Showing papers in "European Journal of Mechanics A-solids in 2010"

A micro scale Timoshenko beam model based on strain gradient elasticity theory

Abstract: A micro scale Timoshenko beam model is developed based on strain gradient elasticity theory. Governing equations, initial conditions and boundary conditions are derived simultaneously by using Hamilton's principle. The new model incorporated with Poisson effect contains three material length scale parameters and can consequently capture the size effect. This model can degenerate into the modified couple stress Timoshenko beam model or even the classical Timoshenko beam model if two or all material length scale parameters are taken to be zero respectively. In addition, the newly developed model recovers the micro scale Bernoulli–Euler beam model when shear deformation is ignored. To illustrate the new model, the static bending and free vibration problems of a simply supported micro scale Timoshenko beam are solved respectively. Numerical results reveal that the differences in the deflection, rotation and natural frequency predicted by the present model and the other two reduced Timoshenko models are large as the beam thickness is comparable to the material length scale parameter. These differences, however, are decreasing or even diminishing with the increase of the beam thickness. In addition, Poisson effect on the beam deflection, rotation and natural frequency possesses an interesting “extreme point” phenomenon, which is quite different from that predicted by the classical Timoshenko beam model.

Dynamic modeling and analysis of a spur planetary gear involving tooth wedging and bearing clearance nonlinearity

Abstract: Tooth wedging, also known as tight mesh, occurs when a gear tooth comes into contact on the drive-side and back-side simultaneously. Tooth wedging risks bearing failures from elevated forces. This work studies the nonlinear tooth wedging behavior and its correlation with planet bearing forces by analyzing the dynamic response of an example planetary gear. This planetary gear is representative of a wind turbine geartrain. A two-dimensional lumped-parameter model is extended to include tooth separation, back-side contact, tooth wedging, and bearing clearances. The results show significant impact of tooth wedging on planet bearing forces for a wide range of operating speeds. To develop a physical understanding of the tooth wedging mechanism, connections between planet bearing forces and tooth forces are studied by investigating physical forces and displacements acting throughout the planetary gear. A method to predict tooth wedging based on geometric interactions is developed and verified. The major causes of tooth wedging relate directly to translational vibrations caused by gravity forces and the presence of clearance-type nonlinearities in the form of backlash and bearing clearance.

Modelling of gearbox dynamics under time-varying nonstationary load for distributed fault detection and diagnosis

Abstract: Fault detection and diagnosis in mechanical systems during their time-varying nonstationary operation is one of the most challenging issues. In the last two decades or so researches have noticed that machines work in nonstationary load/speed conditions during their normal operation. Diagnostic features for gearboxes were found to be load dependent. This was experimentally confirmed by a smearing effect in the spectrum. In order to better understand the involved phenomena and to ensure agreement between simulation and experimental results, two models of gearboxes (a fixed-axis two-stage gearbox and a planetary gearbox) operating under varying load conditions are proposed. The models are based on two mechanical systems used in the mining industry, i.e. the belt conveyor and the bucket wheel excavator. An original transmission error function expressing changes in technical condition and load variation is presented. Energy based parameters (the signal RMS value or the arithmetic sum of the amplitudes of spectral gearmesh components) are adopted as the diagnostic features. Simulation results show a strong correlation between load values, changes in condition and the diagnostic features. The findings are key to condition monitoring. Thanks to the use of the models one can better understand the phenomena identified through an analysis of vibration signals captured from real machines.

Bending and buckling of thin strain gradient elastic beams

Abstract: Bending of strain gradient elastic thin beams is studied adopting Bernoulli-Euler principle. Simple linear strain gradient elastic theory with surface energy is employed. The governing beam equations with its boundary conditions are derived through a variational method. It turns out that new terms are introduced, indicating the importance of the cross-section area in bending of thin beams. Those terms are missing from the existing strain gradient beam theories. Those terms increase highly the stiffness of the thin beam. The buckling problem of the thin beams is also discussed.

Calculations of fracture process zones on meso-scale in notched concrete beams subjected to three-point bending

Abstract: The paper describes investigations on fracture process zones (FPZ) at meso-scale in notched concrete beams subjected to quasi-static three-point bending. The simulations were carried out with the FEM using isotropic damage constitutive model enhanced by a characteristic length of micro-structure by means of a non-local theory. Concrete was modelled as a random heterogeneous three-phase material. The effect of the beam size, aggregate distribution, aggregate density, aggregate shape, aggregate size and characteristic length on the width and shape of FPZ and load-displacement curve was numerically investigated. The numerical results were compared with own test results using Digital Image Correlation method (Skarzynski et al., 2009a), the tests by Le Bellěgo et al., (2003) and the size effect law by Bažant (2004).

Numerical simulation of friction stir butt welding process for AA5083-H18 sheets

Abstract: Thermo-mechanical simulation of the friction stir butt welding (FSBW) process was performed for AA5083-H18 sheets, utilizing a commercial finite volume method (FVM) code, STAR-CCM+, which is based on the Eulerian formulation. Distributions of temperature and strain rate histories were calculated under the steady state condition and simulated temperature distributions (profiles and peak values) were compared with experiments. It was found that including proper thermal boundary condition for the backing plate (anvil) is critical for accurate simulation results. Based on the simulation, thermal and deformation histories of material elements were also calculated, useful to predict material characteristics of the weld such as hardness or grain size, and possibly for the susceptibility of weld to abnormal grain growth (AGG) after post-weld heat treatment.

Dynamic compression of metallic sandwich structures during planar impulsive loading in water

Abstract: The compressive response of rigidly supported stainless steel sandwich panels subject to a planar impulsive load in water is investigated. Five core topologies that spanned a wide range of crush strengths and strain-dependencies were investigated. They included a (i) square-honeycomb, (ii) triangular honeycomb, (iii) multi-layer pyramidal truss, (iv) triangular corrugation and (v) diamond corrugation, all with a core relative density of approximately 5%. Quasi-statically, the honeycombs had the highest peak strength, but exhibited strong softening beyond the peak strength. The truss and corrugated cores had significantly lower strength, but a post yield plateau that extended to beyond a plastic strain of 60% similar to metal foams. Dynamically, the transmitted pressures scale with the quasi-static strength. The final transmitted momentum increased slowly with core strength (provided the cores were not fully crushed). It is shown that the essential aspects of the dynamic response, such as the transmitted momentum and the degree of core compression, are captured with surprising fidelity by modeling the cores as equivalent metal foams having plateau strengths represented by the quasi-static peak strength. The implication is that, despite considerable differences in core topology and dynamic deformation modes, a simple foam-like model replicates the dynamic response of rigidly supported sandwich panels subject to planar impulsive loads. It remains to ascertain whether such foam-like models capture more nuanced aspects of sandwich panel behavior when locally loaded in edge clamped configurations.

Postbuckling of internal pressure loaded FGM cylindrical shells surrounded by an elastic medium

Abstract: This paper presents a study on the postbuckling response of a functionally graded cylindrical shell of finite length embedded in a large outer elastic medium and subjected to internal pressure in thermal environments. The surrounding elastic medium is modeled as a tensionless Pasternak foundation that reacts in compression only. The postbuckling analysis is based on a higher order shear deformation shell theory with von Karman-Donnell-type of kinematic nonlinearity. The thermal effects due to heat conduction are also included and the material properties of functionally graded materials (FGMs) are assumed to be temperature-dependent. The nonlinear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the postbuckling response of the shells and an iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region between the shell and the elastic medium. Numerical solutions are presented in tabular and graphical forms to study the postbuckling behavior of FGM shells surrounded by an elastic medium of tensionless elastic foundation of the Pasternak-type, from which results for conventional elastic foundations are obtained as comparators. The results reveal that the unilateral constraint has a significant effect on the postbuckling response of shells subjected to internal pressure in thermal environments when the foundation stiffness is sufficiently large.

An investigation about interference fit effect on improving fatigue life of a holed single plate in joints

Abstract: In this article, the effect of interference fit on fatigue life of holed plate of mechanical joints was investigated both experimentally and numerically. In the experimental part, fatigue tests were carried out on the holed specimens of Al 7075-T6 alloy in which oversized steel pins were force fitted to them. These fatigue tests were conducted on open hole specimen and specimens with 1, 1.5, 2 and 4% nominal interference fit sizes at different cyclic longitudinal loads. From these tests the stress-life (S–N) data for different interference fit sizes were obtained. The results show that interference fit increases fatigue life compared to open hole specimens. In the numerical part of the investigation, 3D finite element simulations have been performed to obtain stress (or strain) histories and distributions around the hole due to interference fit and subsequent cyclic longitudinal loading using FEM package. The stress history from finite element (FE) simulation was used to explain the reason for fatigue life improvement in the interference fitted specimens.

Band gaps of elastic waves in three-dimensional piezoelectric phononic crystals with initial stress

Abstract: In this paper, the stop band properties of elastic waves in three-dimensional piezoelectric phononic crystals with initial stress are studied taking the mechanical and electrical coupling into account. The band gap characteristics for three kinds of lattice arrangements (i.e. sc, bcc and fcc) are investigated by the plane wave expansion (PWE) method. Regarding the variables of mechanical and electrical fields as the elements of the generalized state vector, the expression of the generalized eigenvalue equation for three-dimensional piezoelectric periodic structures is derived. Numerical calculations are performed for the PZT-2/polymer and ZnO/polymer phononic crystals. It can be observed from the results that the fcc lattice is more favorable to create the stop band than the sc and bcc lattices for the piezoelectric phononic crystals, which has also been proved for the pure elastic periodic structures. Compared with the PZT-2/polymer systems, the band gap of the sc lattice for the ZnO/polymer structures is narrower. However, the widths of the bcc and fcc lattices for the ZnO/polymer phononic crystals are much larger than those for the PZT-2/polymer structures. The lattice arrangements and the piezoelectricity have remarkable influences on the stop band behaviors.

Cosserat model for periodic masonry deduced by nonlinear homogenization

Abstract: The paper deals with the problem of the determination of the in-plane behavior of periodic masonry material. The macromechanical equivalent Cosserat medium, which naturally accounts for the absolute size of the constituents, is derived by a rational homogenization procedure based on the Transformation Field Analysis. The micromechanical analysis is developed considering a Cauchy model for masonry components. In particular, a linear elastic constitutive relationship is considered for the blocks, while a nonlinear constitutive law is adopted for the mortar joints, accounting for the damage and friction phenomena occurring during the loading history. Some numerical applications are performed on a Representative Volume Element characterized by a selected commonly used texture, without performing at this stage structural analyses. A comparison between the results obtained adopting the proposed procedure and a nonlinear micromechanical Finite Element Analysis is presented. Moreover, the substantial differences in the nonlinear behavior of the homogenized Cosserat material model with respect to the classical Cauchy one, are illustrated.

Small-scale effect on torsional buckling of multi-walled carbon nanotubes

Abstract: The small-scale effect on the torsional buckling of multi-walled carbon nanotubes coupled with temperature change is investigated in this paper. A nonlocal multiple-shell model for the multi-walled carbon nanotubes surrounded an elastic medium under torsional and thermal loads is established, and then general solutions are obtained from the governing equations. The influence of the nonlocal effect on critical shear force and change in temperature is investigated. It is demonstrated that the critical shear force could be overestimated by the classical continuum theory and the nonlocal effect on critical buckling force decreases as the change in temperature increases at room or low temperature but increases as the change in temperature increases at higher temperature. Meanwhile, the effect of small size-scale is dependent on the buckling mode under different thermal environments. It is also shown that the innermost radius and the number of layer can affect the small-scale effect on critical change in temperature and buckling shear force. When the ratio of tube length and outmost radius are given, the critical shear force in each layer decreases and the nonlocal effect on the critical shear force becomes weaker as the innermost radius and the layer number increase.

A strain rate dependent yield criterion for isotropic polymers: Low to high rates of loading

Abstract: In this study, strain rate sensitivity of yield behavior in a semicrystalline polymer, Nylon 101, was experimentally investigated. A precise definition of yield was established for the polymer by deforming several specimens to certain levels of strain and measuring the residual strains after unloading and strain recovery. The material was then subjected to different loading conditions (uniaxial to multiaxial) at four different quasi-static and intermediate strain rates to determine several points on the material's yield loci. Due to positive strain rate sensitivity of this polymer, the material's yield loci expanded uniformly as the strain rates were increased to higher values. Further, an empirical hydrostatic pressure dependent yield equation (with four material constants) was developed to simulate these behaviors as a function of strain rate. The capability of the developed criterion was examined by simulating high strain rate yield behavior of the material in tension and in compression. The simulation results revealed very good correlations/predictions between the experimental data and the responses determined from the proposed yield criterion.

Nonlinear buckling of torsion-loaded functionally graded cylindrical shells in thermal environment

Abstract: Based on the nonlinear large deflection theory of cylindrical shells, this paper deals with the nonlinear buckling problem of functionally graded cylindrical shells under torsion load by using the energy method and the nonlinear strain–displacement relations of large deformation. The material properties of the functionally graded shells vary smoothly through the shell thickness according to a power law distribution of the volume fraction of the constituent materials. Meanwhile, on the base of taking the temperature-dependent material properties into account, various effects of external thermal environment on the critical state of the shell are also investigated. Numerical results show various effects of the inhomogeneous parameter, the dimensional parameters and external thermal environment on nonlinear buckling of functionally graded cylindrical shells under torsion. The present theoretical results are verified by those in literature.

Numerical homogenization of cracking processes in thin fibre-epoxy layers

Abstract: Discrete microscale fracture processes in thin fibre-epoxy layers are connected to a mesoscale traction-separation law through a numerical homogenization framework. The microscale fracture processes are studied with the finite element method, where cracking within the epoxy and debonding between fibres and epoxy is simulated by placing interface elements furnished with a mixed-mode interface damage model in between the continuum elements modelling the fibres and epoxy. It is demonstrated how the effective traction-separation response and the corresponding microscale fracture patterns under mesoscale tensile conditions depend on the sample size, the fibre volume fraction and the presence of imperfections.

Fundamental-solution-based finite element model for plane orthotropic elastic bodies

Abstract: A new hybrid finite element formulation is presented for solving two-dimensional orthotropic elasticity problems. A linear combination of fundamental solutions is used to approximate the intra-element displacement fields and conventional shape functions are employed to construct elementary boundary fields, which are independent of the intra-element fields. To establish a linkage between the two independent fields and produce the final displacement-force equations, a hybrid variational functional containing integrals along the elemental boundary only is developed. Results are presented for four numerical examples including a cantilever plate, a square plate under uniform tension, a plate with a circular hole, and a plate with a central crack, respectively, and are assessed by comparing them with solutions from ABAQUS and other available results.

Free vibration analysis of the axially moving Levy-type viscoelastic plate

Abstract: In this paper, the viscoelastic theory is applied to the axially moving Levy-type plate with two simply supported and two free edges. On the basis of the elastic – viscoelastic equivalence, a linear mathematical model in the form of the equilibrium state equation of the moving plate is derived in the complex frequency domain. Numerical calculations of dynamic stability were conducted for a steel plate. The effects of transport speed and relaxation times modeled with two-parameter Kelvin–Voigt and three-parameter Zener rheological models on the dynamic behavior of the axially moving viscoelastic plate are analyzed.

Heat sources, energy storage and dissipation in high-strength steels: Experiments and modelling

Abstract: Tensile tests on three high-strength steels exhibiting Luders band propagation are carried out at room temperature and under quasi-static loading conditions. Displacement and temperature fields on the surface of the flat samples are measured by digital image correlation and digital infrared thermography, respectively. The true stress versus true strain curves were calculated from the displacement data, while the thermal data were used to estimate the heat sources using the local heat diffusion equation. Based on these measurements the stored and dissipated energies were estimated up to diffuse necking. A thermodynamically consistent elastic-plastic constitutive model including the von Mises yield criterion, the associated flow rule and two non-linear isotropic hardening variables is applied to describe the behaviour of the high-strength steels. It is shown that this simple model is able to reproduce both the local behaviour, such as the power associated to heat sources, and the global behaviour, such as Luders band propagation and stored and dissipated energies. It is further shown that the ratio of dissipated power to plastic power varies during plastic straining and that this variation is captured reasonably well in the numerical simulations.

Nonlinear thermoelasticity, vibration, and stress wave propagation analyses of thick fgm cylinders with temperature-dependent material properties

Abstract: In the present paper, nonlinear thermoelasticity, vibration, and stress wave propagation analyses of thick-walled cylinders made of functionally graded materials with temperature-dependent properties are performed. In contrast to researches accomplished so far, a third-order Hermitian finite element formulation is employed to guarantee both radial displacement and normal stress continuities, improve the accuracy, and prevent virtual wave source formations at the mutual boundaries of the elements. Stress wave propagation, reflection, and interference under impulsive mechanical loads in thermal environments are also studied. In contrast to the common procedure, the cylinder is not divided into isotropic sub-cylinders. Therefore, artificial wave reflections from the hard interfaces are avoided. Time variations of the temperatures, displacements, and stresses due to the dynamic loads are determined by solving the resulted highly nonlinear governing equations using an updating iterative time integration scheme and over-relaxation and under-relaxation techniques. A comprehensive sensitivity analysis includes effects of the volume fraction indices, dimensions, and temperature-dependency of the material properties is performed. Results reveal the significant effect of the temperature-dependency of the material properties on the transient stress distribution and elastic wave propagation and reflection phenomena. Interesting phenomena are noticed; among them the oblique wave formations during the wave propagation. Since examples of the present field are rare in literature, the extracted results may serve as reference results for future comparisons.

Biaxial High Cycle Fatigue of a type 304L stainless steel: Cyclic strains and crack initiation detection by digital image correlation

Abstract: A series of biaxial High Cycle Fatigue tests at room temperature is performed to build up an extensive and well-documented database. The testing specimen is a maltese cross thinned in its centre with non-homogeneous strain/stress fields. The experimental protocol uses exclusively full-field strain measurements. The strains (cyclic and residual) as well as the crack initiation detection are obtained by use of Digital Image Correlation (DIC) techniques combined with a multiscale stroboscopic image acquisition in-situ set-up. Nine cruciform specimens made of type 304L austenitic stainless steel are loaded by a multiaxial testing machine. Two kinds of loading paths are presented: equibiaxial with a load ratio of 0.1, non-proportional with a cyclic load in one direction and a constant load in the other. The experimental results are given (strain amplitude, residual strain, number of cycles to crack initiation) for each loading path. The time history of local strain amplitudes and residual strains are recorded and plotted. Total strain vs. number of cycles fatigue curves show the different trends associated with each loading path. For instance, non-proportional loadings are found very damaging and leading to strong ratchetting effects. The tested material is briefly introduced, followed by an in-depth description of the experimental set-up. The fatigue test campaign results are then presented, with a final discussion.

Control of sound radiation and transmission by a piezoelectric plate with an optimized resistive electrode

Abstract: The aim of this work is the application of the piezoelectric effect to the reduction of the sound radiation transmitted through and radiated by an aluminium panel immersed in a light fluid. An innovative Piezoelectric Resistive Electrode (PRE) plate will be introduced here. This structure consists of an aluminium plate entirely covered by two piezoelectric layers with a controlled resistivity electrode bonded on each free piezoelectric surface. This homogeneous system is optimized for all frequencies and performs a good trade-off between good performances and easy implementation. The results will be presented by considering standard acoustic parameters, such as the Sound Reduction Index, far field sound pressure and radiated sound power at plate level. It is shown how this novel smart structure can reduce the sound transmission between two fluid media. To this end, we consider an infinite plate separating two half spaces filled with two identical light fluids, and we analyse how a sound wave is transmitted through the plate. The power of the sound and the far field pressure radiated by a finite structure due to a mechanical input, e.g. a point force, will also be considered. A detailed description of the dynamic and acoustic behaviour of the structure is presented. The performances of the PRE plate are compared with those of a standard viscoelastic damping strategy and of other passive piezoelectric smart structures.

Single point incremental forming of PVC: Experimental findings and theoretical interpretation

Abstract: The aim of the present paper is twofold; (i) to evaluate the possibility of producing low-cost, small-batch, polymer sheet components by means of single point incremental forming (SPIF) and (ii) to provide a first step towards the understanding of the fundamentals of the SPIF of polymers and the identification of the key influential process variables. The experimental research work makes use of Polyvinylchloride (PVC) sheets and was carried out on a CNC milling machine, equipped with a conventional SPIF set-up. Benchmark tests were performed on cones with varying wall angle and results confirm that SPIF of PVC sheets at room temperature has potential for the manufacture of complex parts with very high depths. The overall experimental findings are interpreted by means of an innovative extension of the membrane approach developed by Silva et al. (2008a) that is capable of modelling the cold plastic deformation of polymers with pressure-sensitive yield surfaces. Qualitative evidence of the adequacy of the model to provide explanation of the results and observations provides the link between theory and experimentation.

A unified model for adhesive interfaces with damage, viscosity, and friction

Abstract: A general framework for models describing adhesive contact between rigid bodies is proposed. The intensity of adhesion is supposed to decrease under the action of prescribed tangential and normal relative displacements. The reduction is attributed to progressive damage, and comes with energy dissipation. Additional dissipation due to viscosity and friction is also taken into account. The response of the interface is described by a single state variable. It is determined by general laws expressing a mechanical version of the first two laws of thermodynamics, combined with a set of phenomenological assumptions.

Self-exciting vibrations and Hopf's bifurcation in non-linear stability analysis of rail vehicles in a curved track

Abstract: The main objective of this article is to present the authors' view of and results on non-linear lateral stability of rail vehicles in a curved track. Three elements are exploited in order to secure this objective. Firstly, physical genesis of the problem is discussed, and its similarity to straight track analysis is emphasised. Results of the theories of self-exciting vibrations and bifurcation are the key elements here. Secondly, the method suitable for analysis in a curved track is presented. New necessary elements, extending the better established methods for straight track are clearly mentioned and described. The methodology of building original stability maps, being the basis for the analysis and valid for whole range of curve radii and straight track is represented. Thirdly, a sample of the analysis is shown in order to give the idea how the method can be utilised. The case study refers to the influence of wheel/rail profiles on the stability in circularly curved track and straight track as well. Two different pairs of wheel/rail profiles are used and the corresponding results compared. The main contributions of the article are: a discussion of the physical nature of phenomena related to the stability in a curved tracks, and the method (procedure) established for the reasons of the analysis. Another and more general contribution is our say in the hot polemics on the advisability of stability analysis in curves and the advantages of the non-linear critical speed over the linear one.

Variable kinematic models applied to free-vibration analysis of functionally graded material shells

Abstract: Closed-form solutions of free-vibration problems of simply supported multilayered shells made of Functionally Graded Material have been examined in the present paper. A variable kinematic shell model, which is based on Carrera’ sU ni fied Formulation is extended, in this work, to dynamic shell cases. Classical shell theories are compared to refined ones as well as to layer-wise kinematics and mixed assumptions based on the Reissner mixed variational theorem. A comparison with the few results available in the open literature is presented and conclusions are drawn regarding the accuracy of classical and advanced shell modeling to evaluate lower and higher vibration modes as well as the behavior of these modes in the shell thickness direction.

Static analysis of anisotropic functionally graded magneto-electro-elastic beams subjected to arbitrary loading

Abstract: This paper considers the analytical and semi-analytical solutions for anisotropic functionally graded magneto-electro-elastic beams subjected to an arbitrary load, which can be expanded in terms of sinusoidal series. For the generalized plane stress problem, the stress function, electric displacement function and magnetic induction function are assumed to consist of two parts, respectively. One is a product of a trigonometric function of the longitudinal coordinate (x) and an undetermined function of the thickness coordinate (z), and the other a linear polynomial of x with unknown coefficients depending on z. The governing equations satisfied by these z-dependent functions are derived. The analytical expressions of stresses, electric displacements, magnetic induction, axial force, bending moment, shear force, average electric displacement, average magnetic induction, displacements, electric potential and magnetic potential are then deduced, with integral constants determinable from the boundary conditions. The analytical solution is derived for beam with material coefficients varying exponentially along the thickness, while the semi-analytical solution is sought by making use of the sub-layer approximation for beam with an arbitrary variation of material parameters along the thickness. The present analysis is applicable to beams with various boundary conditions at the two ends. Two numerical examples are presented for validation of the theory and illustration of the effects of certain parameters.

Generalized thermoviscoelastic interaction due to periodically varying heat source with three-phase-lag effect

Abstract: The present paper aims at studying the thermo-visco-elastic interaction in a homogeneous, infinite Kelvin-Voigt-type viscoelastic, thermally conducting medium due to the presence of periodically varying heat sources. Three-phase-lag thermoelastic model, GN model II (TEWOED) and GN model III (TEWED) are employed to study the thermomechanical coupling, thermal and mechanical relaxation effects. In the absence of mechanical relaxations (viscous effect), the results for various generalized theories of thermoelasticity may be obtained as particular cases. The governing equations are expressed in Laplace-Fourier double transform domain and are solved in that domain. The inversion of the Fourier transform is carried out by using residual calculus, where poles of the integrand are obtained numerically in complex domain by using Laguerre’s method and the inversion of Laplace transform is done numerically using a method based on Fourier series expansion technique. The numerical estimates of the displacement, temperature and stress are obtained for a hypothetical material. A comparison of the results for different theories (three-phase-lag model, GN model II, GN model III) is presented and the effect of viscosity is also shown. In absence of viscous effect the results corresponding to GN model II and GN model III agree with the results of the existing literature.

Dynamic stability of axially accelerating Timoshenko beam: Averaging method

Abstract: This study investigates dynamic stability in transverse parametric vibrations of an axially accelerating tensioned beam of Timoshenko model on simple supports. The axial speed is assumed as a harmonic fluctuation about the constant mean speed. The Galerkin method is applied to discretize the governing equation into a finite set of ordinary differential equations. The method of averaging is applied to analyze the instability phenomena caused by subharmonic and combination resonance. Numerical examples demonstrate the effects of the mean axial speed, bending stiffness, rotary inertia and shear modulus on the instability boundaries.

Analytic solutions to crack tip plastic zone under various loading conditions

Abstract: Based on stress field equations and Hill yield criterion, the crack tip plastic zone is determined for orthotropic materials and isotropic materials under small-scale yielding condition. An analytical solution to calculating the crack tip plastic zone in plane stress states is presented. The shape and size of the plastic zone are analyzed under different loading conditions. The obtained results show that the crack tip plastic zones present “butterfly-like” shapes, and the elastic–plastic boundary is smooth. The size of the plastic zone for orthotropic composites is less at the crack tip for various loading conditions, compared with the case of isotropic materials. Crack inclination angle and loading conditions affect greatly the size and shape of crack tip plastic zone. The mode I crack has a crucial effect on the plastic zone for mixed mode case in plane stress state. The plastic zone for pure mode I crack and pure mode II crack have a symmetrical distribution to the initial crack plane.

Transient responses of magnetostrictive plates by using the GDQ method

Abstract: We used the generalized differential quadrature (GDQ) method to compute the transient response of thermal stresses and center displacement in laminated magnetostrictive plates under thermal vibration. We obtained the GDQ solutions in a three-layer (0° m /90°/0) and a 10-layer (0° m /90°/0°/90°/0) s laminated magnetostrictive plate with four simply supported edges. We presented the transient responses of thermal stress and center displacement with and without velocity feedback control, respectively. The advantage of the GDQ method used provide us with an efficient method to compute the results including shear deformation effect with a few grid points. These GDQ results had its potential that could be used and considered as basic data in the future magnetostrictive laminate studies.