Stationary Thermoelasticity Research Articles

Influence of thermoelastic boundary conditions on the mechanical strength of cold-rolled silicon steels

A numerical and experimental framework is proposed for an uncoupled thermoelastic analysis of anisotropic cold-rolled steel alloys Fe-3%Si to explore the influence on the material strength when subjected to thermal and inertial loads. Following the stationary thermoelasticity formulation of the boundary element method (BEM), this model focuses on the 2D study of these materials when the elastic properties are temperature-dependent and inertial forces are considerable. Validations and an industrial application are shown to illustrate the feasibility of using the framework proposed here to study the thermomechanical behavior of the Fe-3%Si, taking into account the influence of temperature on its mechanical and thermal properties. Finally, a complete database is provided for reproducibility purposes.

Approximation of Solutions to Equations in Static Thermoelasticity

Approximation of Solutions to Equations in Static Thermoelasticity

Analytical Solution of Stationary Coupled Thermoelasticity Problem for Inhomogeneous Structures

A mathematical statement for the coupled stationary thermoelasticity is given on the basis of a variational approach and the contact boundary problem is formulated to consider inhomogeneous materials. The structure of general representation of the solution from the set of the auxiliary potentials is established. The potentials are analyzed depending on the parameters of the model, taking into account the restrictions associated with additional requirements for the positive definiteness of the potential energy density for the coupled problem in the one-dimensional case. The novelty of this work lies in the fact that it attempts to take into account the effects of higher order coupling between the gradients of the temperature fields and the gradients of the deformation fields. From a mathematical point of view, this leads to a change in the roots of the characteristic equation and affects the structure of the solution. Contact boundary value problems are formulated for modeling inhomogeneous materials and a solution for a layered structure is constructed. The analysis of the influence of the model parameters on the structure of the solution is given. The features of the distribution of mechanical and thermal fields in the region of phase contact with a change in the parameters, which are characteristic only for gradient theories of coupled thermoelasticity and stationary thermal conductivity, are discussed. It is shown, for example, that taking into account the additional parameter of connectivity of gradient fields of deformations and temperatures predicts the appearance of rapidly changing temperature fields and significant localization of heat fluxes in the vicinity of phase contact in inhomogeneous materials.

Static thermoelasticity problems for layered functionally graded thermosensitive cylinder

Static thermoelasticity problems for layered functionally graded thermosensitive cylinder

Fully coupled meshfree numerical approach based on the finite pointset method for static linear thermoelasticity problems

In this work, a promising fully coupled meshfree numerical approach is extended and implemented for the first time in the field of linear static thermoelasticity. A real meshfree method, the so-called finite pointset method (FPM), is applied and implemented in order to solve the strong/classical form of the governing partial differential equations for static linear thermoelasticity. Several benchmark problems are numerically solved in order to show the proposed coupled FPM numerical performance. The presented FPM meshfree approach shows excellent behavior for 2D linear static thermoelasticity problems even for complex geometries.

The calculation of the thermal stressed state of multilayer platesofa non-canonical shape

A method for solving the problem of stationary thermoelasticity of multilayer plates of non-canonical shape in plan is proposed, which is based on the method of immersing a complex domain into the domain of a canonical form. A non-canonical plate with arbitrary boundary conditions "immerses" into a canonical plate. To ensure that the specified boundary conditions are met, additional compensating loads are added to the auxiliary structure, distributed along the contour of the initial structure. The intensities of compensating loads are determined from a system of integral equations. Deformation of the layers of the plates are described within the framework of the first-order theory, taking into account the transverse shear strains in each layer. The field of temperature loads is obtained by solving the non-stationary problem of thermal conductivity of a multilayer plate. The temperature stresses in a five-layer plate when heated by a film heat source are investigated.

Two-Dimensional Problem of Thermoelasticity for a Half Space Whose Boundary is Either Free or Rigidly, Smoothly, or Flexibly Fastened with Heat Insulation in a Ribbon-Like Domain Parallel to the Boundary

We construct Green’s functions for the problems of stationary heat conduction and thermoelasticity posed for a semiinfinite body subjected to the action of a thermal dipole under plane-strain conditions with either free or rigidly, smoothly, or flexibly fastened boundary kept at a temperature equal to zero. To solve the problem of heat conduction, we use the logarithmic double-layer potential. In the problem of thermoelasticity, we use a thermoelastic potential of displacements in the infinite body with heat dipoles specularly located relative to the boundary of the half space. To satisfy the boundary conditions on the boundary of the body, we construct the Boussinesq functions. We present explicit expressions for temperature, displacements, and stresses that can be used to determine the thermoelastic state of the half space caused by the perturbations of a given heat flux by a heatproof ribbon-like domain parallel to the boundary.

The problem of stationary thermoelasticity for a piecewise homogeneous transversely isotropic space under the influence of a heat flux specified at infinity is considered

An exact solution to the problem of thermoelasticity about interfacial circular inclusion, which is in complete adhesion with different transversely isotropic half-spaces, is constructed. Analytical dependencies are obtained between the parameters of the linear displacement of the inclusion and the characteristics of the force and temperature fields. The order of the singularity of surges and displacements near the inclusion is determined. Expressions are obtained for the stress intensity factor at the inclusion boundary, as well as the numerical dependences of these coefficients on the polar angle, temperature, and load.

Thermally active interphase inclusion in a smooth contact conditions with transversely isotropic half-spaces

An exact solution of the stationary thermoelasticity problem about interfacial circular absolutely rigid inclusion, which is in the smooth contact conditions in a piecewise homogeneous transversely homogeneous space, is constructed. The task with the help of the constructed discontinuous solution, by the method of singular integral relations, is reduced to a system of singular integral equations (SIE). An exact solution has been built for the specified SIE, as a result, dependences of translational displacement of the inclusion on temperature, the resultant load, main moment and thermomechanical characteristics of transversely isotropic materials have been obtained.

Stationary thermoelasticity problem for a solid cylinder with a disc-shaped crack enclosed in a thin shell

Stationary thermoelasticity problem for a solid cylinder with a disc-shaped crack enclosed in a thin shell

Кругове теплоактивне міжфазне включення в кусково-однорідному трансверсального-ізотропному просторі

An exact solution of the stationary thermoelasticity problem about interfacial circular absolutely rigid inclusion, which is under conditions of complete adhesion and under conditions of smooth contact with transversely homogeneous spaces, is constructed. The task with the help of the constructed discontinuous solution, by the method of singular integral relations, is reduced to a system of singular integral equations (SIE). An exact solution has been built for the specified systems of two-dimensional singular integral equations. As a result, dependences jumps of stresses and displacement on temperature, equivalent load, main moments and thermomechanical characteristics of transversally isotropic materials. The influence of the type of contact interaction on the behavior of the solutions is established. In particular, it has been shown that the stresses in the neighborhood of the inclusion with a smooth contact have a root singularity, and with complete coupling, the root singularity, which is amplified by oscillation. The behavior of the generalized intensity coefficient (GCIN) was studied for the combination of various transversely isotropic materials at different power and temperature loads.

Two-Dimensional Problem of Thermoelasticity for a Half Space in the Presence of Heat Release in a Ribbon-Shaped Domain Parallel to its Boundary

Using a logarithmic single-layer potential, thermoelastic displacement potential, Airy stress function, and Boussinesq function, we solve two-dimensional problems of stationary heat conduction and thermoelasticity under the conditions of plane deformation of a semiinfinite body in the presence of heat release in a ribbon-shaped domain parallel to its boundary (in this domain, either a temperature or a heat flux is given). The boundary of the body is kept at temperature equal to zero. We study the distribution of stresses in the domain of heat release with given heat sources of constant intensity at constant temperature.

Numerical calculation and experimental verification of the fictitious angular velocity for transient temperature impact on the fiber-optic gyroscope coil

Numerical simulation and experimental investigation of the effect of two types of quadrupole winding of fiber coil on the fictitious angular velocity of a fiber-optic gyroscope under transient temperature conditions are carried out. The coil is formed by winding optical fiber precovered with two protective-hardening layers on the cylindrical surface and its further fixation by compound. For experimental verification of the fictitious angular velocity, a special device was made, in which the fiber coil was held by rubber gaskets used to maximally exclude the transfer of mechanical loads from the body parts to the coil. A functional for the fictitious angular velocity is represented as a function of temperature and elastic strain rate in the fiber core. In the software ANSYS, a two-dimensional axisymmetric finite-element analog of a structurally inhomogeneous coil in the device is modeled. To verify the elastic strains under uniform thermal actions, the problem of stationary thermoelasticity was solved. With the Brillouin optical time domain analyizer, Brillouin frequencies shifts at two temperatures were established, and the distribution of strains was obtained. A comparison of the calculated and experimental strains made it possible to refine the Poisson's ratio of a weakly compressible primary coating. The solution of the transient thermal problem and temperature sensor readings allowed us to establish the heat-conductivity coefficient between the device and the moving air in the heat chamber. As an impact, we considered the heating of the environment at a rate of 1 °C/min, followed by a steady-state output. To find the temperature and strain fields for the functional of fictitious angular velocity, the unbound quasistationary thermoelasticity problem was solved. Tests were carried out with two types of winding of the coil. The experimental results showed satisfactory agreement with the calculated data.

Analysis of thermo-elastic problems using the improved element-free Galerkin method

The improved element-free Galerkin method (IEFG) is presented to deal with thermo-elastic problems. This mesh-free method is a combination between the element-free Galerkin method and the improved moving least-square approximation. It has not the Kronecker delta property, and the penalty method is used to impose the essential boundary conditions. In this paper, linear and stationary thermo-elasticity is treated. To solve the thermo-elastic problem, this latter is decoupled into two separate parts: first, the heat transfer problem is analyzed to reach the temperature field, which is used as input in the mechanical problem to calculate the displacement field and then the stress fields. Numerical examples with different boundary conditions are illustrated. The performance and the accuracy of the IEFG method are approved when obtained results are compared to finite-element results and analytical solution.

The singular boundary method for two-dimensional static thermoelasticity analysis

Based on the singular boundary method (SBM) coupled with the radial basis functions (RBF), a meshless algorithm is proposed to solve two-dimensional static thermoelasticity problems. The displacements and stresses can be written as the sum of a homogeneous solution and a particular solution. The RBF and SBM are used to construct the corresponding approximate particular and homogeneous parts, respectively. All unknowns are determined by satisfying the governing equations and the boundary conditions. Numerical experiments are performed for different cases, and the proposed meshless method is effectively validated by comparing the results with the available analytical solutions.

Thermoelastic Equilibrium of a Three-Layer Circular Hollow Cylinder Weakened by a Crack

We solve plane problems of stationary heat conduction and thermoelasticity for a hollow three-layer cylinder weakened by a crack by the method of singular integral equations. The cross section of the cylinder is a circular concentric ring with similar rings of a different material inserted into this ring. The inner ring contains an edge radial crack. The surfaces of the cylinder are free of loads and temperature conditions of the first kind are satisfied on these surfaces. On the interface of the media, we impose the conditions of perfect thermal and mechanical contact. The numerical solution is obtained for the case where unequal constant temperatures are given on the inner and outer surfaces of the cylinder. The stress intensity factors at the tip of an edge crack are found for different values of thermal and mechanical parameters of the components of the cylinder.

The method of fundamental solutions for problems in static thermo-elasticity with incomplete boundary data

An inverse problem in static thermo-elasticity is investigated. The aim is to reconstruct the unspecified boundary data, as well as the temperature and displacement inside a body from over-specified boundary data measured on an accessible portion of its boundary. The problem is linear but ill-posed. The uniqueness of the solution is established but the continuous dependence on the input data is violated. In order to reconstruct a stable and accurate solution, the method of fundamental solutions is combined with Tikhonov regularization where the regularization parameter is selected based on the L-curve criterion. Numerical results are presented in both two and three dimensions showing the feasibility and ease of implementation of the proposed technique.

Integral Equations in Two-Dimensional Problems of Thermoelasticity for a Three-Layer Annular Cracked Domain

Two-dimensional problems of stationary heat conduction and thermoelasticity for a three-layer annular domain with cracks are reduced to singular integral equations. The systems of integral equations of the first and second kind are constructed for closed (contours of layers and the external boundary) and open (cracks) contours in the case where the contour of the internal boundary of the domain is a circle.

The method of fundamental solutions for an inverse boundary value problem in static thermo-elasticity

The inverse problem of coupled static thermo-elasticity in which one has to determine the thermo-elastic stress state in a body from displacements and temperature given on a subset of the boundary is considered. A regularized method of fundamental solutions is employed in order to find a stable numerical solution to this ill-posed, but linear coupled inverse problem. The choice of the regularization parameter is based on the L-curve criterion. Numerical results are presented and discussed.

New model representations of dynamic thermoviscoelasticity in the problem of heat shock

Investigation of heat shock is a central problem in thermomechanics because this phenomenon is used in powerful energy sources and different technological processes. The solution of the indicated problem with the use of dynamic and quasi-static thermoelasticity models made it possible to investigate the physical mechanisms of the heat-stressed state of isotropic and anisotropic elastic bodies on the basis of the classical Fourier and Maxwell–Cattaneo–Lykov phenomenologies of the finite velocity of heat propagation in solid bodies, to develop the generalized theory of conjugation of thermomechanical fields with different physical (electric, magnetic) fields, to formulate the main relations of the linearized theory with account for the heat memory of solids, and to determine the relation between the macroscopic behavior of a continuous medium, the internal parameters of its state, and the rate of their change with time. A systematization of the results obtained in this field of thermomechanics is given in the reviews of the author of this work [1, 2] and in his monograph [3, 4]. The problem being considered was investigated mainly for technologically important materials obeying Hooke’s law. In the corresponding mathematical models defining the dynamic, quasi-static, and static thermoelasticity parameters of materials, isotropic materials with constant temperature-independent thermomechanical coefficients, small temperature differences not larger than any limiting value determined by the properties of a material, and stresses lower than the yield point of the material are considered. It is believed [3] that at relatively low temperatures and stresses, the behavior of a wide class of materials is well defined by the thermoelasticity theory. However, at higher temperatures and larger stresses, the notion of elastic body becomes insufficient because in all the materials a viscous flow is present. A real body exhibits elastic and viscous properties and, therefore, it is properly termed the viscoelastic body. The problem on the heat shock of such a body is solved by generalization of the relations between its stresses and deformations. Alfrey, Hilton, and Shternberg [5] concluded that the behavior of a viscoelastic body under the conditions of extremal temperature and chemical actions can be defined in the context of a purely thermoelastic problem