Analytical Solution For Thermal Stresses Research Articles

Numerical modeling of thermo‐mechanical failure processes in granitic rock with polygonal finite elements

AbstractThis paper considers numerical modeling of intensive heating induced thermo‐mechanical failure processes in granitic rock. For this end, a numerical method based on polygonal finite elements and a damage‐plasticity model is developed. A staggered scheme is employed to solve the global thermo‐mechanical problem. The rock failure is described by a Rankine‐Mohr‐Coulomb plasticity model with separate scalar damage variables for tension and compression. Consistent tangent operator is derived for this model. Special attention is given to the temperature dependence of the thermo‐mechanical material properties of heterogeneous rock. In the numerical examples, the method is first verified with an analytical solution of thermal stresses in a hollow cylinder, and then qualitatively validated with the problems of thermal cracking of concentric cylinders and uniaxial compressive test on rock under elevated temperatures. Finally, the method is applied in novel simulations inspired by the degradation of sauna stones under slow heating‐rapid cooling and the comminution by rapid heating‐cooling cycles.

Stresses in radiative annular fin under thermal loading and its inverse modeling using sine cosine algorithm (SCA)

This work presents a novel mathematical model for the analysis of thermal stresses in a radiative annular fin with temperature-dependent thermal conductivity and radiative parameter. An approximate analytical solution for thermal stresses is derived using a homotopy perturbation method (HPM)-based closed-form solution of steady-state nonlinear heat transfer equation, coupled with classical elasticity theory. The effect of thermal parameters on the temperature field and the thermal stress fields are discussed. The various thermal parameters, such as a parameter describing the temperature-dependent thermal conductivity, coefficient of thermal expansion, coefficient of radiative parameter, and the variable radiative parameter, are inversely estimated for a given stress field. For inverse modeling, a population-based sine cosine algorithm (SCA) was employed to estimate the thermal parameters. The inverse modeling is verified by using the estimated thermal parameters in the closed-form solution of stress field. The reconstructed stress fields obtained from the inversely estimated parameters are then compared with the reference stress field. Results show a very good agreement between the reference stress field and the inversely estimated stress fields.

Effect of heat transfer on thermal stresses in an annular hyperbolic fin: an approximate analytical solution

An approximate analytical solution is presented for thermal stresses in an annular convective-conductive fin of a hyperbolic profile with temperature dependent thermal conductivity. The classical thermo-elasticity theory coupled with the ADM based polynomial form of temperature field is employed for an approximate analytical solution of thermal stresses. The influence of thermal parameters, i.e. variable thermal conductivity, the thermo-geometric parameter and the non-dimensional coefficient of thermal expansion on temperature and sttress fields are investigated. The results for the stress field obtained from the ADM based solution are compared with those available in literature and found to be in close agreement.

Analytical Solution of Thermal Stresses in a Functionally Graded Solid Cylinder within Parabolic Continuous Grading

This paper presents analytical solutions of the thermal stresses in a functionally graded solid cylinder with fixed ends in elastic region. These thermal stresses are due to the uniform heat generation inside the cylinder. Material properties of the functionally graded (FG) cylinder vary radially according to a parabolic form. The material properties are assumed to be independent of the temperature which are yield strength, elasticity modulus, thermal conduction coefficient, thermal expansion coefficient and Poisson’s ratio. The solutions for the thermal stresses are valid for both homogeneous and functionally graded materials.

Analytical solution for thermal stresses in a hollow cylinder under periodic thermal loading

The aim of this article is to obtain a comprehensive analytical solution for thermal stresses in a hollow cylinder, subjected to periodic time-varying thermal loading on the inner circular and insulated outer circular surfaces, where both lateral surfaces are kept at constant temperature. Temperature distribution as a function of time, and radial, and longitudinal directions is analytically solved using Fourier series and the resulting thermal stresses are obtained. The proposed method is very comprehensive and covers many theoretical and practical problems. The results for both temperature field and thermal stresses have been compared with those obtained in the former works and show excellent agreement for the same conditions.

Thermal stresses on membrane based microdevices

We developed a closed form analytical solution for thermal stresses on membrane based “released” MEMS devices. As all the layers forming the membrane has thicknesses close to one another, the assumption of having thick substrate fails. We employed stress superposition principles to obtain the intrinsic stresses caused by coefficient of thermal expansion (CTE) mismatch of the membrane layers. We also accounted for the membrane release. We illustrated that for a bilayer strip consisting of a thin film on a thick substrate, our formulation simplifies to the well-known Stoney equation. The results indicate that the thermal stress can be minimized by the appropriate choice of dielectric materials, metal electrode selections and deposition tools. Replacing the silicon nitride (Si3N4) layer deposited by low pressure chemical vapor deposition (LPCVD) with a silicon oxide (SiO2) layer deposited by plasma enhanced chemical vapor deposition (PEVCD) reduces the average thermal stress by 93%.

Analytical solution for thermal stresses during the laser pulse heating process

Laser pulse heating of surfaces initiates thermal stress generation in the region irradiated by a laser beam. Depending on the level of thermal stresses, structural changes occur inside the substrate material. In the present study, laser step input pulse heating and thermal stress generation are considered. The governing equations of heat conduction and momentum are solved analytically. In the analysis, two cases are considered, namely a stress-free surface (σx = 0 at x = 0) and a zero stress gradient at the surface (ϑσx/ϑx = 0 at x = 0). The temperature and stress fields are computed using the closed-form solution, which is derived using a Laplace transformation method. It is found that considerably high stress levels developed at some depth below the surface. The stress-free surface condition suppresses a rise in thermal stress in the surface vicinity of the substrate material, while the zero stress gradient condition at the surface results in compressive stress levels in the surface vicinity.

Thermal Stresses in Solid Propellant Grains

A method is presented for computing the maximum thermal stress in solid propellant grains tha t can result from temperature cycling. The method is based upon a first approximation obtained from the analytical solution for thermal stresses assuming Young's modulus to be independent of temperature. A more accurate solution is then found by numerical integration taking account of the variation of Young's modulus with temperature.