Eigenfrequency changes of structures due to cracks,notches or other geometrical changes

A first order perturbation method is presented which predicts the changes in resonance frequencies of a structure resulting from cracks, notches or other geometrical changes. The eigenfrequency changes due to a crack are shown to be dependent on the strain energy of a static solution which is easily obtainable for small cracks and other small cut-outs. The method has been tested for three different cases, and the predicted results correlate very closely to experimental and numerical results.     

Shape bifurcation of an elastic wafer due to surface stress

IntroductionSurfacestressisresponsibleformanymesoscopicalphenomenainmaterialsandthushasbeenstudiedextensively[1～ 5 ].Althoughtheabsolutevalueofsurfacestressofasolidcurrentlycannotbeobtainedbyexperiments,themethodformeasuringitschangehasbeenwellestablished .Theprincipleisratherclear.Whenthesurfacestressononesurfaceofawafer,eitherfreestandingorclampedatoneend ,changesduetocertainreasonssuchasadsorption ,thedifferencebetweenthesurfacestressonthissurfaceandthatontheoppositeoneresultsinabendingmom…     

Heat transfer to non-Newtonian fluids in laminar flow through concentric annuli with or without suction

Rheologica Acta - In this paper we have investigated the heat transfer aspects of the flow of a power law fluid in an annulus with porous walls. The case of no suction (solid walls annulus) is also...     

On energy changes due to the formation of a circular hole in an elastic plate

The appearance of holes in crystals, developed in stressed biological structures, has motivated us to study the energy release of an initially undisturbed plate subjected to a biaxial stress state which is disturbed by a growing hole. An energy balance allows for a kinetic equation of the hole radius a. The main emphasis is placed on the calculation of the total mechanical energy-release rate by different independent concepts. Specifically, path-independent integrals represent the most convenient approach.     

Stress concentration due to an array or hemispherical cavities at the surface of an elastic half-space

The paper investigates the perturbation in an otherwise uniform stress field in an elastic half-space due to a doubly-periodic array of small hemispherical holes at the free surface. The solution is obtained using three potential functions of double Fourier series form in Galerkin's strain potential solution, the coefficients of which are determined using the collocation method. The unperturbed field is taken to be one of uniform plane stress parallel to the free surface. Two special cases are studied—uniform tension and uniform shear stress. Numerical results for these cases can be generalized by superposition to give solutions for a general state of biaxial plane stress. It is found that, for both tension and shear, the maximum stress concentration occurs at the bottom of the holes. The stress concentration factor increases with the ratio of hole spacing to radius, approaching the known solution for a single hemispherical hole at large ratios.     

Evaluation of residual stress in valve disks due to stellite deposition

Experimental Techniques -     

Determination of the turbulent Prandtl number in an asymptotic boundary layer with suction

The problem of heat transfer in a turbulent asymptotic boundary layer with suction is solved in the framework of the monoharmonic model. The flow is one dimensional on the average, which is why it is chosen for investigation. The theoretically determined mean and pulsation characteristics of the flow, in particular the turbulent Prandtl number, agree with the experimental results for a boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 74–79, January–February, 1981.     

Analysis of the stress state due to impulsive loading in cylindrical rods

Summary This study contains an analysis of the state of stress of two coaxial cylindrical rods of different length, subjected to longitudinal impulsive loads. Two different methods of general validity are used, the first based on the one-dimensional theory of longitudinal impact, and the second on finite element procedures which, though well known, have been specifically adapted for the present purpose in a manner which we believe provides a much more complete picture of the state of stress. One of the many problems of current technical interest which can be solved by means of the suggested procedures, i.e., the problem of impact stresses on rotary — percussive hydraulic drills, is dealt with by way of example.

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Sommario Nel lavoro si riferisce sull'analisi degli stati di tensione di due elementi cilindrici coassiali astiformi di diversa lunghezza, soggetti a forze longitudinali di carattere impulsivo. Vengono utilizzate due diverse metodologie di validità generale, l'una basata sulla teoria monodimensionale dell'urto longitudinale e l'altra su noti procedimenti di discretizzazione agli elementi finiti, ma con specifiche procedure all'uopo studiate, pervenendo alla conclusione che questo secondo metodo fornisce un quadro molto più esauriente dello stato di tensione. In via esemplificativa generale, viene affrontato uno dei numerosi problemi tecnicamente attuali, risolubili con l'impiego delle procedure proposte e, specificamente, quello relativo alle sollecitazioni d'urto nelle perforatrici idrauliche a rotopercussione.

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Thickness effect of a thin film on the stress field due to the eigenstrain of an ellipsoidal inclusion

Solutions of the stress field due to the eigenstrain of an ellipsoidal inclusion in the film/substrate half-space are obtained via the Fourier transforms and Stroh eigenrelation equations. Based on the acquired solutions, the effect of a thin film’s thickness on the stress field is investigated with two types of ellipsoidal inclusions considered. The results in this paper show that if the thickness of the thin film increases, its effect on the stress field will become weaker, and can even be neglected. In the end, a guide rule is introduced to simplify the calculation of similar problems in engineering.     

Water waves generated due to initial axisymmetric disturbances in water with an ice-cover

This paper is concerned with the generation of water waves due to prescribed initial axisymmetric disturbances in a deep ocean with an ice-cover modelled as a thin elastic plate. The initial disturbances are either in the form of an impulsive pressure distributed over a certain region of the ice-cover or an initial displacement of the ice-cover. Assuming linear theory, the problem is formulated as an initial-value problem in the velocity potential describing the ensuing motion in the fluid. In the mathematical analysis, the Laplace and Hankel transform techniques have been utilised to obtain the deformation of the ice-covered surface as an infinite integral in each case. The method of stationary phase is used to evaluate the integral for large values of time and distance. Figures are drawn to show the effect of the presence of ice-cover on the wave motion.     

Modeling transients in the mechanical response of copper due to strain path changes

When copper is deformed to large strains its texture and microstructure change drastically, leading to plastic anisotropy and extended transients when it is reloaded along a different strain path. For predicting these transients, we develop a constitutive model for polycrystalline metals that incorporates texture and grain microstructure. The directional anisotropy in the single crystals is considered to be induced by variable latent hardening associated with cross-slip, cut-through of planar dislocation walls, and dislocation-based reversal mechanisms. These effects are introduced in a crystallographic hardening model which is, in turn, implemented into a polycrystal model. This approach successfully explains the flow response of OFHC Cu pre-loaded in tension (compression) and reloaded in tension (compression), and the response of OFHC Cu severely strained in shear by equal channel angular extrusion and subsequently compressed in each of the three orthogonal directions. This new theoretical framework applies to arbitrary strain path changes, and is fully anisotropic.     

Modelling of stresses and strains in bonded concrete overlays subjected to differential volume changes

The differential volume changes between repair material and substrate concrete induces stresses in concrete overlays. These stresses could cause the repair material cracking or the interface delamination, which facilitate the penetration of harmful substances into concrete and hence accelerate the deterioration of concrete overlays. In order to investigate the characteristics of these stresses, an analytical model has been developed based on the plate theory and the assumption of the linear relation between shear stress and slip at the interface. This model is able to calculate the tensile stress in the repair material, shear and normal stresses at the interface and the corresponding strains. With this model, the influence of the interface shear stiffness, the dimension of the concrete overlay, and the elastic moduli of two materials on stresses and strains was studied.     

Unsteady mixed convection flow over stretching sheet in presence of chemical reaction and heat generation or absorption with non-uniform slot suction or injection

The article examines the unsteady mixed convection flow over a vertical stretching sheet in the presence of chemical reaction and heat generation or absorption with non-uniform mass transfer. The unsteadiness is caused by the time dependent free stream velocity varying arbitrarily with time. Non-similar solutions are obtained numerically by solving the coupled nonlinear partial differential equations using the quasilinearization technique in combination with an implicit finite difference scheme. To reveal the tendency of the solutions, typical results for the local skin friction coefficient and the local Nusselt and Sherwood numbers are presented for different values of parameters. The effects of various parameters on the velocity, temperature, and concentration distributions are discussed here. The present numerical results are compared with the previously published work, and the results are found to be in excellent agreement.     

Diffraction of stress waves by a free or reinforced hole in an orthotropic plate

Photoelastic plates made of an orthotropic material are used to model the dynamic stress state near free and reinforced circular holes under blast loading. The diffraction of stress waves by holes in a thin-walled plate is studied. Experimental data are used to analyze the dynamic stress concentration in a plate with a hole in which quasilongitudinal and quasitransverse waves propagate __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 73–78, July 2007.     

Analysis of uncertainty effects due to microstructural disorder in cellular or porous materials

Aim of the present study is an analysis of the effect of microstructural uncertainties on the scatter in the macroscopic material properties of highly porous materials consisting of metallic or other constituents. For the numerical analysis of the uncertainty effects, a probabilistic homogenization scheme is proposed. In contrast to direct Monte-Carlo approaches, the thermomechanical response of a limited number of pre-selected cases throughout the range of possible microstructures is analyzed. Their effective properties are determined by means of an energy based homogenization procedure. In a stochastic evaluation, the results of the individual computations are weighted with the probability of the occurrence of the underlying microstructures. As a result, the probability distributions for the effective properties are obtained. The basic uncertain microstructural properties considered in the investigation are the microstructural geometry and orientation, the local relative density and the local pore size distribution. In an application to an experimental data base from other sources, the approach proves to be accurate and numerically efficient compared to direct Monte-Carlo approaches. Parameter studies reveal that uncertainties in the local relative density are the most important factor leading to scatter in the macroscopic material properties of cellular materials.     

Micromechanics of residual stress and texture development due to poling in polycrystalline ferroelectric ceramics

This paper presents micromechanics based analysis of elastic strain and changes in the texture of poled polycrystalline ferroelectric PZT ceramics for direct comparison with synchrotron X-ray measurements. The grains are modelled as spherical inclusions, to which transformation strains are assigned depending on the fractions of different ferroelectric domains. Eshelby's inclusion problem with the classical self-consistent method is applied to evaluate the elastic state of the grains. In particular, the elongation due to lattice elastic strain is calculated as a function of inclination Ψ relative to the polar axis. The ratio of diffraction peak intensities, corresponding to the domain fractions, is also expressed as a function of Ψ. This analysis identifies the special character of the reflection, for which the lattice strain along in the stress free state is independent of ferroelectric domain population and hence unaffected by poling. The elongation due to the lattice strain parallel to and peak intensity ratio are expressed in terms of the overall macroscopic strain of a poled specimen, each having a dependence.