Analytical modelling for static stress analysis of pin-loaded lugs with bush fitting

Pin-loaded connections are widely used in the industry. Connecting rods of reciprocating engines in automotive applications or pin-loaded lugs of landing gears and airframe structures can be cited as examples. These systems are subject to thermomechanical cyclic loadings and fatigue mechanisms are often observed. The calculation of stresses in the lug is crucial in view of a fatigue lifetime analysis. Analytical modelling may be very helpful in the early design stage, by allowing fast parametric studies and the identification of the most influent parameters on the response in stresses. In this paper, we propose analytical models for bush fitting and pin-loading conditions, leading to the complete calculation of the stress distribution in the lug. In each case, the analytical solutions are compared with finite element simulations. In the last part, we perform a sensitivity analysis as an application of the presented analytical tools.     

Dynamical and statistical properties of a rotating oval billiard

Some dynamical and statistical properties of a time-dependent rotating oval billiard are studied. We considered cases with (i) positive and (ii) negative curvature for the boundary. For (i) we show the system does not present unlimited energy growth. For case (ii) however the average velocity for an ensemble of noninteracting particles grows as a power law with acceleration exponent well defined. Finally, we show for both cases that after introducing time-dependent perturbation, the mixed structure of the phase space observed for static case is recovered by making a suitable transformation in the angular position of the particle.     

Bending analysis of a functionally graded rotating disk based on the first order shear deformation theory

The theoretical formulation for bending analysis of functionally graded (FG) rotating disks based on first order shear deformation theory (FSDT) is presented. The material properties of the disk are assumed to be graded in the radial direction by a power law distribution of volume fractions of the constituents. New set of equilibrium equations with small deflections are developed. A semi-analytical solution for displacement field is given under three types of boundary conditions applied for solid and annular disks. Results are verified with known results reported in the literature. Also, mechanical responses are compared between homogeneous and FG disks. It is found that the stress couple resultants in a FG solid disk are less than the stress resultants in full-ceramic and full-metal disk. It is observed that the vertical displacements for FG mounted disk with free condition at the outer surface do not occur between the vertical displacements of the full-metal and full-ceramic disk. More specifically, the vertical displacement in a FG mounted disk with free condition at the outer surface can even be greater than vertical displacement in a full-metal disk. It can be concluded from this work that the gradation of the constitutive components is a significant parameter that can influence the mechanical responses of FG disks.     

Exact solution for rotating flows of a generalized Burgers’ fluid in a porous space

This article considers the oscillatory flows of a generalized Burgers’ fluid on an infinite insulating plate when the fluid is permeated by a transverse magnetic field. The effects of Hall current are taken into account. Modified Darcy’s law for a generalized Burgers’ fluid has been used to discuss the flows in a porous medium. The governing time dependent equations in a rotating frame are first developed and then solved for the two problems. The influence of various emerging parameters is discussed through various graphs. The solutions for the Newtonian, second grade, Maxwell, Oldroyd-B and Burgers’ fluids can be obtained from our solutions as the limiting cases.     

Stresses of a rotating circular disk of variable thickness carrying a current and bearing a coaxial viscoelastic coating

In the present work we consider a circular elastic disk (conductor) of variable thickness under the influence of a steady coaxial current and bearing a coaxial viscoelastic coating (insulator). In both conductor and insulator there exist a heat source generation. As a first step, the solution of purely elastic conductor and insulator is obtained. Then the problem of model with viscoelastic coating is solved using the correspondence principle and Ilyushin’s approximation method. A numerical example is given and the results are discussed in order to investigate the influences of time, temperature, and rotation on the stresses and displacements.     

Couette flow of a third grade fluid with rotating frame and slip condition

An incompressible third grade fluid occupies the porous space between two rigid infinite plates. The steady rotating flow of this fluid due to a suddenly moved lower plate with partial slip of the fluid on the plate is analysed. The fluid filling the porous space between the two plates is electrically conducting. The flow modeling is developed by employing a modified Darcy’s law. A numerical solution of the governing problem consisting of a non-linear ordinary differential equation and non-linear boundary conditions is obtained and discussed. Several limiting cases of the arising problem can be obtained by choosing suitable parameters.     

Stabilization and optimal decay rate for a non-homogeneous rotating body-beam with dynamic boundary controls

In this paper, we consider the boundary stabilization of a flexible beam attached to the center of a rigid disk. The disk rotates with a non-uniform angular velocity while the beam has non-homogeneous spatial coefficients. To stabilize the system, we propose a feedback law which consists of a control torque applied on the disk and either a dynamic boundary control moment or a dynamic boundary control force or both of them applied at the free end of the beam. By the frequency multiplier method, we show that no matter how non-homogeneous the beam is, and no matter how the angular velocity is varying but not exceeding a certain bound, the nonlinear closed loop system is always exponential stable. Furthermore, by the spectral analysis method, it is shown that the closed loop system with uniform angular velocity has a sequence of generalized eigenfunctions, which form a Riesz basis for the state space, and hence the spectrum-determined growth condition as well as the optimal decay rate are obtained.     

Heat and mass transfer investigation of rotating hydrocarbons droplet which behaves as a hard sphere

The steady state boundary layer equations around rotating pure hydrocarbon droplet are solved numerically. The droplet is simulated to behave as a hard sphere. The transfer equations are discretized using an implicit finite difference method where Thomas algorithm solves the system of algebraic equations. Moreover, dimensionless parameters of heat and mass transfer phenomena around a rotating hexane droplet concluded. The thickness of the boundary layer is unknown for this model and therefore, it is determined. Further, this work proposes correlations of Nusselt and Sherwood numbers for monocomponent hydrocarbon droplets in evaporation. These correlations consider the rotation phenomena and further, the variation of the thermophysical and transport properties in the vapour phase.     

Hamiltonian restriction of Vlasov equations to rotating isopycnic and isentropic two-layer equations

A direct link between a Vlasov equation and the equations of motion of a rotating fluid with an effective pressure depending only on a pseudo-density is illustrated. In this direct link, the resulting fluid equations necessarily appear in flux conservative form when there are no topographical and rotational terms. In contrast, multilayer isopycnic and isentropic equations used in atmosphere and ocean dynamics, in the absence of topographical and rotational terms, cannot be brought into a conservative flux form, and, hence, cannot be derived directly from the Vlasov equations. Another route is explored, therefore: deriving the Hamiltonian formulation of the two-layer isopycnic and isentropic equations as a restriction from a Hamiltonian formulation of two decoupled Vlasov equations. The work is motivated by our search for energy-preserving or even Hamiltonian (kinetic) numerical schemes.     

Contact inhibition of growth described using a multiphase model and an individual cell based model

In this work the phenomenon of contact inhibition of growth is studied by applying an individual based model and a continuum multiphase model to describe cell colony growth in vitro. The impact of different cell behavior in response to mechanical cues is investigated. The work aims at comparing the results from both models from the qualitative and, whenever possible, also the quantitative point of view.     

Development of a model for a two-station serial transfer line subject to machine and buffer failure

In modern automated production lines, it is common to connect pairs of machines with mechanical storage devices in order to provide buffering between processing stations. Since these devices are mechanical, they are prone to failure. Previous research concerning the analytical modeling of a class of production lines, the serial transfer line, assumes that these buffers are completely reliable. The concept of an unreliable buffer is introduced and an analytic model of a two machine line with an unreliable buffer is developed. It is proposed that this model will form the foundation for an analytic model of the more complex K > 2 machine serial transfer line with unreliable buffers.     

Contact problem for a thin elastic layer with variable thickness: Application to sensitivity analysis of articular contact mechanics

In the framework of the recently developed asymptotic models for tibio-femoral contact incorporating frictionless elliptical contact interaction between thin elastic, viscoelastic, or biphasic cartilage layers, we apply an asymptotic modeling approach for analytical evaluating the sensitivity of crucial parameters in joint contact mechanics due to small variations in the thicknesses of the contacting cartilage layers. The four term asymptotic expansion for the normal displacement at the contact surface is explicitly derived, which recovers the corresponding solution obtained previously for the 2D case in the compressible case. It was found that to minimize the influence of the cartilage thickness non-uniformity on the force–displacement relationship, the effective thicknesses of articular layers should be determined from a special optimization criterion.     

Stress analysis of a truck chassis with riveted joints

In this study, stress analysis of a truck chassis with riveted joints was performed by using FEM. The commercial finite element package ANSYS version 5.3 was used for the solution of the problem. Determination of the stresses of a truck chassis before manufacturing is important due to the design improvement. In order to achieve a reduction in the magnitude of stress near the riveted joint of the chassis frame, side member thickness, connection plate thickness and connection plate length were varied. Numerical results showed that stresses on the side member can be reduced by increasing the side member thickness locally. If the thickness change is not possible, increasing the connection plate length may be a good alternative.     

Gearbox failure diagnosis based on vector autoregressive modelling of vibration data and dynamic principal component analysis

Email: mgt.liu{at}utoronto.ca Email: makis{at}mie.utoronto.ca Received on 4 August 2006. Accepted on 14 December 2006. An effective gearbox failure diagnosis helps prevent catastrophicgearbox failure and can contribute to significant economic benefits.This paper proposes a gear failure diagnosis method based onvector autoregressive modelling of high-frequency vibrationdata, dimensionality reduction applying dynamic principal componentanalysis (PCA) and condition monitoring using a multivariatecontrol chart. After extracting useful information from thevibration data obtained from distinct directions via dynamicPCA, a failure diagnosis scheme is implemented and tested usingreal gearbox vibration data. It is shown that the failure diagnosisscheme can indicate the gear teeth failure pattern when thegear is damaged, which has not been demonstrated in the previousstudies. For a comparison, PCA is applied to the same data set.The results show that the advantages of dynamic PCA over PCAfor failure diagnosis using vibration data consist not onlyin indicating more accurately the occurrence of incipient faultand the actual gear condition, but also in a much lower falsealarm rate.     

Effects of radiation and variable viscosity on unsteady MHD flow of a rotating fluid from stretching surface in porous medium

This work is focused on the study of unsteady magnetohydrodynamics boundary-layer flow and heat transfer for a viscous laminar incompressible electrically conducting and rotating fluid due to a stretching surface embedded in a saturated porous medium with a temperature-dependent viscosity in the presence of a magnetic field and thermal radiation effects. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. With appropriate transformations, the unsteady MHD boundary layer equations are reduced to local nonsimilarity equations. Numerical solutions of these equations are obtained by using the Runge–Kutta integration scheme as well as the local nonsimilarity method with second order truncation. Comparisons with previously published work have been conducted and the results are found to be in excellent agreement. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity in primary and secondary flows as well as the local skin-friction coefficients and the local Nusselt number are illustrated graphically to show interesting features of Darcy number, viscosity-variation, magnetic field, rotation of the fluid, and conduction radiation parameters.     

Modelling the bending behaviour of a new hybrid glulam beam reinforced with FRP and ultra-high-performance concrete

The main objective of this research project to develop a new type of hybrid glulam beam that will increase the performance of a timber structural element by combining it with ultra-high-performance concrete with short fibre reinforcement (UHPC-SFR). The hybrid beam is obtained is a layered structures obtained by combining a glued-laminated (glulam) wood beam with UHPC-SFR lamellae that is bonded to its top and bottom faces. The obtained hybrid beam possesses a lower bending stiffness than a glulam beam of similar overall dimensions but has a higher ultimate load capacity. Two models that were developed to validate this concept are presented in this paper. The first is an analytical model based on hypotheses related to the usual strength of materials, and the second is a finite element model. The load–displacement and moment–curvature relationships from both models are compared to the experimental results obtained from the large-scale specimens. The results show good correlation between the analytical modelling and experimental results and illustrate the potential applications of such composite beam configurations for civil engineering structures.     

Performance analysis of a batch service queue arising out of manufacturing system modelling

In this paper, we present an exact analysis of a queueing system with Poisson arrivals and batch service. The system has a finite numberS of waiting places and a batch service capacityb. A service period is initialized when a service starting thresholda of waiting customers has been reached. The model is denoted accordingly byM/G ^[a,b] /1–S. The motivation for this model arises from manufacturing environments with batch service work stations, e.g. in machines for computer components and chip productions. The method of embedded Markov chain is used for the analysis, whereby a representation of the general service time is obtained via a moment matching approach. Numerical results are shown in order to illustrate the dependency of performance measures on special sets of system parameters. Furthermore, attention is devoted to the issues of starting rules, where performance objectives like short waiting time, small blocking probability and minimal amount of work in progress are taken into account.     

Modelling and analysis of a non-regular electronic circuit via a variational inequality formulation

In this paper, we present a new and alternative mathematical modelling and analysis methodology for a class of non-regular electronic circuits through a rectifier-stabilizer circuit using the superpotentiel of Moreau and the theory of variational inequalities. This methodology is suitable for engineers to study a large class of applications.