面上的衔接条件,求解了桩身的动力平衡方程,并在频域内得到了桩身转角、扭矩和桩顶复刚度的解析解.最后分析了横观各向同性土体的力学参数对动力响应的影响.结果表明,横观各向同性土体的力学参数对桩顶复刚度、桩身转角和扭矩沿深度方向的变化均有着显著影响.     

域外奇点法分析薄板的弯曲和平面应力问题

本文首先给出了作者推导的两边简支无限长薄板弯曲问题和平面应力问题的基本解，然后运用域外奇点法及给出的基本解分析了一对边简支矩形薄板的弯曲和平面应力问题．计算结果表明，这种方法具有计算量少、精度高等优点。     

机敏杆压电扭转驱动器／传感器优化布置

提出一种由薄壁杆、压电扭转驱动器、压电传感器组成的机敏杆,针对机敏杆扭转振动控制中驱动器/传感器优化配置问题,对机敏杆的扭转振动进行了深入的研究,采用拉格朗日方程和假设模态法推导了机敏杆系统的动力学方程,建立了系统的状态空间表达式.将机敏杆划分为若干个位置单元,选取主动控制器的最大耗能作为优化准则,运用遗传算法获得了压电扭转驱动器/传感器的最佳配置位置及最优反馈增益.结果表明:所获得的最优位置、反馈增益是合理的,将驱动器/传感器同位配置在最优位置并实施相应的闭环最优控制,主动控制器的耗能最大,并能有效抑制机敏杆的扭转振动.     

纵—扭复合振动模式超声变幅杆研究

本文对窄端带有均匀截面直棒的指数型纵-扭复合振动模式超声变幅杆进行了理论及实验研究,推出了该复合模式变幅杆纵向振动及扭转振动的共振频率方程。为了克服同一变幅杆纵向与扭转振动很难实现同频共振的问题,提出了一种通过改变指数型变幅杆的截面变化规律而实现改变纵向及扭转振动传播速度的方法。通过合理选择指数变幅杆的截面半径减缩系数(即参数β),实现了纵-扭复合变幅杆纵向振动与扭转振动的同频共振。实测结果表明,共振频率的理论值与测试值基本一致,变幅杆纵向及扭转振动共振频率的测试值也比较符合。该变幅杆具有比较高的位移放大系数。可望应用于超声加工、超声疲劳实验及超声焊接等功率超声技术中。     

非线性材料圆杆的扭转固有振动分析

利用非线性材料的本构关系,建立了非线性材料圆杆的扭转固有振动方程,然后采用傅立叶级数法求得了圆杆扭转固有振动的所似解,通过实例计算讨论分析了非线性材料圆杆的扭转固有振动特性。     

The exact moment for the plastic torsion of a cylindrical bar of elliptical cross section

Summary An exact expression for the limiting moment of the torsion of an isotropic, perfectly plastic elliptical bar has not been previously derived. In this note, the solution of this classical problem is reduced in form to a single quadrature. It is shown by comparison that an approximation due to Sokolovsky is inaccurate for large aspect ratios of semiaxes. Through a transformation of coordinates, the exact solution is also applicable to the plastic torsion of an orthotropic circular cylinder with generators perpendicular to a principal axis. It follows that for highly orthotropic materials an approximate solution derived by Hill may also prove inaccurate.With 1 Figure     

Modeling and experimental validation of the surface residual stresses induced by deep rolling and presetting of a torsion bar

During the production of torsion bars, two different mechanical processes of inducing the residual stresses into the torsion bar are used: the presetting of the torsion bar and the deep rolling of the torsion bar. The process of presetting the torsion bar is carried out by twisting the torsion bar to the desired angle and releasing it to the new residual angle position. With controlled overstraining, favorable residual shear stresses are induced into the torsion bar, so the material is strain hardened and the yield point of the material is shifted and increased in the stress and strain space. The objective of the deep rolling process is to introduce compressive residual stresses into near-surface regions in order to increase the fatigue strength of the torsion bar. These two processes influence each other. The final level of residual stresses depends on the production sequence of these two processes and the production parameters of each process. The correct production sequence of these two operations and distribution of beneficial residual stress was simulated using the finite element (FE) method. To validate this model, the predicted surface residual stresses were compared by the X-ray diffraction (XRD) measurements of residual stresses.     

The reflected caustics formed from cross-sections of twisted prismatic bars

Summary If a prismatic bar made of a homogeneous isotropic and elastic material is submitted to torsion, cross sections of the bar are twisted and warped. In this paper the shape and size of the caustics and pseudocaustics formed from reflections of light rays on these cross sections were analytically and experimentally studied. This study is concerned with cross sections of circular, elliptic, triagular, and rectangular shapes of different ratios between their characteristic dimensions. It was proved that the experimentally derived caustics are in good agreement with the theoretical curves. Then this method of reflected caustics is a sensitive device for the detection and the accurate measurement of the torsional loading of such elements of structures. With 15 Figures     

Dual finite element analysis for plasticity–friction torsion of composite bar

The quasi-static problem of torsion of an elastic–plastic, prismatic, composite bar is considered in the paper. The phenomenon of slip on the interfaces between the components of the bar is taken into account. The elastic–plastic behaviour of the material is described by the Prandtl-Reuss constitutive relation. The slip on the interface is governed by the Coulomb friction law—it is assumed that there is no cohesion between components of the bar. The stresses normal to the interfaces are considered to be caused by shrinkage of the matrix of the bar or by external forces acting perpendicularly to its longitudinal axis. The problem is set in the dual variational forms and solved with the help of the finite element method. Two approximate kinematically and statically admissible solutions are obtained. The stress function is used for calculation of the second one. The iterative algorithms solving the problem and some numerical results are presented in the paper.     

Application of the superelement method in a mode III crack problem

An application of the superelement method in linear fracture mechanics is analysed. The case of a pure torsion problem is cited as an example. A convenient form of the superelement for a mode III crack problem at the crack tip and formation of the superelement stiffness matrix are discussed. A numerical example for a bar with a slit is also shown.     

双横臂双扭杆悬架中上下扭杆的刚度匹配和等强度设计

 通过对双横臂双扭杆悬架中上下扭杆的刚度匹配和等强度设计问题的研究,提出了扭杆的设计方法.分析了双横臂双扭杆悬架的导向机构模型简图,得到了导向机构的运动关系和进行悬架刚度计算的方程;以满足悬架载荷要求和悬架刚度要求为前提,分析了上下扭杆的刚度匹配条件;在上下扭杆在悬架运动时的强度始终相等的前提下,分析了上下扭杆的等强度条件.通过对扭杆直径和有效长度的实例计算,证明所提出的上下扭杆的刚度匹配和等强度设计的方法是可行的.     

Approximate Torsional Analysis of Multi-layered Tubes with Non-circular Cross-Sections

In this paper an approximate formulation for torsional analysis of tubes with multi-layered non-circular cross-sections is presented. A previously presented method based on Bredt’s theory is extended to achieve these formulas. Layers are assumed to be isotropic and may possess different thicknesses and material properties. The obtained formulas for shear stress and angle of twist are applicable to thin to moderately thick closed cross-sections. It is shown that depending on the properties of the layers, maximum shear stress does not necessarily happen on the outer boundary. Furthermore, the effect of different cross-sectional shapes on torsional response is studied. Using the presented method, one can achieve desirable shear stresses and angles of twist for a polygonal multi-layered tube with a proper choice of bluntness. The method can be extended for torsion problem of FGM tubes as well. The presented formulas for torsion problem are relatively accurate and suitable to be implemented in optimization programs.     

Modified torsion coefficients for a 3-D brick Cosserat point element

A simple deformation field associated with an exact torsion-like solution of the equilibrium equations of linear elasticity is shown to provide a good approximation of the deformation field in interior elements of a mesh that models pure torsion of a right cylindrical bar with rectangular cross-section. Using this solution, modified torsion coefficients are proposed for a 3-D brick Cosserat point element (CPE) which are shown to improve convergence properties for solutions of pure torsion.