Showing papers in "Journal of Thermal Stresses in 1978"
TL;DR: In this paper, a uniqueness theorem for the solutions of the differential equations of thermopiezoelectricity is given, on the basis of the energy balance, and the generalized Hamilton principle and the theorem of reciprocity of work are also deduced.
Abstract: In this paper a uniqueness theorem for the solutions of the differential equations of thermopiezoelectricity is given, on the basis of the energy balance. The generalized Hamilton principle and the theorem of reciprocity of work are also deduced.
225 citations
TL;DR: In this paper, the matrix exponential method was applied to the non-dimensional equations of coupled thermoelasticity and the results obtained can be used to generate solutions in the Laplace transform domain to a broad class of problems in thermo-elasticy.
Abstract: The method of the matrix exponential, which constitutes the basis of the state space approach of modern control theory, is applied to the nondimensional equations of coupled thermoelasticity. The disadvantages of using the thermoelastic potential are thus avoided. The results obtained can be used to generate solutions in the Laplace-transform domain to a broad class of problems in thermoelasticity. Applications to problems pertaining to a half-space and a layer are presented.
147 citations
TL;DR: A decomposition theorem of the Boggio type for the linear thermoelasticity proposed by Green and Lindsay was established in this article, and a decomposition of the linear linear thermasticity was also established for the non-linear thermodynamic linear thermodynamic properties.
Abstract: A decomposition theorem of the Boggio type is established for the linear thermoelasticity proposed by Green and Lindsay.
61 citations
TL;DR: In this paper, the authors evaluated the interlaminar stresses in layered beam composites subjected to differential expansions and contractions of the individual beam elements and demonstrated that the stress responsible for delamination failures can be made to vanish by an appropriate choice of material and beam-section properties.
Abstract: Interlaminar stresses are evaluated in layered beam composites subjected to differential expansions and contractions of the individual beam elements. It is shown that the maximum interlaminar stresses occur at the free ends of the beam and increase as the effective bond-layer stiffness increases, whereas the stress distribution is confined to a narrower region. It is also demonstrated that the stress responsible for delamination failures can be made to vanish by an appropriate choice of material and beam-section properties.
54 citations
TL;DR: In this paper, a hollow orthotropic elastic cylinder due to a steady-state plane temperature distribution T(r,θ) is analyzed for traction-free boundary conditions, and exact solution using the Airy stress function in a Fourier-series form is developed.
Abstract: Stresses in a hollow orthotropic elastic cylinder due to a steady-state plane temperature distribution T(r,θ) are analyzed for tractionfree boundary conditions An exact solution is developed using the Airy stress function in a Fourier-series form Numerical results are given for a fiber-reinforced composite material
37 citations
TL;DR: In this paper, a theoretical study of the stresses in an infinite circular solid cylinder subjected to rapid surface heating and cooling is presented, where a quasistatic, uncoupled, thermo-elastic analysis based on the incremental theory of plasticity is formulated, and a numerical procedure is developed for a method of successive elastic solutions.
Abstract: This paper presents a theoretical study of the stresses in an infinite circular solid cylinder subjected to rapid surface heating and cooling. A quasistatic, uncoupled, thermoelastoplastic analysis based on the incremental theory of plasticity is formulated, and a numerical procedure is developed for a method of successive elastic solutions. The material of the cylinder is assumed to have temperature-dependent properties and to be characterized by the Romberg-Osgood stress-strain relation. The transient and residual stress distributions are discussed in detail, along with variations of the equivalent stress and plastic strain with time.
24 citations
TL;DR: In this article, the general approaches to the solution of asymmetrical three-dimensional unsteady thermal stress problems are explained for curvilinear aeolotropic solids that are transversely isotropic about the radius vector.
Abstract: The general approaches to the solution of asymmetrical three-dimensional unsteady thermal-stress problems are explained for curvilinear aeolotropic solids that are transversely isotropic about the radius vector. As an example, the temperature and stresses for a specific case are solved and computed.
20 citations
TL;DR: A uniqueness theorem for the stress-temperature equations of linear thermoelasticity proposed by Green and Lindsay is established in this paper, which covers an unconventional initial-boundary-value problem with arbitrary initial tensorial data.
Abstract: A uniqueness theorem for the stress-temperature equations of linear thermoelasticity proposed by Green and Lindsay is established The theorem covers an unconventional initial-boundary-value problem with arbitrary initial tensorial data
13 citations
TL;DR: In this paper, the authors considered the steady-state plane-strain thermoelastic problem of an elastic layer with one face stressfree and the other face resting on a rigid frictionless foundation; the free surface of the layer is subjected to arbitrary temperature on the part a < x < b, whereas the rest of the surface is insulated and the surface in contact with the foundation is insulated.
Abstract: We consider the following two mixed boundary-value problems: (1) The steady-state plane-strain thermoelastic problem of an elastic layer with one face stressfree and the other face resting on a rigid frictionless foundation; the free surface of the layer is subjected to arbitrary temperature on the part a < x < b, whereas the rest of the surface is insulated and the surface in contact with the foundation is insulated. (2) The two-dimensional electrostatic problem of the electrostatic potential due to two coplanar strips that are charged to equal and opposite potentials and that are parallel to and equidistant from a grounded strip. By the use of Fourier transforms, both problems are reduced to the solution of triple trigonometric integral equations. The closed-form solution of these triple-integral equations is obtained by using the finite Hilbert-transform technique. Closed-form expressions are obtained for the physical quantities in both problems.
10 citations
TL;DR: In this article, a theory in terms of the coldness, which is the reciprocal of the temperature, was developed for the case in which the temperature change ∣T − T 0 ∣ is much less than To.
Abstract: The linear coupled theory of thermoelasticity, with a modified Fourier heat-conduction law to include the thermal-relaxation effect, has been applied in studying heat pulses in solids at very low reference temperature T 0. The theory is limited to the case in which the temperature change ∣T − T 0∣ is much less than To. This restriction is relaxed in this work by developing a theory in terms of the coldness, which is the reciprocal of the temperature; in any heating process the net change in coldness is always less than the coldness at the reference state. Linear and nonlinear constitutive equations in terms of the coldness variable as well as the balance equations are proposed. They might be useful for investigating heat-pulse propagation in solids at extremely low temperature.
9 citations
TL;DR: In this article, an approximate method of analysis for the nonlinear bending of shallow sandwich shells is proposed by extending the well-known Berger approach for single-layer isotropic elastic plates.
Abstract: By extending the well-known Berger approach for single-layer isotropic elastic plates, an approximate method of analysis for the nonlinear bending of shallow sandwich shells is proposed. Governing field equations are derived for shallow sandwich shells subjected to mechanical as well as thermal effects. Numerical calculations are carried out for large deflections of shells and flat plates due to a temperature difference between the upper and lower faces, and the applicability of the approximate field equations is discussed.
Abstract: This paper is a theoretical analysis of the thermoelastic effect upon accuracy in the machining of metals. The problem is reduced to the unsteady thermoelastic analysis of a solid cylinder heated on the surface axisym-metrically by a moving heat source under an axial restraint. The thermal and elastic distortions of the workpiece are computed, and the error in the shape is plotted. The authors are grateful to Mi. Ishikawa and Mr. Omichi for their computer calculations. Professor Takeuti's mailing address is Department of Mechanical Engineering, University of Osaka Prefecture, Mozu, Sakai, 591, Japan.
TL;DR: In this paper, a constitutive relation for thermoviscoelastic-plastic material is derived in terms of internal variables, including the stress-strain relations for a material subjected to uniaxial tension, and rate-dependent behavior is discussed.
Abstract: A constitutive relation for thermoviscoelastic-plastic material is derived in terms of internal variables. Three types of internal variables-plastic strain, the hardening parameter, and a variable exhibiting viscous effects-are introduced, and the thermoviscoelastic strain and rate-dependent plastic strain are given in the framework of the thermodynamics of solids. As an example, stress-strain relations are calculated for a material subjected to uniaxial tension, and the rate-dependent behavior is discussed.
TL;DR: In this article, a method of solving the problem of thermal stresses for composite Cosserat elastic cylinders is given, where the cross section of the cylinder is occupied by inhomogeneous and isotropic elastic materials.
Abstract: A method of solving the problem of thermal stresses for composite Cosserat elastic cylinders is given, where the cross section of the cylinder is occupied by inhomogeneous and isotropic elastic materials. The thermoelastic coefficients are independent of the axial coordinate
TL;DR: In this paper, a simple supported curved plate, cut from a complete thin-walled cylindrical shell of radius a, subject to an arbitrary three-dimensional temperature distribution is presented as non-dimensional curves.
Abstract: The paper begins with a statement of a reciprocal theorem in thermoelasticity based on a generalization of Betti's reciprocal theorem. This is followed by the application to and solution of a simply supported curved plate, cut from a complete thin-walled cylindrical shell of radius a, subject to an arbitrary three-dimensional temperature distribution. The general solution is then used to determine the stresses and displacements resulting from a specified three-dimensional temperature distribution. The results are presented as non-dimensional curves. The usefulness of the theorem resides in the fact that, by appropriate application, existing solutions in elasticity may be used to obtain solutions of thermoelastic problems.
TL;DR: In this paper, the formulation of coupled thermoelasticity in terms of Green's function is presented and a formal solution for the quasistatic linear problem is given.
Abstract: The formulation of coupled thermoelasticity is presented in terms of Green's function. A formal solution for the quasistatic linear problem is given.
TL;DR: In this article, the first stage of the problem of specification of the temperature field in a uniform, infinitely long, elastic bar heated by an electric current, the surface of the bar being kept at zero temperature.
Abstract: The method of orthogonal projection is applied in the first stage of thermoelastic problems involving specification of the temperature field in a uniform, infinitely long, elastic bar heated by an electric current, the surface of the bar being kept at zero temperature. Three kinds of cross sections of the bar are considered: elliptical, equilateral triangular, and in the form of a circular sector. All the function-space concepts that are used are briefly explained, but the treatment is purely intuitive.
TL;DR: In this article, the mechanocaloric effect on magnetothermoelastostatic interactions in a cylindrical conductor carrying a uniform electric current was investigated and it was found that this effect reduces the Joule heating effect and induces non-linearity into the behavior of stresses.
Abstract: The mechanocaloric effect on magnetothermoelastostatic interactions in a cylindrical conductor carrying a uniform electric current is investigated. It is found that this effect reduces the Joule heating effect and induces non-linearity into the behavior of stresses. A condition under which the mechanocaloric effect nullifies the Joule effect is also obtained.
TL;DR: In this paper, a method for determining the transient thermal stresses that evolve during the molding process within a material hardening as the result of an exothermic chemical reaction is presented.
Abstract: A method is formulated for determining the transient thermal stresses that evolve during the molding process within a material hardening as the result of an exothermic chemical reaction. The formulation is applied to the restricted case in which the shear-to-bulk-modulus ratio for the fully hardened material is small, and where the material is cast in the form of an infinitely long solid cylinder in a thermally thin elastic mold. The heat-generation rate and temperature variation are derived from a first-order chemical reaction. The solidification of the material is described by a transformation from an initial liquidlike state to an elastic solid, with thermoelastic constitutive rate equations during the hardening process based upon a two-component mixture model whose composition is related to the degree of reaction. Graphs for transient stresses and residual stress distributions are shown in terms of dimensionless variables, with hardening rate related to thermochemical constants, and with the ...
TL;DR: In this paper, the stability and accuracy of finite-element analyses of transient thermoviscoelasticity subjected to irreversible thermodynamic processes are investigated, including the use of an incremental free energy that incorporates internal state variables in terms of a discretized generalized Maxwell model.
Abstract: This paper is concerned with the stability and accuracy of finite-element analyses of transient thermoviscoelasticity subjected to irreversible thermodynamic processes. The study includes the use of an incremental free energy that incorporates internal state variables in terms of a discretized generalized Maxwell model. Numerical integration is then performed, with past histories being updated in each discretized time step. The effects of thermomechanical coupling, internal dissipation, boundary conditions, and various temporal operators are studied with respect to spectral radii, phase errors, numerical damping, etc. A stability criterion predicted by spectral radii for combined equations of motion and heat conduction confirms the consequent numerical results for transient response according to the estimated degree of stability. Stable solutions generally lead to convergence to the exact solution, but with lower rates of convergence than those of linear-uncoupled equations. For simplicity, the numerical ...