Quasi-static Thermoelastic Problem Research Articles

Termostressed state of a three-layer rectangular plate under non-stationary convective heating conditions

The study considers a rectangular isotropic plate with a layered irregular structure. It is convectively non-stationarily heated by an external environment. The initial relationships of the non-stationary heat conduction and thermoelasticity problem are formulated using a five-mode mathematical model based on the shear deformation theory of thermoelasticity. Using the methods of Fourier and Laplace integral transforms, general solutions have been obtained for the non-stationary heat conduction problem and the quasi-static thermoelasticity problem for a hinge-supported plate along its edges. A numerical analysis of the temperature field, radial deflections, normal forces, bending moments, and normal stresses, depending on geometric parameters and the Bi criterion, has been performed for a three-layer plate. The materials of its layers are made of ceramics and metal. The temperature and mechanical parameters have been analyzed for the layering configuration of the plate: metal-ceramic-metal.

Quasi-static problem of thermoelasticity for layered shallow cylindrical shells of irregular structure

For rectangular layered shallow cylindrical shells of irregular structure, the quasi-static problem of unbound thermoelasticity is formulated. As a mathematical model, the equations of the shear theory of shallow shells of Timoshenko type are used. The closed solution for the formulated problem is found by the methods of integral transformations. The distribution of temperature, displacements, forces and moments in a two-layer cylindrical shell under local convective heating is analyzed numerically.

Determination and analysis of the thermoelastic state of layered orthotropic cylindrical shells

The fundamental relations of the quasi-static problem of thermoelasticity are written for a finite layered orthotropic cylindrical shell of an antisymmetric structure. Under convective heat transfer on the surfaces of this shell and under a linear dependence of temperature on the transverse coordinate, the basic system of equations for the integral characteristics of temperature is given. The method is proposed for solving the formulated problems of thermoelasticity and thermal conductivity, using the double finite integral Fourier transform with respect to the corresponding coordinates of the transformation and Laplace transform with respect to the time. The results of a numerical analysis of temperature, deflections, and stresses for the considered two-layer shell hinged at the edges under local heating by the initially specified temperature field are presented.

Quasi-Static problem of Thermoelasticity for a Band in Stress

С использованием интегральных преобразований Фурье и Лапласа численно получено аналитическое решение квазистатической задачи термоупругости для полосы с постоянными свойствами. Приведены результаты численных расчетов.

Stressed and strained state of layered cylindrical shell under local convective heating

The stress-strain state of a layered composite cylindrical shell under local heating by the environment due to convective heat exchange has been studied. The equation of the six-modal theory of thermoelasticity and the two-dimensional equation of thermal conductivity of inhomogeneous anisotropic shells are used for this purpose. The solution of the nonstationary heat transfer problem and the quasi-static thermoelasticity problem for a finite hinged orthogonally reinforced shell of symmetric structure is found by the methods of integral Fourier and Laplace transforms. Numerical results are given for the three-layer shell.

Uncoupled Quasistatic Problem of Thermoelasticity for a Two-Layer Hollow Thermally Sensitive Cylinder Under the Conditions of Convective Heat Exchange

We determine the unsteady temperature field depending on the radial coordinate and the thermoelastic state caused in a two-layer hollow thermally sensitive cylinder both by this field and the action of external force loads. The nonlinear boundary-value problem of heat conduction with discontinuous coefficients is reduced by the integro-interpolation method to the Cauchy problem for a system of ordinary differential equations, which is solved numerically. The stressed state is determined from the integral equations of the second kind and integral conditions obtained as a result of direct integration of the problem of quasistatic thermoelasticity in stresses. We study the influence of the temperature dependence of the thermal and mechanical characteristics of the layers of materials on the values and character of distributions of temperature and stresses caused by this dependence in a two-layer cylinder.

An analytical solution to the problem of thermoelastic bending of a multilayer beam with different temperature of longitudinal faces

An exact analytical solution of the quasistatic problem of thermoelasticity is presented for a section of a narrow multilayer beam with different temperatures of the longitudinal lower and upper faces and a heat flow of arbitrary height across the sections through the lateral faces. The solution was obtained for the entire package of layers by sequentially solving the heat equation for an inhomogeneous beam, taking into account the ideal thermal contact of the layers and the system of equations of the plane problem of the theory of elasticity under the assumption of a rigid connection of the layers. To take into account the inhomogeneity of the beam, a continuum approach is used, in which the multilayer material is considered continuous with variable physical and mechanical characteristics. The resulting relations take into account the orthotropy of the physico-mechanical properties of the materials of the layers and their compliance with the transverse shear and compression strains. An example of implementation of a solution for a five-layer beam with combined rigid and articulated fastening of the ends is given.

Thermoelastic Analysis of Functionally Graded Cylindrical Shells

We perform the analytic investigation of the stress-strain state of a functionally graded cylindrical shell of finite length heated by a two-dimensional temperature field. The properties of the shell material are regarded as analytic functions of the thickness coordinate. In our investigations, we use the equations of the refined theory of shells that takes into account the deformation of transverse shear and the transverse normal deformation. The heat-conduction equation is deduced under the assumption of linear temperature distribution over the thickness of the shell. For the boundary conditions of simply supported shell, the quasistatic uncoupled problem of thermoelasticity is solved by the methods of Fourier and Laplace transforms. Numerical examples are presented and discussed to show that it is important to take into account the influence of inhomogeneity of the properties of materials of the metal–ceramics composites.

Influence of the Solid Shape on the Solution for the Uncoupled Quasi-Static Cyclic Thermoelasticity Problem in a Thermal Layer (Using Regular Solids as Example)

Analytical solutions are obtained for an uncoupled quasi-static cyclic thermoelasticity problem for regular solids: a half-space, a plate, a space with a cylindrical channel, a cylinder, a space with a spherical cavity, and a sphere. The solutions, which are trigonometric Fourier series of temporary variable, are transformed by changing the spatial variable into a form convenient for analysis of temperature oscillations and thermocyclic stresses in the thermal layer. For the solutions found, simple asymptotic dependences are established, suitable for large radii of curvature of the surface and body size. The influence of the solid shape on temperature oscillations and thermocyclic stresses in the thermal layer has been studied.

RESIDUAL STRESSES IN A THERMOELASTIC CYLINDER RESULTING FROM LAYER-BY-LAYER SURFACING

The article investigates the residual stresses arising in a thermoelastic cylinder as a result of layer-by-layer deposition of material on its lateral surface. Residual stresses are defined as the limiting values of internal stresses developing during the technological process. Internal stresses are caused by incompatible deformations that accumulate in the body as a result of joining parts with different temperatures. For the analysis of internal stresses, an analytical solution of the axisymmetric quasi-static problem of thermoelasticity for a layer-by-layer growing cylinder is constructed. It is shown that the distribution of residual stresses dependson the scenario of the surfacing process. In this case, the supply of additional heat to the growing body can significantly reduce the unevenness of the temperature fields and reduce the intensity of residual stresses. The most effective is uneven heating, which can be realized, for example, by the action of an alternating current with a tunable excitation frequency. This is illustrated by the calculations performed using the constructedanalytical solution.

Non-steady wear of a two-layer coating taking into account frictional heating

The application of two-layer coatings is one of the most widely used ways to increase the performance capacity of heavily loaded frictional joints. Designing of two-layer coatings for dry sliding friction surfaces and the estimation of their efficiency require the development of mathematical models of sliding contact allowing for wear and frictional heating. To achieve this goal, we consider a transient quasi-static contact problem of uncoupled thermoelasticity of a rigid punch sliding with a constant velocity over the surface of a two-layer elastic coating bonded on its bottom face to a rigid half-plane (the substrate). During sliding, the punch penetrates the two-layer coating perpendicular to its surface. The friction between the punch and the coating surface is modelled taking into account the Coulomb friction. The heat flow generated by friction is directed into the depth of coating. The frictional sliding contact leads to wear of the two-layer coating. A solution to this problem is developed using the Laplace integral transform. As a result, the basic characteristics of each layer (displacements, stresses) are presented in the form of contour integrals of the meromorphic functions. The analysis of the properties of the integrand poles in the complex plane of integration makes it possible to evaluate contour integrals. The influence of the problem parameters on the main characteristics of the sliding contact (temperature, wear, stress) is investigated. As an example, the problem of wear of a two-layer titanium nitride/titanium (TiN/Ti) coating is considered. The numerical results show that by adjusting the coating layer thickness one can improve the wear resistance and reduce the contact temperature.

Laminated cross-ply cylindrical shell due to transient heating

The stress-deformed state of an antisymmetric cross-ply laminated circular closed cylindrical shell subjected to initial local heating in initially is investigated. For the study, the mathematical model of the shear theory of inhomogeneous shells of the Tymoshenko type is used. The two-dimensional heat equation is deduced under the linear distribution of temperature over the thickness. By methods of Fourier and Laplace integral transformations the solution of the non-stationary heat conduction problem and the quasi-static thermoelasticity problem for a finite simply supported circular cylindrical shell is obtained. Numerical results are presented for four-layer orthotropic composite. Cite as: U. V. Zhydyk, “Laminated cross-ply cylindrical shell due to transient heating,” Prykl. Probl. Mekh. Mat. , Issue 17, 113–120 (2019) (in Ukrainian), https://doi.org/10.15407/apmm2019.17.113-120

Cylindrical Shell of Finite Length with Low Shear Stiffness Under the Action of Local Heat Sources

We consider a quasistatic problem of thermoelasticity for a cylindrical shell of finite length in a variable temperature field. The surface of the shell exchanges heat with the ambient medium of constant temperature according to Newton’s law. The problem is solved with regard for the shear strains. The asymptotic state of the shell in which the computed quantities attain their maximal values is studied in detail. We also perform the comparative analysis of the thermoelastic state of the shell of finite length and the corresponding state of a shell of infinite length.

Temperature Stresses in a Functionally Graded Cylindrical Shell

For functionally gradient isotropic circular cylindrical shells, we propose the nonstationary heatconduction and thermoelasticity equations with appropriate boundary conditions. The thermoelasticity equations take into account both transverse shear and transverse normal strains. The temperature distribution over the thickness of the shell is assumed to be linear. As the shell material, we take a metal–ceramics composite. The volume fractions of these components vary across the thickness of the shell according to a power law. The solution of the quasistatic problem of thermoelasticity for a finite simply supported shell subjected to local heating is obtained by the methods of Fourier and Laplace transformations.

Influence of spatial inhomogeneity of environment temperature on temperature oscillations and thermocyclic stresses in elastic half-space

Elastic half-space on which surface the heat transfer follows the Newton-Richmann law where enviroment temperature is a periodic function of time and spatial variable is investigated. A temperature field and a stressed deformed state of half-space is found after the solution of a quasistatic problem of thermoelasticity. The solution is received in the form of double Fourier series.

Совершенствование трибологических параметров поршня телескопического автомобильного амортизатора

At present, when designing a vehicle, increased requirements are imposed on its suspension, primarily related to the task of ensuring a high level of smoothness, isolation of the body from vibration and road noise. The shock absorber is equally designed to ensure both comfort and driving safety. To operate the vehicle suspension even on small road bumps, the shock absorber should have as little internal friction as possible. The piston–cylinder interface of the shock absorber is one of the main sources of tribological losses. One of the most promising means of reducing losses is profiling the guide part of the piston. The paper proposes a method to determine the hydromechanical characteristics of a tribo-conjugate in a shock absorber, such as friction power loss, lubricant consumption through the gap, the minimal thickness of the lubricant layer for a cycle. For this purpose, an approximation of the profile shape of the piston guide part by continuous dependencies is proposed. To solve the Reynolds equation, numerical-analytical methods based on the finite-difference approximation of the differential operators of the boundary-value problem with free boundaries are used. To assess the influence of design parameters on hydromechanical characteristics, parametric studies were carried out. The finite-element method was used to solve the quasistatic problem of thermoelasticity, and temperature deformations of the piston were determined. A method for improving the hydromechanical characteristics by varying the geometric parameters of the conjugation is proposed. The results of calculations of various designs are presented. The proposed methods are universal, the use of the developed approaches at the design stage allows us to create more reliable, durable and efficient telescopic car shock absorbers.

Analysis of the thermoelastic state of the inhomogeneous through the thickness isotropic cylindrical shell

The stress-deformed state of a functionally graded isotropic circular closed cylindrical shell subjected to local heating of the outer surface of the environment by means of convective heat transfer is investigated. For the study, the mathematical model of the shear theory of inhomogeneous shells of the Tymoshenko type is used. The two-dimensional heat equation is deduced under the linear distribution of temperature over the thickness. By methods of Fourier and Laplace integral transformations the solution of the non-stationary heat conduction problem and the quasi-static thermoelasticity problem for a finite simply supported circle cylindrical shell is obtained. Numerical results are presented for metal–ceramic composites. Cite as: U. V. Zhydyk, “Analysis of the thermoelastic state of the inhomogeneous through the thickness isotropic cylindrical shell,” Prykl. Probl. Mekh. Mat. , Issue 16, 119–125 (2018) (in Ukrainian), http://doi.org/10.15407/apmm2018.16.119-125

Coupled Thermoelasticity Problem for Multilayer Composite Shells of Revolution. II. Applied Problems

We deduce a system of nonclassical nonlinear differential equations of coupled thermoelasticity for multilayer composite anisotropic shells of revolution in a coordinate system connected with the lines of curvature of the reference surface. The constructed nonclassical model of deformation of a multilayer shell and the nonlinear model of distribution of heat fluxes over the thickness of the shell enable us to take into account the transverse shear strains and guarantee the validity of the conditions of thermal and mechanical conjugation of the layers and the conditions of thermomechanical loading on the faces of the shell. We deduce the linearized differential equations of the axisymmetric coupled problem of thermoelasticity for a conic reinforced multilayer shell and solve the quasistatic problem of thermoelasticity for a two-layer cylindrical shell cross-reinforced in the direction of helical lines. By using the structural approach to the formulation of the criteria of strength for composite materials, we determine the loads of the onset of fracture of the binder and reinforcing elements of a two-layer metal-composite cylindrical shell.

Laser Pulse Annealing of Glass Plates Partially Covered by Radiation

The action of pulsed laser radiation on a plate is studied as a quasi-static problem of thermoelasticity. An analytic relation expressing the thermal strength condition for a plate is derived, making it possible to determine non-destructive regimes of laser processing in the case where the diameter of the laser beam is smaller than the diameter of the worked plate. The obtained results were checked experimentally.

Solution of the non-axisymmetric quasistatic thermoelasticity problem for multilayer cylinder with identical Lamé coefficients

За допомогою побудованих функцій Гріна квазістатичної задачі термопружності визначено неосесиметричний термопружний стан багатошарового необмеженого порожнистого циліндра з однаковими коефіцієнтами Ламе шарів за дії внутрішніх та поверхневих джерел тепла і нерівномірного розподілу початкової температури. Досліджено термопружний стан двошарового циліндра, зумовлений нормально розподіленим на зовнішній поверхні циліндра потоком тепла, який рухається по твірній циліндра.