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1.
Thermoelastic interaction with energy dissipation in a transversely isotropic thin circular disc 总被引:1,自引:0,他引:1
The distribution of stresses due to step input of temperature on the boundaries of a homogeneous transversely isotropic circular disc is investigated by applying Laplace transform technique in the context of generalized theories of thermo-elasticity. The inverse of the transformed solution is carried out by applying a method of Bellman et al. The stresses are computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (CTE, CCTE, TRDTE(GL), TEWED(GN)) and the effect of anisotropy on the stresses are also presented. When the material is isotropic and outer radius of the disc tends to infinity, the corresponding result agrees with that of existing literature. 相似文献
2.
This problem deals with the determination of thermo-elastic interaction due to step input of temperature on the boundaries of a functionally graded orthotropic hollow sphere in the context of linear theories of generalized thermo-elasticity. Using the Laplace transformation the fundamental equations have been expressed in the form of vector–matrix differential equation which is then solved by eigenvalue approach. The inverse of the transformed solution is carried out by applying a method of Bellman et al. Stresses, displacement and temperature distributions have been computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (TEWOED(GN-II), TEWED(GN-III) and three-phase-lag model) is presented. When the material is homogeneous, isotropic and outer radius of the hollow sphere tends to infinity, the corresponding results agree with that of existing literature for GN-III model. 相似文献
3.
In this work, the magneto-thermoelastic problem of an infinite microstretch homogeneous isotropic plate placed in a transverse
magnetic field is studied in the context of different theories of generalized thermoelasticity. The upper surface of the infinite
plate is subjected to a zonal time-dependent heat shock. The problem is investigated by applying finite element method. The
solution is obtained by solving finite element governing equations of the problem in time domain directly. The results, including
temperature, stresses, displacements, microrotation, microstretch, induced magnetic field, and induced electric field, are
presented graphically. Comparison is made in the results predicted by different theories of generalized thermoelasticity,
to show that the micropolar effect has a slight influence on the results while the microstretch effect has a great influence
on the results. Finally, a parameter study provides an idea about the influence of the respective terms of the theories. 相似文献
4.
The model of generalized micropolar magneto-thermoelasticity for a thermally and perfectly conducting half-space is studied. The initial magnetic field is parallel to the boundary of the half-space. The formulation is applied to the generalized thermo-elasticity theories of Lord and Shulman, Green and Lindsay, as well as to the coupled dynamic theory. The normal mode analysis is used to obtain expressions for the temperature increment, the displacement, and the stress components of the model at the interface. By using potential functions, the governing equations are reduced to two fourth-order differential equations. By numerical calculation, the variation of the considered variables is given and illustrated graphically for a magnesium crystal micropolar elastic material. Comparisons are performed with the results predicted by the three theories in the presence of a magnetic field. 相似文献
5.
The present paper is aimed at studying the effect of rotation on the general model of the equations of generalized thermo-microstretch for a homogeneous isotropic elastic half-space solid whose surface is subjected to a Mode-I Crack problem considered. The problem is in the context of the generalized thermoelasticity Lord-?hulman??s (L-S) theory with one relaxation time, as well as the classical dynamical coupled theory (CD) The normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses and microstress distribution. The variations of the considered variables through the horizontal distance are illustrated graphically. Comparisons are made with the results in the presence and absence of rotation and in the presence and absence of microstretch constants between the two theories. 相似文献
6.
《International Journal of Solids and Structures》2005,42(14):4192-4203
The paper deals with the thermo-elastic interactions due to distributed periodically varying heat sources in a homogeneous, isotropic, unbounded elastic medium in the context of the theory of thermo-elasticity without energy dissipation. Closed form solutions for displacement, temperature, stress and strain are derived by using Laplace transform on time and then Fourier transform on space. It reveals that the interactions consist of two coupled modified dilatational and thermal waves modified by finite thermal wave speed and thermo-elastic coupling traveling with finite speeds and without attenuation. The results are compared with previous results derived by using other generalized thermo-elasticity theories. Numerical results for a hypothetical material are presented. 相似文献
7.
Ibrahim A. Abbas Abo-el-nour N. Abd-alla 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(4):283-293
Thermoelastic interactions in an infinite orthotropic elastic medium with a cylindrical cavity are studied. The cavity surface
is subjected to ramp-type heating of its internal boundary, which is assumed to be traction free. Lord–Shulman and Green–Lindsay
models for the generalized thermoelasticity theories are selected since they allow for second-sound effects and reduce to
the classical model for an appropriate choice of the parameters. The temperature, radial displacement, radial stress, and
hoop stress distributions are computed numerically using the finite-element method (FEM). The results are presented graphically
for different values of the thermal relaxation times using the three different theories of generalized thermoelasticity. Excellent
agreement is found between the finite-element analysis and analytical and classical solutions. 相似文献
8.
S. M. Abo-Dahab 《Meccanica》2012,47(3):613-620
The present work is devoted to study effects of the thermally induced vibration, magnetic field and viscoelasticity in an
isotropic homogeneous unbounded body with a spherical cavity. The GN model of thermoelasticity without energy dissipation is applied. The closed form solutions for distributions of displacement,
temperature and radial and hoop stresses are illustrated. The boundary conditions for the temperature and mechanical and Maxwell’s
stresses are employed. The solutions valid in the case of small frequency are deduced and the results are compared with the
corresponding results obtained in other generalized thermoelasticity theories. The results obtained are calculated for a copper
material and presented graphically. It’s deduced that the magnetic field, viscosity and thermally induced vibration are very
pronounced on displacement, temperature and stresses. 相似文献
9.
Santwana Mukhopadhyay 《Mechanics Research Communications》2004,31(1):81-89
The present work is concerned with the thermally induced vibration in a homogeneous and isotropic unbounded body with a spherical cavity. The Green and Nagdhi model of thermoelasticity without energy dissipation is employed. The closed form solutions for distributions of displacement, temperature and stresses are obtained. The solutions valid in the case of small frequency are deduced and the results are compared with the corresponding results obtained in other generalized thermoelasticity theories. Numerical results applicable to a copper-like material are also presented graphically and the nature of variations of the physical quantities with radial coordinate and with frequency of vibration is analyzed. 相似文献
10.
《International Journal of Solids and Structures》2006,43(9):2761-2798
The present problem is the deformation of micropolar thermoelastic solids with cubic symmetry under the influence of various sources acting on the plane surface. Analytic expressions for displacement components, microrotation, force stress, couple stress, and temperature distribution are obtained in the physical domain for Lord–Shulman (L–S) and Green–Lindsay (G–L) theories of thermoelasticity by applying integral transforms. A numerical inversion technique has been applied to obtain the solution in the physical domain. The numerical results are presented graphically for a particular model. 相似文献
11.
This paper deals with a two-dimensional (2D) problem for a transverselyisotropic thick plate having heat sources and body
forces. The upper surface of the plate is stress free with the prescribed surface temperature, while the lower surface of
the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of the generalized
thermoelasticity proposed by Green and Naghdi. The governing equations for displacement and temperature fields are obtained
in the Laplace-Fourier transform domain by applying the Laplace and Fourier transforms. The inversion of the double transform
is done numerically. Numerical inversion of the Laplace transform is done based on the Fourier series expansion. Numerical
computations are carried out for magnesium (Mg), and the results are presented graphically. The results for an isotropic material
(Cu) are obtained numerically and presented graphically to be compared with those of a transversely isotropic material (Mg).
The effect of the body forces is also studied. 相似文献
12.
A matrix technique is formulated to efficiently solve stationary two-dimensional thermo-elasticity problems in simply supported multilayered beams and plates with an arbitrary number of layers which may be in imperfect mechanical and thermal contact. The method uses local transfer matrices and continuity conditions at the layer interfaces to establish explicit relationships between the unknown integration constants in the solution of a generic layer and those of the first layer. Explicit expressions are then derived for temperature, displacements and stresses through the imposition of the boundary conditions at the top and bottom surfaces of the plate. The dimensionless expressions allow to easily generate exact solutions, also for plates with many layers and interfacial thermal and mechanical imperfections. The solutions can be used for parametric analyses, to investigate the influence of the inhomogeneous material structure and interfacial imperfections on local fields or to verify the accuracy of approximate theories and numerical models. 相似文献
13.
14.
《European Journal of Mechanics - A/Solids》2008,27(4):607-621
This paper deals with a two dimensional problem for a transversely isotropic thick plate having heat source. The upper surface of the plate is stress free with prescribed surface temperature while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of generalized thermoelasticity proposed by Green and Naghdi. The governing equations for displacement and temperature fields are obtained in Laplace–Fourier transform domain by applying Laplace and Fourier transform techniques. The inversion of double transform has been done numerically. The numerical inversion of Laplace transform is done by using a method based on Fourier Series expansion technique. Numerical computations have been done for magnesium (Mg) and the results are presented graphically. The results for an isotropic material (Cu) have been deduced numerically and presented graphically to compare with those of transversely isotropic material (Mg). 相似文献
15.
Franz Ziegler 《International Applied Mechanics》2003,39(1):1-19
A review of the modern multiple field theory is given. The theory is derived from the classical two-field theory of linearized thermo-elasticity. Extensions of Maysel's formula are described. They allow formulating an optimal solution strategy using the Green function. Various applied problems are solved and commented on. The advantages of the multiple field theory are discussed 相似文献
16.
Coupled nonlinear constitutive models for rarefied and microscale gas flows: subtle interplay of kinematics and dissipation effects 总被引:1,自引:0,他引:1
R. S. Myong 《Continuum Mechanics and Thermodynamics》2009,21(5):389-399
The constitutive relations of gases in a thermal nonequilibrium (rarefied and microscale) can be derived by applying the moment
method to the Boltzmann equation. In this work, a model constitutive relation determined on the basis of the moment method
is developed and applied to some challenging problems in which classical hydrodynamic theories including the Navier–Stokes–Fourier
theory are shown to predict qualitatively wrong results. Analysis of coupled nonlinear constitutive models enables the fundamentals
of gas flows in thermal nonequilibrium to be identified: namely, nonlinear, asymmetric, and coupled relations between stresses
and the shear rate; and effect of the bulk viscosity. In addition, the new theory explains the central minimum of the temperature
profile in a force-driven Poiseuille gas flow, which is a well-known problem that renders the classical hydrodynamic theory
a global failure. 相似文献
17.
《International Journal of Solids and Structures》2007,44(7-8):2324-2348
The theory of diffusive stresses based on the time-fractional diffusion equation is formulated. The source problem is discussed as well as the Cauchy problem. The stresses are found in axially symmetric cases (for plane deformation). The numerical results for the concentration and stress distributions are presented graphically for various values of order of fractional derivative. 相似文献
18.
《International Journal of Solids and Structures》2005,42(18-19):5224-5242
A two-dimensional solution is presented for bending analysis of simply supported functionally graded ceramic–metal sandwich plates. The sandwich plate faces are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity and Poisson’s ratio of the faces are assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic ceramic material. Several kinds of sandwich plates are used taking into account the symmetry of the plate and the thickness of each layer. We derive field equations for functionally graded sandwich plates whose deformations are governed by either the shear deformation theories or the classical theory. Displacement functions that identically satisfy boundary conditions are used to reduce the governing equations to a set of coupled ordinary differential equations with variable coefficients. Numerical results of the sinusoidal, third-order, first-order and classical theories are presented to show the effect of material distribution on the deflections and stresses. 相似文献
19.
Wolfgang G. Knauss 《Experimental Mechanics》1968,8(4):177-181
The principal stresses in the vicinity of the crack tip in a rubber sheet have been determined experimentally by measuring the strain field with the aid of an imprinted grid work and calculating the stresses by assuming neo-Hookean material behavior. The principal stresses in the crack-tip vicinity are presented graphically. A correlation between the measured maximum tensile stress on the crack axis and that obtained from infinitesimal-elasticity theory is established. Information is given which provides bounds on the loading and deformation within which a large-deformation elastic analysis is valid before geometric deformations due to tearing must be considered. 相似文献
20.
A two variable refined plate theory for the bending analysis of functionally graded plates
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Ismail Mechab Hassen Ait Atmane Abdlouahed Tounsi Hichem Abdesselem Belhadj EI Abbas Adda Bedia 《Acta Mechanica Sinica》2010,26(6):941-949
Bending analysis of functionally graded plates using the two variable refined plate theory is presented in this paper.The number of unknown functions involved is reduced to merely four,as against five in other shear deformation theories. The variationally consistent theory presented here has, in many respects,strong similarity to the classical plate theory. It does not require shear correction factors,and gives rise to such transverse shear stress variation that the transverse shear stresses vary parabolically across the thickness and satisfy shear stress free surface conditions.Material properties of the plate are assumed to be graded in the thickness direction with their distributions following a simple power-law in terms of the volume fractions of the constituents.Governing equations are derived from the principle of virtual displacements, and a closed-form solution is found for a simply supported rectangular plate subjected to sinusoidal loading by using the Navier method.Numerical results obtained by the present theory are compared with available solutions,from which it can be concluded that the proposed theory is accurate and simple in analyzing the static bending behavior of functionally graded plates. 相似文献