Showing papers in "Acta Mechanica in 2004"
TL;DR: In this paper, a steady unidirectional flow of an Oldroyd 8-constant magnetohydrodynamic (MHD) fluid in bounded domains is analyzed using homotopy analysis method (HAM).
Abstract: This paper deals with some steady unidirectional flows of an Oldroyd 8-constant magnetohydrodynamic (MHD) fluid in bounded domains. The fluid is electrically conducting in the presence of a uniform magnetic field. Three nonlinear flows are produced by the motion of a boundary or by sudden application of a constant pressure gradient or by the motion of a boundary and pressure gradient. The governing nonlinear differential equations are solved analytically using homotopy analysis method (HAM). Expressions for the velocity distribution are given. It is noted that for steady flow the solutions are strongly dependent on the non–Newtonian and magnetic parameters. The MHD solutions for a Newtonian fluid, as well as those corresponding to the Oldroyd 3 and 6-constant fluids, a Maxwell fluid and a second grade one, appear as limiting cases of our solutions. Finally, a physical interpretation of the results is given with the help of several graphs.
233 citations
TL;DR: In this paper, the problem of axial shear of a circular cylindrical tube subject to a radial magnetic field was formulated and then solved for a specific constitutive law with a magnetic field that is initially radial.
Abstract: Magneto-sensitive (MS) elastomers are “smart materials” whose mechanical properties may be changed rapidly by the application of a magnetic field Such materials typically consist of micron-sized ferrous particles dispersed within an elastomeric matrix The equations governing deformations of these materials were discussed in a recent paper by the present authors and applied in a particular specialization of the constitutive model to the problem of axial shear of a circular cylindrical tube subject to a radial magnetic field In the present paper we develop the governing equations for a more general form of constitutive model and provide alternative forms of the equations, including a Lagrangian formulation To illustrate the theory the problem of azimuthal shear of a circular cylindrical tube is formulated and then solved for a specific constitutive law with a magnetic field that is initially radial The results, which show the stiffening of the azimuthal shear stress/strain response with increasing magnetic field strength, are illustrated graphically
180 citations
TL;DR: In this article, an analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow over a permeable, inclined surface with variable wall temperature and concentration, taking into consideration the effects of ohmic heating and viscous dissipation.
Abstract: An analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow over a permeable, inclined surface with variable wall temperature and concentration, taking into consideration the effects of ohmic heating and viscous dissipation. Power-law temperature and concentration variations are assumed at the inclined surface. The resulting governing equations are transformed using suitable transformations and then solved numerically by an implicit finite-difference method. The solution is found to be dependent on several governing parameters, including the magnetic field strength parameter, Eckert number, the buoyancy ratio between species and thermal diffusion, Prandtl number, Schmidt number, wall temperature and concentration exponent, the inclination angle from the vertical direction, and the injection parameter. A parametric study of all the governing parameters is carried out and representative results are illustrated to reveal a typical tendency of the solutions. Representative results are presented for the velocity, temperature, and concentration distributions as well as the local friction coefficient, local Nusselt number, and the local Sherwood number.
120 citations
TL;DR: In this paper, the authors considered the boundary initial value problem of thermoelasticity with two temperatures, and studied the structural stability with respect to the parameter which is typical in this theory.
Abstract: This paper concerns the thermoelasticity with two temperatures. First, we state the suitable frame where the boundary initial value problem of thermoelasticity with two temperatures is well posed. Second we study the structural stability with respect the parameter which is typical in this theory. When this parameter tends to zero we obtain the system of the usual thermoelasticity. We also study the convergence of the solutions in this theory to the classical one. Last section is devoted to study the spatial behavior for the backward-in-time problem.
104 citations
TL;DR: In this paper, the propagation behavior of Love wave in a piezoelectric layered structure with inhomogeneous initial stress is studied and the influence of the initial stress gradient coefficient on the stress, mechanical displacement and electrical potential distribution in the layer and the substrate is investigated in detail.
Abstract: The propagation behavior of Love waves in a piezoelectric layered structure with inhomogeneous initial stress is studied. Solutions of the mechanical displacement and electrical potential function are obtained for the isotropic elastic layer and transversely isotropic piezoelectric substrate, respectively, by solving the coupled electromechanical field equations. Firstly, effects of the inhomogeneous initial stress on the dispersion relations and phase velocity of Love wave propagation are discussed. Then the influence of the initial stress gradient coefficient on the stress, mechanical displacement and electrical potential distribution in the layer and the substrate is investigated in detail. The results reported in this paper are not only meaningful for the design of surface acoustic wave (SAW) devices with high performance, but also effective for evaluating the residual stress distribution in the layered structures.
92 citations
TL;DR: In this paper, the steady and incompressible flow of non-Newtonian fluids past a circular cylinder is investigated for power law indices n between 0.2 and 1.4, blockage ratios of 0.037, 0.082 and 0.164, and the Reynolds numbers Re of 1, 20 and 40, using a stream function/vorticity formulation.
Abstract: The steady and incompressible flow of non-Newtonian fluids past a circular cylinder is investigated for power law indices n between 0.2 and 1.4, blockage ratios of 0.037, 0.082 and 0.164, and the Reynolds numbers Re of 1, 20 and 40, using a stream function/vorticity formulation. The governing field equations have been solved by using a second-order accurate finite difference method to determine the drag coefficient, wake length, separation angle and flow patterns, and to investigate their dependence on power law index, blockage ratio and Reynolds number. The results reported here provide fundamental knowledge on the dependence of engineering flow parameters on blockage ratio and power law index, and further show that the effects on stream line and iso-vorticity patterns which result from an increase in the blockage ratio are similar to those which result from a decrease in the power law index.
89 citations
TL;DR: In this paper, the effects of inertia and curvature on the flow of an incompressible viscous fluid driven by the travelling waves along the boundaries of an asymmetric channel is studied when inertia and streamline curvature effects are not negligible.
Abstract: The flow of an incompressible viscous fluid driven by the travelling waves along the boundaries of an asymmetric channel is studied when inertia and streamline curvature effects are not negligible. The channel asymmetry is produced by choosing the wave train on the walls to have different amplitudes and phases. An asymptotic solution is obtained to second order in δ, a ratio of channel width to the wavelength, giving the curvature effects. A domain transformation is used to transform the channel of variable cross section to a uniform cross section, and this facilitates in easy way of finding closed form solutions at higher orders. The relation connecting the pressure gradient and time rate of flux is a cubic leading to non-uniqueness of flux. A uniqueness criterion is derived which restricts the parameters to get a unique flux for a prescribed pressure gradient. The effects of inertia and curvature on pumping, trapping and shear stress are discussed for symmetric and asymmetric channels and compared with the existing results in the literature. Even under a favorable pressure gradient the possibility of fluid flow in a direction opposite to the direction of the waves propagating on the walls is detected as in the case of some non–Newtonian fluids. It is noticed that the effects of Reynolds number and asymmetry may play an important role in producing mixing. Another interesting observation is that the shear stress distribution on the walls vanishes at some points and this will not indicate any flow separation.
71 citations
TL;DR: In this paper, an analytical method based on a representation of the solution of the Stokes equations in terms of holomorphic functions is presented, and the problem is reduced to solving ordinary differential equations and integral equations at the boundaries only.
Abstract: We study the influence of an undulated bottom profile on steady two–dimensional gravity driven film flows of a Newtonian fluid. Traditional approaches towards this topic are based on lubrication approximation, on special perturbation methods or on numerics. However, lubrication approximation and perturbation methods deliver acceptable results only within their range of validity. Especially if the bottom is strongly undulated, conventional analytical methods fail. Neither can the classical separation solution of the biharmonic equation in terms of an infinite series be applied because of massive convergence problems if the waviness exceeds a limit. In this paper we present an analytical method based on a representation of the solution of Stokes equations in terms of holomorphic functions. Applying the complex function theory, convergence problems are avoided and the problem is reduced to solving ordinary differential equations and integral equations at the boundaries only. Our calculations show the creation, formation and evolution of vortices if waviness and film thickness exceed critical values. A detailed parameter study on size and strength of the vortices is shown. Moreover, we present a quantitative study on the effect of the vortices on the flow rate. Our calculations show very good agreement with experimental results.
69 citations
TL;DR: In this paper, the free energy and dissipation function of a granular material undergoing simple shear were derived using a micromechanical analysis of a cluster consisting of a particle and its immediate neighbors.
Abstract: In this paper, we lay the groundwork for the development of micropolar (Cosserat) constitutive relations for granular media within the framework of the theory of thermomechanics. Expressions for the free energy and the dissipation function have been derived using a micromechanical analysis of a cluster consisting of a particle and its immediate neighbors (i.e., “the first ring”). Fluctuations in particle displacements and rotations within this mesoscale assembly as well as fluctuations in strain and curvature are represented by internal variables. Using thermomechanical techniques previously employed for classical materials, a non-local micropolar model is constructed and then subsequently applied to a granular material undergoing simple shear. The effects of the boundaries through particle rotations are discussed.
61 citations
TL;DR: In this article, the static thermo-viscoelastic responses of fiber-reinforced composite plates are investigated by the use of a refined shear deformation theory, in which trigonometric terms are used for the displacements in addition to the initial terms of a power series through the thickness.
Abstract: The static thermo-viscoelastic responses of fiber-reinforced composite plates are investigated by the use of a refined shear deformation theory. In this theory, trigonometric terms are used for the displacements in addition to the initial terms of a power series through the thickness. The form of the assumed displacements of this theory is simplified by enforcing traction-free boundary conditions at the plate faces. No transverse shear correction factors are needed because a correct representation of the transverse shear strain is given. Using the method of effective moduli solves the equations governing the bending of simply supported fiber-reinforced viscoelastic composite plates. An exact closed-form solution is presented for plates subjected to nonuniform distributions of temperature. The validity of the present theory is demonstrated by comparison with solutions available in the literature. A wide variety of results are presented for the bending response of viscoelastic rectangular plates under thermal loads. The influences of plate aspect ratio, side-to-thickness ratio, thermal expansion coefficients ratio and constitutive and volume fraction parameters on the thermally induced response are studied.
60 citations
TL;DR: In this paper, a spectral layer element (SLE) is used to model the material properties in anisotropic inhomogeneous layered media with high frequency impact loading, where the material property variation is assumed to follow an exponential function.
Abstract: Wave propagation in anisotropic inhomogeneous layered media due to high frequency impact loading is studied using a new Spectral Layer Element (SLE). The element can model functionally graded materials (FGM), where the material property variation is assumed to follow an exponential function. The element is exact for a single parameter model which describes both moduli and density variation. This novel element is formulated using the method of partial wave technique (PWT) in conjunction with linear algebraic methodology. The matrix structure of finite element (FE) formulation is retained, which substantially simplifies the modeling of a multi-layered structure. The developed SLE has an exact dynamic stiffness matrix as it uses the exact solution of the governing elastodynamic equation in the frequency domain as its interpolation function. The mass distribution is modeled exactly, and, as a result, the element gives the exact frequency response of each layer. Hence, one element may be as large as one complete layer which results in a system size being very small compared to conventional FE systems. The Fast-Fourier Transform (FFT) and Fourier series are used for the inversion to the time/space domain. The formulated element is further used to study the stress distribution in multi-layered media. As a natural application, Lamb wave propagation in an inhomogeneous plate is studied and the time domain description is obtained. Further, the advantage of the spectral formulation in the solution of inverse problems, namely the force identification and system identification is investigated. Constrained nonlinear optimization technique is used for the material property identification, whereas the transfer function approach is taken for the impact force identification.
TL;DR: In this article, the complex potentials in the inclusion region were expressed in the form of Faber series with unknown coefficients and all unknown coefficients can be determined from a set of linear equations.
Abstract: This paper presents a simple method for the two-dimensional electroelastic problem of an arbitrarily shaped inclusion in an infinite piezoelectric solid, which is subjected to out-of-plane shear stress and in-plane electric field at infinity. The most remarkable feature of the method is to express the complex potentials in the inclusion region in the form of Faber series with unknown coefficients. By use of continuity conditions on the interface, all unknown coefficients can be determined from a set of linear equations. At first, we derive a general solution for an arbitrarily shaped inclusion in form of infinite series. Then, we give exact solutions for an elliptical inclusion, and approximate solutions for a square inclusion and an equilateral triangle inclusion, respectively. More importantly, this method can be extended to solve the 2-D interface crack problems of any isotropic inclusion-matrix system, provided that one knows the mapping function which maps the infinite region outside the inclusion into the outside of a unit circle. In fact, the function has been well studied in Muskhelishvili’s masterpiece.
Journal Article•
TL;DR: In this article, the propagation of Love waves on a piezoelectric half space of polarized ceramics carrying an elastic layer was studied from the three-dimensional equations of linear PEM with full electromagnetic coupling.
Abstract: The propagation of Love waves on a piezoelectric half space of polarized ceramics carrying an elastic layer is studied from the three-dimensional equations of linear piezoelectromagnetism with full electromagnetic coupling. Two cases when the elastic layer is a perfect conductor or a dielectric are analyzed.
TL;DR: In this paper, the effects of the variable viscosity parameter θr, the thermal diffusion parameter Sr, the diffusion-thermo parameter Df, suction or blowing parameter m, heat flux parameter s and Schmidt number Sc have been examined on the flow field of a hydrogen-air mixture as a non-chemical reacting fluid pair.
Abstract: An analysis has been carried out to obtain the thermal-diffusion and the diffusion-thermo effects on the mixed free-forced convective and mass transfer steady laminar boundary-layer flow over an accelerating surface with a heat source in the presence of suction and blowing. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The partial differential equations governing the problem under consideration have been transformed by a similarity transformation into a system of ordinary differential equations which is solved numerically by applying the shooting method. The results for an impermeable accelerating surface are discussed. The effects of the variable viscosity parameter θr, the thermal diffusion parameter Sr, the diffusion-thermo parameter Df, suction or blowing parameter m, heat flux parameter s and Schmidt number Sc have been examined on the flow field of a hydrogen-air mixture as a non-chemical reacting fluid pair. The effects of varying these parameters are studied in the case of a surface with prescribed wall temperature and a surface with prescribed wall heat flux.
TL;DR: The generalized dispersion model is applied to a specific problem in clinical medicine – dispersion of solutes in blood flow in a catheterized artery and predicts that the oscillatory flow augments the mass transfer and that an increase in the frequency parameter helps in the longitudinal disp immersion of the dye.
Abstract: The effect of the irreversible boundary reaction on the dispersion of a tracer in an annular region in presence of oscillatory flow is studied. The solution of the mathematical model, based on the generalized dispersion model, brings out the dispersive transport following the injection of a tracer in terms of the three effective transport coefficients, the exchange, the convection and the dispersion coefficients. The model is applied to a specific problem in clinical medicine – dispersion of solutes in blood flow in a catheterized artery. The model predicts that the oscillatory flow augments the mass transfer and that an increase in the frequency parameter helps in the longitudinal dispersion of the dye. But the presence of the catheter and increase in the catheter size inhibit the dispersion process. Also, there is more absorption of solute at the wall as the catheter size increases.
TL;DR: In this article, the effect of the radiation parameter in the boundary layer adjacent to the vertical flat plate with fluid suction/injection through it is analyzed in both aiding and opposing flow situations.
Abstract: Mixed convection flow of an absorbing fluid up a uniform non–Darcy porous medium supported by a semi-infinite ideally transparent vertical flat plate due to solar radiation is considered. The external flow field is assumed to be uniform, the effect of the radiation parameter in the boundary layer adjacent to the vertical flat plate with fluid suction/injection through it is analyzed in both aiding and opposing flow situations. It is observed that the similarity solution is possible only when the fluid suction/injection velocity profile varies as x
−1/2. The velocity and temperature profiles in the boundary layer and the heat transfer coefficient are presented for selected values of the parameters. It is observed that the Nusselt number increases with the increase in the radiation parameter and also when the value of the surface mass flux parameter moves from the injection to the suction region.
TL;DR: In this paper, it is shown that the Cauchy-green deformation tensor can be derived from a complementary potential as function of the basic invariants of the deviatoric Caichy stress, which automatically satisfies the hyperelasticity condition, the isotropy condition, and the incompressibility condition.
Abstract: It is demonstrated that of all finite strain measures there is one and only one able to realize fully uncoupled separation of the volumetric and the isochoric deformation in a natural, additive manner. This unique measure is Hencky’s logarithmic strain, and its remarkable property is utilized to establish dual stress-strain and strain-stress relations for isotropic, incompressible hyperelastic solids. It is indicated that the deviatoric Hencky strain and the deviatoric Cauchy stress are derivable straightforwardly from two dual elastic potentials with respect to each other. Further, the three basic invariants of Hencky’s strain naturally reduce to two in the case of incompressibility, and these two invariants may be used to express the isotropic elastic potential. This results in simple, explicit dual representations for the foregoing dual stress-strain and strain-stress relations. In particular, it is shown that the Cauchy-Green deformation tensor can be explicitly derived from a complementary potential as function of the basic invariants of the deviatoric Cauchy stress, which automatically satisfies the hyperelasticity condition, the isotropy condition, and the incompressibility condition.
TL;DR: In this paper, the authors studied the problem of two-dimensional electromagneto-thermovisco-elasticity based on Lord-Shulman theory for a thermally and electrically conducting half-space solid whose surface is subjected to a thermal shock.
Abstract: This paper studies the problem of two-dimensional electromagneto-thermovisco-elasticity based on Lord-Shulman theory for a thermally and electrically conducting half-space solid whose surface is subjected to a thermal shock. There acts an initial magnetic field parallel to the plane boundary of the half-space. The medium deforms because of thermal shock and due to the application of the magnetic field, it results in induced magnetic and electric fields in the medium. The normal mode analysis is used to obtain the exact expressions for the considered variables. The distributions of the temperature, displacement, stress, induced magnetic and electric fields are represented graphically. Comparisons are made with the results predicted by both the coupled theory and with the theory of generalized thermo-viscoelasticity with one relaxation time.
TL;DR: In this paper, the conditions under which a natural extension of the dynamics at an impact is possible without taking additional impact laws, and which additional assumptions have to be made to solve the impact for different classes of systems.
Abstract: There are three basic equations in mechanics for treating collisions: the law of impact, kinematic compatibility, and energetic consistency. In this paper, the conditions are examined under which a natural extension of the dynamics at an impact is possible without taking additional impact laws, and which additional assumptions have to be made to solve the impact for different classes of systems. It will be shown that Newton’s law of impact for two colliding point masses can be derived from the concept of energy conservation and the principle of maximum dissipation, and has therefore not to be regarded as an independent equation. Moreover, it can be assigned to single-contact impacts in multibody systems as soon as the classical definition of perfect constraints is being extended to impulsive dynamics and unilateral contacts. It will further be shown that the principle of maximum dissipation leads to a unique post-impact velocity in the case of multi-contact collisions. In all other cases, however, the velocities remain undetermined, and laws of impact have to be postulated as additional and independent equations, whereas the classic definition of the restitution coefficient as a dissipation parameter can still be kept.
TL;DR: In this paper, a finite crack propagating at constant speed in a functionally graded piezoelectric material (FGPM) is studied, and the analysis is conducted on the electrically unified (natural) crack boundary condition related to the ellipsoidal crack parameters.
Abstract: In this paper, a finite crack propagating at constant speed in a functionally graded piezoelectric material (FGPM) is studied. It is assumed that the electroelastic material properties of the FGPM vary continuously according to exponential gradients along the thickness of the strip, and that the strip is under anti-plane shear mechanical and in-plane electrical loads. The analysis is conducted on the electrically unified (natural) crack boundary condition, which is related to the ellipsoidal crack parameters. By using the Fourier transform, the problem is reduced to the solutions of Fredholm integral equations of the second kind. Numerical results for the stress intensity factor and crack sliding displacement are presented to show the influences of the elliptic crack parameters, crack propagation speed, electric field, FGPM gradation, crack length, and electromechanical coupling coefficient. It reveals that there are considerable differences between traditional electric crack models and the present unified crack model.
TL;DR: In this paper, the mass and energy balances for a multicomponent solid, changing its composition by diffusion, are derived both in the bulk and at a moving non-material (singular) interface like a phase boundary.
Abstract: The mass and energy balances for a multicomponent solid, changing its composition by diffusion, are derived both in the bulk and at a moving non-material (singular) interface like a phase boundary. The body is deformable and diffusion of interstitial and substitutional species as well as vacancies is considered. The thermodynamic driving forces and corresponding fluxes are calculated in an interface point derived from the study of the local dissipation. The surface growth terms, as introduced recently by Irschik [1], can be identified via the flux of vacancies.
TL;DR: In this article, a higher-order spectral element (SE) was developed for wave propagation analysis of a functionally graded material (FGM) beam in the presence of thermal and mechanical loading.
Abstract: A new higher-order spectral element (SE) is developed for wave propagation analysis of a functionally graded material (FGM) beam in the presence of thermal and mechanical loading. The element is based on first order shear deformation theory (FSDT) and takes into account the depthwise contraction due to Poisson’s ratio. A new method of element formulation is employed, which is the most general one and devoid of all previous cumbersome wavenumber and wave amplitude computation. The beam can be subjected to temperature variation in depth direction. This variation is found by solving the one-dimensional heat conduction equation uncoupled from the elasticity equation. The effect of the computed temperature field is subsequently superimposed on the mechanical loading in the form of an equivalent nodal load. Numerical examples are directed towards highlighting the effect of the Poisson’s contraction on the structural response and stress wave. The spectrum and the dispersion relation are studied in detail. The stress field generated by the element and its difference from the FSDT stress field is outlined. The response of an FGM beam to thermo-mechanical loading is analysed and the effect of thermal loading on the overall response is elicited.
TL;DR: In this article, a similarity solution is proposed for the analysis of the steady free convection boundary layers over a non-isothermal axisymmetric body embedded in a fluid saturated porous medium.
Abstract: A similarity solution is proposed for the analysis of the steady free convection boundary layers over a non-isothermal axisymmetric body embedded in a fluid saturated porous medium. The effect of temperature dependent viscosity on heat transfer rates in the presence of internal heat generation is investigated. The linearized version of the Arrhenius law for the temperature dependent viscosity is considered. It is shown that the heat transferred is more for a less viscous fluid.
TL;DR: In this paper, a computational model is developed to estimate the stress distributions in rotating elastic-plastic solid and hollow shafts by the use of von Mises' yield criterion, deformation theory of plasticity and a Swift-type hardening law.
Abstract: A computational model is developed to estimate the stress distributions in rotating elastic-plastic solid and hollow shafts by the use of von Mises’ yield criterion, deformation theory of plasticity and a Swift-type hardening law. An efficient numerical solution procedure based on the shooting method and Newton iterations is designed and used throughout this work to treat shafts with fixed and free ends. The results of the computations are verified by comparison with analytical solutions in the elastic range as well as with analytical elastic-plastic solutions employing Tresca’s yield criterion available in the literature. The stresses, displacement and plastic strains are computed for nonlinearly hardening elastic-plastic solid and hollow shafts rotating at different speeds, and the results are presented in graphical form.
TL;DR: In this article, the properties of internal flows of dense gases having large specific heats are discussed on the basis of two prototypical examples: inviscid nozzle flows and laminar boundary-layer flows.
Abstract: The properties of internal flows of dense gases having large specific heats are discussed on the basis of two prototypical examples: inviscid nozzle flows and laminar boundary-layer flows. In the first case it is shown that rarefaction shocks may be completely admissible. Also it is shown that the transition from a subsonic to a supersonic state may require a rather unusual nozzle shape having two throats rather than a single throat. Under adiabatic wall conditions the energy equation is found to play a minor role in the description of laminar boundary layers. New effects not possible in dilute gases are seen to result from the non-monotonous Mach number variation in external supersonic flow fields.
TL;DR: In this article, the influence of temperature-dependent fluid properties on the boundary layers over a continuously stretching surface with constant temperature was investigated, and the coupled similarity equations were obtained for special situations, in which the fluid density and heat capacity are assumed without dependence on the temperature.
Abstract: In this work, the influences of temperature-dependent fluid properties on the boundary layers over a continuously stretching surface with constant temperature are investigated. Based on the boundary layer assumptions, the coupled similarity equations are obtained for special situations, in which the fluid density and heat capacity are assumed without dependence on the temperature. Those similarity equations are solved numerically. The influences of property variation on wall stresses and heat fluxes are discussed. It is found that the property variation can influence the distributions of both fluid velocity and temperature across the boundary layers. For the thermal boundary layer, using mean properties evaluated at the average temperature of wall and ambient fluid can give good results for the temperature distribution. However, for the momentum boundary layer, the difference of velocity distributions can be large.
TL;DR: In this article, the propagation of anti-plane surface waves in a piezoelectric ceramic half-space carrying a thin layer of a semiconducting material was studied and two-dimensional equations for the extensional motion of a thin membrane of semiconductors were derived to model the semiconductor layer.
Abstract: We study the propagation of anti-plane surface waves in a piezoelectric ceramic half-space carrying a thin layer of a semiconducting material. Two-dimensional equations for the extensional motion of a thin membrane of piezoelectric semiconductors are derived to model the semiconductor layer. A surface wave solution is obtained.
TL;DR: A numerical study of natural convection in a two-dimensional porous cavity saturated with water which possesses a density maximum in the vicinity of 398°C is carried out in this paper.
Abstract: A numerical study of natural convection in a two-dimensional porous cavity saturated with water which possesses a density maximum in the vicinity of 398°C is carried out in the present paper It is assumed that one of the cavity vertical walls is heated differentially by an isothermal discrete heater The other vertical wall is cooled to a constant temperature, while the horizontal walls are adiabatic Non-Boussinesq and Darcy models are used in the mathematical formulations The effects of the location of the center of the discrete isothermal heater, the length of the heater and the aspect ratio of the porous cavity are studied for a wide range of modified Rayleigh numbers (50 ≤Ra≤1000) For long heater and low Ra, it is required to place the heater in the middle of the vertical wall in order to get maximum heat transfer For short heater and high Ra, fixing the heater in the upper half of the vertical wall leads to an enhancement of the heat transfer When the aspect ratio A=05, the heater is far from the cold wall and hence more thermal resistance in this case reduces the average Nusselt number On the other hand, higher values of average Nusselt numbers are found for specified Ra and L when the aspect ratio A is increased
TL;DR: In this article, it was shown that for some finite amplitude transverse waves in rotating incompressible elastic solids with general shear response the solutions are obtained by reduction of the equations of motion to a system of ordinary differential equations equivalent to the system governing the central motion problem of classical mechanics.
Abstract: Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic half-space put into uniform rotation? It is seen that nonlinear finite elasticity provides such a framework for incompressible solids. Second: how can finite amplitude exact solutions be generated? It is seen that for some finite amplitude transverse waves in rotating incompressible elastic solids with general shear response the solutions are obtained by reduction of the equations of motion to a system of ordinary differential equations equivalent to the system governing the central motion problem of classical mechanics. In the special case of circularly-polarized harmonic progressive waves, the dispersion equation is solved in closed form for a variety of shear responses, including nonlinear models for rubberlike and soft biological tissues. A fruitful analogy with the motion of a nonlinear string is pointed out.
TL;DR: In this article, a boundary element method is developed for the construction of a 14 × 14 stiffness matrix and a nodal load vector that take into account the additional warping degrees of freedom in a member of arbitrary variable composite cross section.
Abstract: In this paper, a boundary element method is developed for the construction of a 14 × 14 stiffness matrix and a nodal load vector that take into account the additional warping degrees of freedom in a member of arbitrary variable composite cross section. The member is subjected to an arbitrarily concentrated or distributed twisting moment and consists of materials in contact each of which can surround a finite number of inclusions. The developed method takes into account the variable torsional and warping rigidities along the member length. Two boundary value problems with respect to the variable along the beam angle of twist and to the primary warping function are formulated and solved employing a pure BEM approach, that is only boundary discretization is used. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The discrepancy in the elements of the resulting stiffness matrix using the developed procedure and a fine mesh of elements having “average” values for the cross section parameters necessitates the consideration of the derivatives of the variable torsional and warping rigidities along the member length. Moreover, the influence of the warping effect, especially in composite members of open form cross section of variable thickness, is analyzed in examples demonstrating the importance of the inclusion of the warping degrees of freedom in the analysis of a space frame.