An approximate analysis of non-linear non-conservative systems subjected to step function excitation

This paper deals with the approximate analysis of the step response of non-linear nonconservative systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on ultraspherical polynomial expansions. The Krylov-Bogoliubov results are given by a particular set of these polynomials. The method has been applied to study the step response of a cubic spring mass system in presence of viscous, material, quadratic, and mixed types of damping. The approximate results are compared with the digital and analogue computer solutions and a close agreement has been found between the analytical and the exact results.

Analysis of Long Cantilever Cylindrical Shell Subjected to Wind Loading

Bending analysis of closed cylindrical shells subjected to asymmetric load and having different support conditions is of interest in the design of chimneys, water towers, oil storage tanks, etc. A simple method of analyzing a long cantilever cylindrical shell, subjected to asymmetric load, is presented in the paper, using Schorer’s shell theory and orthogonal functions. The application of the solution has been illustrated with an example of a cantilever shell subjected to wind loads. The results obtained for this problem have been compared with the previously available results to illustrate the accuracy of the results obtained here. The solution presented can also be extended to a cylindrical shell with other support conditions, as well as to the study of free vibration of a cylindrical shell. The present solution will be very useful for designers who need to obtain numerical results for specific problems with minimum computational effort.

On the investigation of singular stress field around radial cracks in annulii subjected to diametrical tension

Results of photoelastic investigation conducted on annulii containing a radial crack at inner edge and subjected to diametrical tension are reported. The cracks are oriented at 90°, 60° and 45° to the loading direction. The Stress-Intensity Factors (SIFs) were determined by analysing the crack-tip stress fields. Smith and Smith's method [Engng Fracture Mech.4, 357–366 (1972)] and a modified method developed earlier by the authors (to be published) were adopted in the evaluation of SIFs.

Stress intensity factor determination of radially cracked circular rings subjected to tension using photoelastic technique

A parametric study was carried out to determine the Stress Intensity Factor (SIF) in a cracked circular ring by using the photoelastic technique. The stress intensity factors for mode I deformation were determined by subjecting the specimens to the tensile loading from inner boundary and through the holes. The results of Non-Dimensional Stress Intensity Factor (NDSIF) variation with non-dimensional crack length for both methods of loading are compared with each other and with published results.

Deformation and failure of a film/substrate system subjected to spherical indentation: Part 1. Experimental validation of stresses and strains derived using Hankel transform technique in an elastic film/substrate system

Our concern here is to rationalize experimental observations of failure modes brought about by indentation of hard thin ceramic films deposited on metallic substrates. By undertaking this exercise, we would like to evolve an analytical framework that can be used for designs of coatings. In Part I of the paper we develop an algorithm and test it for a model system. Using this analytical framework we address the issue of failure of columnar TiN films in Part II [J. Mater. Res. 21, 783 (2006)] of the paper. In this part, we used a previously derived Hankel transform procedure to derive stress and strain in a birefringent polymer film glued to a strong substrate and subjected to spherical indentation. We measure surface radial strains using strain gauges and bulk film stresses using photo elastic technique (stress freezing). For a boundary condition based on Hertzian traction with no film interface constraint and assuming the substrate constraint to be a function of the imposed strain, the theory describes the stress distributions well. The variation in peak stresses also demonstrates the usefulness of depositing even a soft film to protect an underlying substrate.

Analysis of a thick plate with a circular hole resting on a smooth rigid bed and subjected to axisymmetric normal load

A solution for the stresses and displacements in an radially infinite thick plate having a circular hole, one face of which resting on a smooth rigid bed and the other face subjected to axisymmetric normal loading is given. The solution is obtained in terms of Fourier-Bessel series and integral for the Love's stress function. Numerical results are presented for one particular ratio of thickness of plate to the hole radius and loading. It is also shown that the Poisson's ratio has a predominant effect on certain stresses and displacements. The solution would be useful in the stress analysis of bolted joints.Eine Lösung für die Spannungen und Verschiebungen in einer radial, unendlich ausgedehnten, dicken Platte mit einem kreisförmigen Loch, wobei eine Seite auf einer ebenen, starren Unterlage aufliegt, die andere Seite durch eine achsensymmetrische Vertikallast belastet ist, wird angegeben. Die Lösung wird in Form von Fourier-Bessel-Reihen und Integralen der Loveschen Spannungsfunktion angegeben. Numerische Ergebnisse werden für ein bestimmtes Verhältnis der Plattendicke zum Lochradius sowie zur Belastung angegeben. Es wird auch gezeigt, daß das Poisssonsche Verhältnis einen besonderen Einfluß auf bestimmte Spannungen und Verschiebungen hat. Die Lösung ist anwendbar für die Spannungsermittlung von Bolzenverbindungen.

Numerical estimation of hotspot temperatures in electrodes subjected to pulsed electron beam heating in vacuum

A numerical solution for the transient temperature distribution in a cylindrical disc heated on its top surface by a circular source is presented. A finite difference form of the governing equations is solved by the Alternating Direction Implicit (ADI) time marching scheme. This solution has direct applications in analyzing transient electron beam heating of target materials as encountered in the prebreakdown current enhancement and consequent breakdown in high voltage vacuum gaps stressed by alternating and pulsed voltages. The solution provides an estimate of the temperature for pulsed electron beam heating and the size of thermally activated microparticles originating from anode hot spots. The calculated results for a typical 45kV (a.c.) electron beam of radius 2.5 micron indicate that the temperature of such spots can reach melting point and could give rise to microparticles which could initiate breakdown.

On determining the elastic modulus of a cylindrical sample subjected to flexural excitation in a resonant column apparatus

For resonant column tests conducted in the flexure mode of excitation, a new methodology has been proposed to find the elastic modulus and associated axial strain of a cylindrical sample. The proposed method is an improvement over the existing one, and it does not require the assumption of either the mode shape or zero bending moment condition at the top of the sample. A stepwise procedure is given to perform the necessary calculations. From a number of resonant column experiments on aluminum bars and dry sand samples, it has been observed that the present method as compared with the one available in literature provides approximately (i) 5.9%-7.3% higher values of the elastic modulus and (ii) 6.5%-7.3% higher values of the associated axial strains.

The inelastic vibration absorber subjected to earthquake ground motions

Two storey bilinear hysteretic structures have been studied with a view to exploring the possibility of using the dynamic vibration absorber concept in earthquake-resistant design. The response of the lower storey has been optimized for the Taft 1952, S69°E accelerogram with reference to parameters such as frequency ratio, yield strength ratio and mass ratio. The influence of viscous damping has also been examined.

Thermomechanical behaviour of pin joints subjected to sheet loads

An important problem regarding pin joints in a thermal environment is addressed. The motivation emerges from structural safety requirements in nuclear and aerospace engineering. A two-dimensional model of a smooth, rigid misfit pin in a large isotropic sheet is considered as an abstraction. The sheet is subjected to a biaxial stress system and far-field unidirectional heat flow. The thermoelastic analysis is complex due to non-linear load-dependent contact and separation conditions at the pin-hole interface and the absence of existence and uniqueness theorems for the class of frictionless thermoelastic contact problems. Identification of relevant parameters and appropriate synthesis of thermal and mechanical variables enables the thermomechanical generalization of pin-joint behaviour. This paper then proceeds to explore the possibility of multiple solutions in such problems, especially interface contact configuration.

Microstructure evolution and hardness variation during annealing of equal channel angular pressed ultra-fine grained nickel subjected to 12 passes

The microstructure, thermal stability and hardness of ultra-fine grained (UFG) Ni produced by 12 passes of equal channel angular pressing (ECAP) through the route Bc were studied. Comparing the microstructure and hardness of the as-ECAPed samples with the published data on UFG Ni obtained after 8 passes of ECAP through the route Bc reveals a smaller average grain size (230 nm in the present case compared with 270 nm in 8-pass Ni), significantly lower dislocation density (1.08 x 10(14) m(-2) compared with 9 x 10(14) m(-2) in 8-pass Ni) and lower hardness (2 GPa compared with 2.45 GPa for 8-pass Ni). Study of the thermal stability of the 12-pass UFG Ni revealed that recovery is dominant in the temperature range 150-250A degrees C and recrystallisation occurred at temperatures > 250 A degrees C. The UFG microstructure is relatively stable up to about 400 A degrees C. Due to the lower dislocation density and consequently a lower stored energy, the recrystallisation of 12-pass ECAP Ni occurred at a higher temperature (similar to 250 A degrees C) compared with the 8-pass Ni (similar to 200 A degrees C). In the 12-pass Nickel, hardness variation shows that its dependence on grain size is inversely linear rather than the common grain size(-0.5) dependence.

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. Copyright (C) 1996 Elsevier Science Ltd

Study of fracture features in foam bearing glass epoxy composites subjected to repeated impacts

The paper reports the failure features observed in low mass repeatedly (pendulum) impacted glass epoxy composites with and without the mid section having either 2-layers or 3-layers of flexible foam. Features such as through width and inclined cracks as well as adhering of foam observed in the experiments are explained. The significance of the foam material in modifying the impact response of the composite is stressed.

The role of the interface in foam-bearing glass-epoxy composites subjected to impact loading

foam, either stacked together as three layers (MC) or inserted at three different positions (3L) while arranging the stacking sequence during the fabrication of glass fiber-epoxy composites, form the subject of investigation. This stacking variation resulted in a different interfacial area between these foam materials and the glass-epoxy regions in the laminates. This area in designed to be maximum for the 3L variety. The energy of impact being high enough to cause development of the crack in the samples, how the change in interfacial area affects the traverse of the crack front and the failure feature of the laminated composite are reported in the form of photomacrographs in this work. The results point to significant changes for the impact data, like for instance the peak load attained by the different samples, through thickness crack propagation and tensile fracture features on the non-impacted end for the plain variety, separation about the mid-zone for the MC laminates and two or more layer separations for the 3L variety. The separation for the foam-bearing systems occur invariably at the interface and here again one of the (two identical) interfaces only is chosen for the separation.