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1.
E. Yu. Vitokhin M. B. Babenkov 《Journal of Applied Mechanics and Technical Physics》2016,57(3):537-549
The thermoelastic problem of laser exposure of metals and dielectrics is studied taking into account the finite speed of propagation of thermal waves and using a numerical finite-difference algorithm. The resulting numerical solution is compared with the analytical one. The problem is solved in coupled and uncoupled formulations. The solutions of the hyperbolic thermoelastic problem are compared with the solutions of the classical problem. Analytical expressions are obtained for the propagation speeds of the thermoelastic wave components. Times are determined at which the difference between the solutions of the hyperbolic and classical thermoelastic problems can be detected experimentally. 相似文献
2.
Yu. V. Nemirovskii K. M. Shlemenzon 《Journal of Applied Mechanics and Technical Physics》1981,22(3):426-434
In the present work, the dynamic problem of coupled thermoelasticity with the most general type of nonuniformity and anisotropy is analyzed. The hyperbolic nature of the system of equations of coupled thermoelasticity is demonstrated, effects of extinction of separate waves by superposition of elastic and thermoelastic wave fronts are investigated, and the interrelationship of different orders of discontinuity of stresses, displacements, and temperature is determined. The case of the uncoupled problem of thermoelasticity is especially analyzed. Sufficient conditions are obtained for the dynamic density for wave processes in thermoelasticity, previously investigated for boundary value problems of hyperbolic systems of second order differential equations [1], andelastic stress waves [2] are obtained. The generally accepted system of tensor notation for the theory of thermoelasticity is used [3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 154–163, May–June, 1981. 相似文献
3.
Santwana Mukhopadhyay Roushan Kumar 《Archive of Applied Mechanics (Ingenieur Archiv)》2010,80(8):869-881
The present work is attempted to formulate the state-space approach to the problems of thermoelastic interactions with energy
dissipation on the basis of the theory of generalized thermoelasticity type-III, recently developed by Green and Naghdi. The
formulation is then applied to solve a boundary value problem of an isotropic elastic half space with its plane boundary subjected
to two different types of boundary conditions: (1) sudden increase in temperature and zero stress and (2) sudden increase
in load and zero temperature change. Integral transform method is applied to obtain the solution of the problem. The short
time approximated solutions for the field variables have been constructed analytically for both the cases. The problem is
illustrated with the help of different graphs of numerical values of the field variables. 相似文献
4.
N. G. Khomasuridze 《International Applied Mechanics》2005,41(9):1076-1083
Consideration is given to a class of static boundary-value problems of thermoelasticity and their solutions for bodies bounded
by surfaces in orthogonal curvilinear coordinates. The following parameters are given: heat intensity, normal displacement,
the tangential component of the curl of the displacement vector or temperature, the divergence of the displacement vector,
and tangential displacement. The problem is reduced to the successive integration of the Laplace and Poisson equations with
the classical boundary conditions. Specific problems of thermoelasticity are solved in Cartesian and cylindrical coordinates
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 137–144, September 2005. 相似文献
5.
The two‐dimensional convection–diffusion‐type equations are solved by using the boundary element method (BEM) based on the time‐dependent fundamental solution. The emphasis is given on the solution of magnetohydrodynamic (MHD) duct flow problems with arbitrary wall conductivity. The boundary and time integrals in the BEM formulation are computed numerically assuming constant variations of the unknowns on both the boundary elements and the time intervals. Then, the solution is advanced to the steady‐state iteratively. Thus, it is possible to use quite large time increments and stability problems are not encountered. The time‐domain BEM solution procedure is tested on some convection–diffusion problems and the MHD duct flow problem with insulated walls to establish the validity of the approach. The numerical results for these sample problems compare very well to analytical results. Then, the BEM formulation of the MHD duct flow problem with arbitrary wall conductivity is obtained for the first time in such a way that the equations are solved together with the coupled boundary conditions. The use of time‐dependent fundamental solution enables us to obtain numerical solutions for this problem for the Hartmann number values up to 300 and for several values of conductivity parameter. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
6.
S. C. Gupta 《Applied Scientific Research》1995,54(2):137-160
Analytical and numerical solutions have been obtained for some moving boundary problems associated with Joule heating and distributed absorption of oxygen in tissues. Several questions have been examined which are concerned with the solutions of classical formulation of sharp melting front model and the classical enthalpy formulation in which solid, liquid and mushy regions are present. Thermal properties and heat sources in the solid and liquid regions have been taken as unequal. The short-time analytical solutions presented here provide useful information. An effective numerical scheme has been proposed which is accurate and simple. 相似文献
7.
Coupled equations of thermoelasticity take into account the effect of nonuniform heating on the medium deformation and that
of the dilatation rate on the temperature distribution. As a rule, the coupling coefficients are small and it is assumed,
sometimes without proper justification, that the effect of the dilatation rate on the heat conduction process can be neglected.
The aim of the present paper is to construct analytical solutions of some model boundary-value problems for a thermoelastic
bounded body and to determine the body characteristic dimensions and the medium thermomechanical moduli forwhich it is necessary
to take into account that the temperature and displacement fields are coupled. We consider some models constructed on the
basis of the Fourier heat conduction law and the generalized Cattaneo-Jeffreys law in which the heat flux inertia is taken
into account. The solution is constructed as an expansion in a biorthogonal system of eigenfunctions of the nonself-adjoint
operator pencil generated by the coupled equations of motion and heat conduction. For the model problem, we choose a special
class of boundary conditions that allows us to exactly determine the pencil eigenvalues. 相似文献
8.
Dominic Groulx 《Heat and Mass Transfer》2010,46(7):707-716
An analytical resolution of the time-dependent one-dimensional heat conduction problem with time-dependent boundary conditions using the method of separation of variables and Duhamel’s theorem is presented. The two boundary conditions used are a time-dependent heat flux at one end and a varying temperature at the other end of the one-dimensional domain. It is put forth because the author found that the prescribed resolution method using separation of variables and Duhamel’s theorem presented in heat conduction textbooks is not directly applicable to problems with more than one time-dependent boundary condition. The analytical method presented in this paper makes use of one of the property of the heat conduction equation: the apparent linearity of the solutions. For that reason, in order to solve a problem with two time-dependent boundary conditions, the author first separates the initial problem into two independent but complementary problems, each with only one time-dependent boundary condition. Doing that, both simpler problems can be solved independently using a prescribed method that is known to work and the final solution can be obtained by joining the two independent solutions from the simpler separated problems. Every step of the resolution method is presented in this paper, along with a numerical validation of the final solution of three test case problems. 相似文献
9.
M. B. Babenkov 《Journal of Applied Mechanics and Technical Physics》2011,52(6):941-949
Dispersion relations for a coupled thermoelasticity problem including a hyperbolic heat conduction equation are derived, and their asymptotic analysis is performed. Dependences of the wave number and characteristics of the vibration damping rate on frequency are obtained and compared with similar diagrams in the classical model. 相似文献
10.
《International Journal of Solids and Structures》2004,41(22-23):6233-6247
A general analytical solution for an isotropic trimaterial interacted with a point heat source is provided in this paper. Based on the method of analytical continuation in conjunction with the alternating technique, the solutions to heat conduction and thermoelasticity problems for three dissimilar media are first derived. A rapidly convergent series solution for both the temperature and stress functions, which is expressed in terms of an explicit general term of the complex potential of the corresponding homogeneous problem, is obtained in an elegant form. As a numerical illustration, the distributions of thermal stresses along the interface are presented for various material combinations and for different positions of the applied heat source and heat sink. 相似文献
11.
Analysis of non-Fourier heat conduction in a solid sphere under arbitrary surface temperature change
Wei Tao Zhao Jiu Hui Wu Zhe Chen 《Archive of Applied Mechanics (Ingenieur Archiv)》2014,84(4):505-518
In this paper, the non-Fourier heat conduction in a solid sphere under arbitrary surface thermal disturbances is solved analytically. Four cases including sudden, simple harmonic periodic, triangular and pulse surface temperature changes are investigated step-by-step. The analytical solutions are obtained using the separation of variables method and Duhamel’s principle along with the Fourier series representation of an arbitrary periodic function and the Fourier integral representation of an arbitrary non-periodic function. Using these analytical solutions, the temperature profiles of the solid sphere are analyzed, and the differences in the temperature response between the “hyperbolic” and “parabolic” are discussed. These solutions can be applicable to all kinds of non-Fourier heat conduction analyses for arbitrary boundary conditions occurred in technology. And as application examples, particular attention is devoted to the cases of triangular surface temperature change and pulse surface temperature change. The examples presented in this paper can be used as benchmark problems for future numerical method validations. 相似文献
12.
13.
《International Journal of Solids and Structures》2003,40(15):3913-3933
Although the classical lamination theory was developed long time ago, it is still not easy to apply this theory to find the analytical solutions for the curvilinear boundary value problems especially when the stretching and bending are coupled each other. To overcome the difficulties, recently we developed a Stroh-like formalism for the general composite laminates. By using this formalism, most of the relations for the coupled stretching–bending problems can be organized into the forms of Stroh formalism for two-dimensional anisotropic elasticity problems. With this newly developed Stroh-like formalism, it becomes easier to obtain an analytical solution for the coupled stretching–bending problems of holes in composite laminates. Because the Stroh-like formalism is a complex variable formalism, the analytical solutions for the whole field are expressed in complex form. Through the use of some identities derived in this paper, the resultant forces and moments around the hole boundary are obtained explicitly in real form. Due to the lack of analytical solutions for the general cases, the comparison is made with the existing analytical solutions for some special cases. In addition, to show the generality of our analytical solutions, several numerical examples are presented to discuss the coupling effect of the laminates and the shape effect of the holes. 相似文献
14.
J. R. Barber 《Flow, Turbulence and Combustion》1983,40(2):135-157
The paper reviews the method of complex potential functions developed by Green and Collins as applied to axisymmetric mixed boundary value problems in elasticity for the half-space. It is shown how the method can be applied to problems in several coupled potential functions such as adhesive and frictional contact problems, to problems involving annular regions and to problems in thermoelasticity. Attention is given to the question of choosing a formulation which leads to a well-behaved numerical solution. Tables are given of the most commonly needed inversion formulae and of expressions for total load and stress intensity factor. 相似文献
15.
16.
T. HAYAT S. A. SHEHZAD A. ALSAEDI M. S. ALHOTHUALI 《应用数学和力学(英文版)》2013,34(4):489-500
The present study addresses the three-dimensional flow of an Oldroyd-B fluid over a stretching surface with convective boundary conditions. The problem formulation is presented using the conservation laws of mass, momentum, and energy. The solutions to the dimensionless problems are computed. The convergence of series solutions by the homotopy analysis method (HAM) is discussed graphically and numerically. The graphs are plotted for various parameters of the temperature profile. The series solutions are verified by providing a comparison in a limiting case. The numerical values of the local Nusselt number are analyzed. 相似文献
17.
《International Journal of Solids and Structures》2014,51(21-22):3798-3806
A finite element discretized symplectic method is introduced to find the thermal stress intensity factors (TSIFs) under steady-state thermal loading by symplectic expansion. The cracked body is modeled by the conventional finite elements and divided into two regions: near and far fields. In the near field, Hamiltonian systems are established for the heat conduction and thermoelasticity problems respectively. Closed form temperature and displacement functions are expressed by symplectic eigen-solutions in polar coordinates. Combined with the analytic symplectic series and the classical finite elements for arbitrary boundary conditions, the main unknowns are no longer the nodal temperature and displacements but are the coefficients of the symplectic series after matrix transformation. The TSIFs, temperatures, displacements and stresses at the singular region are obtained simultaneously without any post-processing. A number of numerical examples as well as convergence studies are given and are found to be in good agreement with the existing solutions. 相似文献
18.
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
19.
The problem of the steady flow of three classes of non-linear fluids of the differential type past a porous plate with uniform suction or injection is studied. The flow which is studied is the counterpart of the classical ‘asymptotic suction’ problem, within the context of the non-Newtonian fluid models. The non-linear differential equations resulting from the balance of momentum and mass, coupled with suitable boundary conditions, are solved numerically either by a finite difference method or by a collocation method with a B-spline function basis. The manner in which the various material parameters affect the structure of the boundary layer is delineated. The issue of paucity of boundary conditions for general non-linear fluids of the differential type, and a method for augmenting the boundary conditions for a certain class of flow problems, is illustrated. A comparison is made of the numerical solutions with the solutions from a regular perturbation approach, as well as a singular perturbation. 相似文献