Development of special fastener elements

A special finite element (FASNEL) is developed for the analysis of a neat or misfit fastener in a two-dimensional metallic/composite (orthotropic) plate subjected to biaxial loading. The misfit fasteners could be of interference or clearance type. These fasteners, which are common in engineering structures, cause stress concentrations and are potential sources of failure. Such cases of stress concentration present considerable numerical problems for analysis with conventional finite elements. In FASNEL the shape functions for displacements are derived from series stress function solutions satisfying the governing difffferential equation of the plate and some of the boundary conditions on the hole boundary. The region of the plate outside FASNEL is filled with CST or quadrilateral elements. When a plate with a fastener is gradually loaded the fastener-plate interface exhibits a state of partial contact/separation above a certain load level. In misfit fastener, the extent of contact/separation changes with applied load, leading to a nonlinear moving boundary problem and this is handled by FASNEL using an inverse formulation. The analysis is developed at present for a filled hole in a finite elastic plate providing two axes of symmetry. Numerical studies are conducted on a smooth rigid fastener in a finite elastic plate subjected to uniaxial loading to demonstrate the capability of FASNEL.     

An improved iterative finite element solution for pin joints

Accurate, reliable and economical methods of determining stress distributions are important for fastener joints. In the past the contact stress problems in these mechanically fastened joints using interference or push or clearance fit pins were solved using both inverse and iterative techniques. Inverse techniques were found to be most efficient, but at times inadequate in the presence of asymmetries. Iterative techniques based on the finite element method of analysis have wider applications, but they have the major drawbacks of being expensive and time-consuming. In this paper an improved finite element technique for iteration is presented to overcome these drawbacks. The improved iterative technique employs a frontal solver for elimination of variables not requiring iteration, by creation of a dummy element. This automatically results in a large reduction in computer time and in the size of the problem to be handled during iteration. Numerical results are compared with those available in the literature. The method is used to study an eccentrically located pin in a quasi-isotropic laminated plate under uniform tension.     

Non-linear finite element analysis of flexible pavements

A research study is being undertaken to incorporate the realistic material properties of the pavement layers and the moving traffic load, in the analysis of flexible pavements, using the finite element theory. As a preliminary step taken herein in this direction, a pavement structure where field measurements have been carried out when subjected to a cyclic loading, is selected and modelled as a finite element model. The analysis is being carried out using the finite element computer package ABAQUS/STANDARD, when this pavement model is subjected to static and cyclic loading while considering the linear and non-linear material properties of the pavement layers. The results indicate that displacements under cyclic loading when non-linear materials are present, are the closest to field measured deflections.     

Finite element analysis and contact modelling considerations of interference fits for fretting fatigue strength calculations

This paper presents a 3D finite element study of an interference fit assembly subjected to bending. The results accuracy and the solution convergence are governed by mesh size and contact algorithms options. Their influences were investigated to evaluate displacements and stresses near the contact edge where fretting fatigue failure occurs. Four contact algorithms were tested: Penalty function, Augmented Lagrangian, Normal Lagrange and Pure Lagrange. Performance criteria such as precision and time were highlighted and specific convergence control parameters were found. Finally, best practice rules for interference fit FEA are specified.     

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.     

Design of experiments and energy dissipation analysis for a contact mechanics 3D model of frictional bolted lap joints

Bolted lap joints allow structural assemblies to be made. The answer to requirements, both static and dynamic, depends on the joint behaviour. Bolted joints are a primary source of energy dissipation in dynamic built-up and space structures among others. This paper presents an analysis of a bolted lap joint, subjected to a relative displacement after applying a pre-stress on the bolt in order to characterise the joint behaviour. For this purpose a 3D modelling is made by means of finite elements, using design techniques of experiments (DOE) to fit constitutive contact parameters. The theoretical results relative to elasto-plastic hysteresis cycles of the joint are experimentally validated. Finally, the preload effect and the magnitude of the displacement on the non-linear joint behaviour are analysed to determine equivalent stiffness and dissipated energy in the hysterical loops of the joint.     

A mixed computational algorithm for plane elastic contact problems—I. formulation

A mixed variational statement and corresponding finite element model are developed for an arbitrary plane body undergoing large deformations (i.e. large displacements, large rotations and small strains) under external loads using the updated Lagrangian formulation. The mixed finite element formulation allows the nodal displacements and stresses to be approximated independently. Two different contact algorithms are presented for the separate cases of a thin plate in contact with a rigid pin and a flexible pin, and the algorithms account for the computational difficulties that arise from the unknown contact area and the presence of friction between the pin and the plate.     

平面联接固定结合部动力学模型的一种建模方法

机械结构结合部精确建模是对含结合部的机械结构进行动态分析和优化设计的关键问题之一。文章主要研究块体结构和平板由螺栓联接后构成的固定结合部的动力学建模问题。将结合部区域的刚度特性用结合部的材料机械特性参数等效表达,提出了虚拟接触材料的结合部刚度表达模型。通过模态实验和模型修正识别出不同结合面工况下虚拟接触材料的弹性模量,建立了含结合部动力特性的有限元模型。该模型可方便用于含结合部结构的有限元计算,经试验验证满足实际工程应用要求。     

An iterative procedure for finite-element stress analysis of frictional contact problems

A simple, efficient, versatile and easily adaptable, iterative finite-element technique is described for solving frictional contact problems. The method is based on logical steps to establish the contact geometry and regions of slip and nonslip. Unlike previous techniques, the approach can be extended readily to multiple contact surfaces. The scheme is demonstrated by analyzing a mechanical joint in orthotropic wood. In this case, mixed coordinate systems are used to enhance accuracy of the stresses near the pin contact region. The numerically computed values agree with those reported elsewhere.     

A Continuous Analysis Method for Planar Multibody Systems with Joint Clearance

Clearance from manufacturing tolerances or wear is likely to degrade the dynamic performance of connected machine parts. When joint clearance is introduced, the dynamic response of the mechanical system is substantially changed, seen as high acceleration and force peaks and dissipation of energy. Looking at contact models, the simpler ones, such as the linear Kelvin–Voigt or the nonlinear Hertz model, are characterized by a set of parameters. These include material parameters, coefficient of restitution and possibly a coefficient of friction. The analysis models can be divided into two groups – continuous and dis-continuous, related to whether integration is carried out through the period of contact, or stopped and restarted after the impact.Based on the equations of motion for a multibody system of rigid bodies, it is suggested that the continuous analysis approach is combined with a contact force model to describe joint clearance in rotational joints. Performing simulations with this methodology allows not only to quantify the overall mechanism behaviour, but also in-depth analysis of the impact mechanics in the clearance joint. Experimental data from a double pendulum impacting a rigid plate is used to verify the suggested continuous analysis method.     

Aspects of soil-structure-water interaction problems

The application of numerical methods, the finite element, the finite difference and dynamic relaxation, for the solution of problems in soil-structure interaction is considered. Some results of centre line stresses, contact and radial stresses are given for a plate of variable stiffness resting on a non-homogeneous elastic half-space. The paper discusses recent developments on the analysis of foundations, joints and fluid systems. The development of a fluid element for the analysis of fluid-solid systems and a new free-field element for earthquake analysis is presented. The introduction of relative displacements in the equilibrium equations of interface elements is also described.     

Applicability of stress–force–fabric relationship for non-proportional loading

Starting from the micro-structural definition of the stress tensor, Rothenburg and Bathurst (1989) [1] derived a stress–force–fabric relationship for granular materials by approximating the directional distributions of the fabric, more specifically, the contact normal density distribution in this paper and the contact forces with Fourier functions and integrating over directions. This paper aims to assess the validity of the two key assumptions made during their derivation using particle-based numerical simulation in the cases of proportional loading and non-proportional loading. These two assumptions are (i) the 2nd-rank Fourier functions adopted are good enough to approximate the directional distributions of contact normal densities and contact forces and (ii) the principal directions of contact forces and contact normal density are coaxial. Numerical simulations have been carried out to conduct virtual experiments on the behaviour of isotropic specimens to monotonic loading, of isotropic specimens to stress rotation, and of anisotropic specimens to monotonic loading. The first one stands for the case of proportional loading while the latter two are non-proportional loading paths involving rotation of the frame of principal stresses and the frame of fabric, respectively. The directional distributions of contact normal density and contact forces are traced during these three typical loading processes. The simulation results indicate that the 2nd-rank Fourier functions give reasonable approximations, while the coaxial assumption is generally not valid in non-proportional loading. In the case that the principal directions of contact normal density and contact force differ, a more general expression of the stress–force–fabric relationship is required. This research can help to improve our understanding of the stress state and hence shear strength of granular materials based on the particle scale investigation.     

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.     

膝关节矢状面接触分析的研究

软骨给膝关节提供了一种摩擦系数比最好的人工材料要低许多倍的低摩擦抗磨损的支撑面,而且会减小下面胫骨的接触应力.为了了解和比较软骨在正常情况下和病理状态下的相关生物力学机理,建立了矢状面上包含胫股和膑股关节的膝关节二维有限元接触模型,认为模型所有组成部件都为弹性体,运用有限元方法求解了膝关节屈曲过程中矢状面上股骨与胫骨接触过程中有无覆盖软骨层对应力及接触面积的变化.结果表明由于自然关节覆盖着软骨层,在屈膝过程中增大了股胫关节的接触线,减小了股骨屈膝所需要的力矩和胫骨应力.从力学角度解释了膝关节软骨对膝关节的保护作用,从而更加真实地描述了膝关节的力学接触机制.     

Formulation of a Class of Higher Pair Joints in Multibody Systems Using Joint Coordinates

This paper describes the development of general formulations of higher pair joints in multibody systems. A class of higher pair joints, described as a spatial point contact between the surfaces of two interacting bodies is formulated by means of Joint Coordinate Formulation and implemented in a general purpose multibody analysis program. The joint is formulated as remaining within the reduced open loop system according to the notation applied in the Joint Coordinate Method. This representation necessitates an evaluation of the degrees of freedom in the joint. Based on these considerations, the point contact joint is also formulated to cut a loop in the mechanical system. In this case, the appropriate constraint equations and a set of artificial variables are introduced in the analysis. The surfaces in the point contact joint are represented as parametric cubic spline patches but can also be introduced using other methods. Examples illustrating the implemented types of joints are presented at the end of the paper.     

Investigation of joint clearance effects on the dynamic performance of a planar 2-DOF pick-and-place parallel manipulator

In this study, the effects of joint clearance on the dynamic performance of a planar 2-DOF pick-and-place parallel manipulator are investigated. The parallel manipulator is modeled by multi-body system dynamics. The contact effect in revolute joints with clearance is established by using a continuous analysis approach that is combined with a contact force model considering hysteretic damping. The evaluation of the contact force is based on Hertzian contact theory that accounts for the geometrical and material properties of the contacting bodies. Furthermore, the incorporation of the friction effect in clearance joints is performed using a modified Coulomb friction model. By numerical simulation, variations of the clearance joint's eccentric trajectory, the joint reaction force, the input torque, the acceleration, and trajectory of the end-effector are used to illustrate the dynamic behavior of the mechanism when multiple clearance revolute joints are considered. The results indicate that the clearance joints present two obvious separation leaps in a complete pick-and-place working cycle of the parallel manipulator, following a collision. The impact induces system vibration and thus reduces the dynamic stability of the system. The joint clearances affect the amplitudes of the joint reaction force, the input torque, and the end-effector's acceleration, additionally the joint clearances degrade the kinematic and dynamic accuracy of the manipulator's end-effector. Finally, this study proposes related approaches to decrease the effect of joint clearances on the system's dynamic properties for such parallel manipulator and prevent “separation-leap-impact” events in clearance joints.     

基于塑性修正系数的矩形薄板屈曲计算方法

为探究薄板的屈曲破坏性能,以飞机机身设计中最常用的铝合金薄板结构为研究对象,利用金属材料塑性修正系数分析矩形薄板的屈曲失效,得到在均布压力和不同约束条件下矩形薄板的临界屈曲应力。数值仿真算例及其有限元计算结果对比,验证该方法的正确性。     

Pattern optimization of eccentrically loaded multi-fastener joints

For structural joints subject to dynamic loading, the fatigue strength is controlled by local stresses. For steel plate structures joined with fasteners, fatigue is governed by local friction and slip near the fasteners. As a working hypothesis for this study, a “weakest link” approach has been adopted. An optimum fastener pattern is attained by reducing the shear load in the most severely loaded fastener in the group. In this study, a typical eccentric multi-fastener bracket-to-beam joint was studied using constrained geometric optimization. Alternate assumptions concerning the distribution of the direct shear force between fasteners in a group were assessed. An analytical expression for non-uniform direct shear force resulted in an optimized fastener pattern with approximately 20% lower von Mises equivalent strain. The comparative finite element method based topology optimization analysis resulted in a contour, which was in close agreement with the fastener pattern attained analytically by exploiting geometry optimization.     

Finite element analysis of a laminated composite plate subjected to circularly distributed central impact loading

A two dimensional finite element analysis has been made for a fiber-reinforced composite laminate subjected to circularly distributed impact load which results, for example, from impacting the plate with a blunt-ended projectile. A finite element displacement model which includes the effects of transverse shear deformation and rotary inertia was used along with Hamilton's principle to derive the finite element matrices. Newmark's direct integration technique was used to integrate with respect to time. The interaction force between the projectile and the plate was calculated by using the Hertzian law of contact. Results for laminate deformations are shown to compare quantitatively with experimental results. Numerical values for stresses in the plate were calculated.     

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.