Out-of-plane flexibilities of dovetail joints in machine tool structures

The paper aims to model the flexibility of a dovetail joint encountered in machine-tool structures. The investigation is concerned with the determination of a flexibility matrix through an approximate semianalytical procedure using finite element analysis. The contact region and the pressure distribution on the two mating surfaces are assumed. The deformation pattern of the male and female parts are separately analysed and from compatibility and equilibrium considerations, the overall deformation pattern of the joint is calculated for the three out of plane external force/moment components. The joint flexibility is represented by a 3 × 3 flexibility matrix. Results are presented for the knee-column joint and the column-overarm joint of a milling machine structure.     

叶片-轮盘榫联结构的接触分析

叶片与轮盘之间的榫联结构存在接触和摩擦组合运动,在较高的热-机械载荷作用下容易发生微动磨损并导致疲劳破坏.本文采用有限元法对叶片-轮盘榫联结构进行接触分析,计算不同摩擦系数和不同转速情况下的叶片榫头和轮盘榫槽之间的接触压力、接触滑动距离.结果表明,摩擦系数增大,榫联结构接触面上的接触压力和滑动距离减小;转速增加,则接触压力和滑动距离增大.     

含摩擦滑移铰及驱动约束多刚体系统数值算法

研究了具有驱动约束及非光滑滑移铰多体系统动力学方程的建模与数值计算方法．将驱动约束视为非定常约束，非光滑滑移铰视为双边定常约束，滑移铰的摩擦模型采用库仑摩擦模型；应用第一类Lagrange方程建立系统的动力学方程，应用距离函数建立滑移铰的约束方程；将线性互补方法和Baumgarte约束稳定化方法引入，以解决滑移铰法向约束力的计算以及约束方程违约问题．最后应用曲柄摇杆机构作为算例，说明该方法的有效性．     

Elastic analysis of pin joints

The advent of large and fast digital computers and development of numerical techniques suited to these have made it possible to review the analysis of important fundamental and practical problems and phenomena of engineering which have remained intractable for a long time. The understanding of the load transfer between pin and plate is one such. Inspite of continuous attack on these problems for over half a century, classical solutions have remained limited in their approach and value to the understanding of the phenomena and the generation of design data. On the other hand, the finite element methods that have grown simultaneously with the recent development of computers have been helpful in analysing specific problems and answering specific questions, but are yet to be harnessed to assist in obtaining with economy a clearer understanding of the phenomena of partial separation and contact, friction and slip, and fretting and fatigue in pin joints. Against this background, it is useful to explore the application of the classical simple differential equation methods with the aid of computer power to open up this very important area. In this paper we describe some of the recent and current work at the Indian Institute of Science in this last direction.     

The brownian excursion area: a numerical analysis

Using an explicit expression for the Laplace transform of the Brownian excursion area generating function, a numerical analysis gives moments, density, and distribution function. An asymptotic formula is given for small argument.     

Viscoelastic analysis of adhesively bonded joints

A direct formulation for the viscoelastic analysis of adhesively bonded joints using finite element method is presented. A six-noded quadratic isoparametric element is developed. Two variations for the adhesive layer element are presented. Hereditary integrals are used to represent the stress-strain relations. Relaxation modulus, either experimentally obtained or theoretically generated, can be directly used. Memory load storage/use is minimised using Prony series for the relaxation modulus.A usual eight-noded quadratic isoparametric plane strain element is used to idealise the adherends. As the adhesive layer element is a curved one it can be effectively employed for the analysis of curved adhesive-bonded joints. It is seen from the results that the stress distributions in the joints are accurately determined using both the adhesive layer element formulations. As the element formulation 1 is stiff and formulation 2 is flexible, the average of these solutions using moderate mesh is an accurate solution for the given configuration.     

Elastoplastic analysis of tubular joints of offshore platforms

The subject of this paper is the analysis and design of complex tubular joints, eventually including internal and external gussets and stiffener rings, corresponding to fixed and mobile offshore structures.Two different joints are analysed. In the first case an X joint is studied for elastic and elastoplastic behaviour, loading up to collapse in order to determine ultimate strength and safety factor. Finite elements which can reproduce the elastic and plastic singularities of the stress and the strain fields in the crack tip, are then used for the analysis of a T joint. Both direction and rate are considered in the crack propagation, and an elastoplastic analysis is carried out, to determine the crack opening displacement (COD).Finally, the consideration of fatigue effects in tubular joints is discussed, and techniques for evaluating fatigue life are outlined.     

System theory for numerical analysis

Many numerical schemes can be suitably studied from a system theoretic point of view. This paper studies the relationship between the two disciplines, that is, numerical analysis and system theory. We first see that various iterative solution schemes for linear and nonlinear equations can be suitably transformed into the form of a closed-loop feedback system, and show the crucial role of the internal model principle in such a context. This leads to new stability criteria for Newton's method. We then study Runge-Kutta type methods for solving differential equations, and also derive new stability criteria based on recent results on LMI. A numerical example is given to illustrate the advantage of the present theory.     

IC热阻简化模型的数值分析应用

采用集成电路的热阻简化模型的方法,以DIP封装芯片为例,建立了元件传热的数值模型;分别对两热阻模型和单热阻模型,这两种不同的建模方法在自然对流的情况下进行了稳态分析,并以详细模型的分析结果作为基准进行了对比,获得了使用这两种简化模型进行分析时结果的准确性;对工程师在进行热分析和热设计仿真时,建模方法的选取具有重要的参考价值.     

防坠安全器自动检测的数值算法分析

本文主要对施工升降机安全器的自动检测的数值算法作了系统的研究,主要分析了安全器主要技术参数的计算方法,并且时每种方法进行了理论分析,指出她们的计算精度和误差.     

The quantum square well with moving boundaries: A numerical analysis

We present some numerical discussions concerning the infinite square well in one dimension with moving boundaries. Our results show that if the speed of displacement is small, objects of physical relevance like probability density, averaged position or mean value of the energy have a smooth behavior. On the contrary, if this speed becomes large, many irregularities arise, which has a difficult qualitative explanation. These irregularities manifest themselves as sharp bumps on the probability distribution or a chaotic shape on the averaged values of position and energy. None of these patterns is the result of numerical errors and, therefore, we conclude that an unknown and very nontrivial effect is produced at high speeds of the moving wall.     

The queueing system EkMa,b1 and its numerical analysis

In this paper steady-state random-point results for single-server bulk-service system ${}_{\mathrm{k}}\text{M}{}^{\mathrm{a,b}}\text{1}$ are related to imbedded Markov Chain results using the Erlangian technique. Steady-state results, including the expected number in queue at random and arrival epochs, and waiting time distribution are found in terms of the unique root of the characteristic equation. Examples of extensive numerical work are presented in tabular forms.     

Computer graphics assisted numerical analysis instruction

A computer assisted instruction package for use in a first course in numerical analysis is discussed. Its use is illustrated by examples from two programs for polynomial interpolation.     

On the numerical analysis of eddy-current problems

Starting from Maxwell's equations, we derive a general variational formulation suitable for eddy-current problems in non-magnetic, non-moving conductors disposed in an arrangement of closed multiply-connected circuits. The related problem of open circuits is considered and the validity of the notion of impedance is discussed. A finite element approach is described and illustrated by two examples, one of them from a real problem in electrical engineering.     

Minimal cycle bases for analysis of frames with semi-rigid joints

For an efficient force method of frame analysis, special cycle bases should be generated for the formation of localized self-equilibrating systems, leading to sparse flexibility matrices. In this paper, an algorithm is presented using a fundamental cycle basis, where the selected cycles are improved via an algebraic exchange method. Optimal analysis is performed for frames with semi-rigid joints. In this method, flexibility matrices are generated which are highly sparse. An ordering algorithm is also used for profile reduction to acquire an efficient method for the solution of the corresponding equations. Thus a complete force method analysis of semi-rigid frames is formulated and a computer code is developed. Examples are analyzed with the present approach and the results are compared to those of a stiffness method program with semi-rigid joints.     

Frictional contact analysis of spatial prismatic joints in multibody systems

The contact analysis of spatial prismatic joints remains a hard problem due to its complex nature. In this paper, a methodology for the frictional contact analysis of rigid multibody systems with spatial prismatic joints is presented, which is free of calculating the relative motion between the slider and guide, and is particularly suitable to the case of clearances being tiny. Under the assumption of the slider and guide being rigid, we prove that all types of contacts in the joint can be converted to point-to-point contacts. At each of the candidate points, two gap functions are introduced. However, in the proposed method, not the values of these gap functions but the relations between them are essential. In view of the non-colliding contacts being predominant when clearances of joints are tiny, we formulate the contact forces in terms of resultant frictional forces in the joint, resulting in a linear complementarity problem. By the proposed method, details about the contacts including the impact instants can be obtained, although impacts are not taken into consideration explicitly, as indicated by the numerical examples in this paper.     

Elasto-plastic contact stress analysis of joints subjected to cyclic loading

Rigorous elastic-plastic finite element analysis of joints subjected to cyclic loading is carried out. An incremental-iterative algorithm is developed in a modular form combining elasto-plastic material behaviour and contact stress analysis. For the case of the interference fit, the analysis sequentially carries out insertion of the pin and application of the load on the joint, covering possible initiation of separation (and/or yielding) and progressively the receding/advancing contact at the pin-plate interface. Deformations of both the plate and the pin are considered in the analysis. Numerical examples are presented for the case of an interference fit pin in a large plate under remote cyclic tension, and for an interference fit pin lug joint subjected to cyclic loading. A detailed study is carried out for the latter problem considering the effect of change in contact/separation at the pin-plate interface on local stresses, strains and redistribution of these stresses with the spread of a plastic zone. The results of the study are a useful input for the estimation of the fatigue life of joints.