Types Of Thermal Loading Research Articles

Steady-state analysis of a three-layered electro-magneto-elastic strip in a thermalenvironment

In this paper, a three-layered electro-magneto-elastic strip is investigated under a planestress condition using finite element procedures. Two types of thermal loading, uniformtemperature rise and non-uniform temperature distribution, are used. A two-dimensionalrectangular element with four nodal degrees of freedom viz. thermal displacements in thex1 and x3 directions, and electric and magnetic potentials, is used to discretize the finite elementmodel. The uncoupled and coupled analysis is carried out for two types of stackingsequence (B/F/B and F/B/F) under fixed–fixed and fixed–simply supportedboundary conditions. Steady-state analysis is carried out to study the influence ofpiezo and magnetic constants on displacement, electric and magnetic potentialacross the thickness direction. It is found that the discontinuities of normal stressσ1 occur on interfaces of two dissimilar materials across the thickness direction.

Thermomechanical Stability of Imperfect Functionally Graded Plates Based on the Third Order Theory

Mechanical and thermal buckling analysis of rectangular functionally graded plates with initial geometric imperfections is presented in this paper. It is assumed that the nonhomogeneous mechanical properties vary linearly through the thickness of the plate. The plate is assumed to be under three types of mechanical loadings, namely, uniaxial compression, biaxial compression, and biaxial compression and tension; and two types of thermal loadings, namely, the uniform temperature rise and nonlinear temperature gradient through the thickness. The equilibrium, stability, and compatibility equations are derived using the third-order shear deformation plate theory. Resulting equations are employed to obtain the closed-form solution for the critical buckling load for each loading case. The results are compared with the known data in the literature.

Thermal Instability of Functionally Graded Shallow Spherical Shell

In this paper, thermal instability of shallow spherical shells made of functionally graded material (FGM) is considered. The governing equations for a thin spherical shell based on the Donnell–Mushtari–Vlasov theory are obtained. The equations are derived using the Sanders simplified kinematic relations and variational method. It is assumed that the mechanical properties vary linearly through the shell thickness. The constituent material of the functionally graded shell is assumed to be a mixture of ceramic and metal. Analytical solutions are obtained for three types of thermal loading including Uniform Temperature Rise (UTR), Linear Radial Temperature (LRT), and Nonlinear Radial Temperature (NRT). The results are validated with the known data in the literature. Communicated by Theodore R. Tauschert on September 1, 2005.

Micromechanics-based thermoelastic model for functionally graded particulate materials with particle interactions

Thermoelastic behavior of functionally graded particulate materials is investigated with a micromechanical approach. Based on a special representative volume element constructed to represent the graded microstructure of a macroscopic material point, the relation between the averaged strains of the particle and matrix phases is derived with pair-wise particle interactions, and a set of governing equations for the thermoelastic behavior of functionally graded materials is presented. The effective coefficient of thermal expansion at a material point is solved through the overall averaged strain of two phases induced by temperature change under the stress-free condition, and is shown to exhibit a weak anisotropy due to the particle interactions within the graded microstructure. When the material gradient is eliminated, the proposed model predicts the effective coefficient of thermal expansion for uniform composites as expected. If the particle interactions are disregarded, the proposed model recovers the Kerner model. The proposed semi-analytical scheme is consistent and general, and can handle any thermal loading variation. As examples, the thermal stress distributions of graded thermal barrier coatings are solved for two types of thermal loading: uniform temperature change and steady-state heat conduction in the gradation direction.

Buckling of thick functionally graded plates under mechanical and thermal loads

Buckling analysis of rectangular thick functionally graded plates under mechanical and thermal loads is presented in this paper. It is assumed that the non-homogeneous mechanical properties vary linearly through the thickness of the plate. The plate is assumed to be under three types of mechanical loadings, namely; uniaxial compression, biaxial compression, and biaxial compression and tension and two types of thermal loadings, namely; uniform temperature rise and non-linear temperature rise through the thickness. The equilibrium and stability equations are derived using the third order shear deformation plate theory. Resulting equations are employed to obtain the closed-form solution for the critical buckling load for each loading case. The results are verified with the known data in the literature.

Effect of Initial Imperfections on Thermal Buckling of Functionally Graded Plates

ABSTRACT Thermal buckling analysis of rectangular functionally graded plates with initial geometrical imperfections is presented in this article. The equilibrium, stability, and compatibility equations of an imperfect functionally graded plate are derived using the first-order shear deformation plate theory. It is assumed that the nonhomogeneous mechanical properties of the plate, graded through the thickness, are described by a power function of the thickness variable. The plate is assumed to be under three types of thermal loading, namely: uniform temperature rise, nonlinear temperature rise through the thickness, and axial temperature rise. Resulting equations are employed to obtain the closed-form solutions for the critical buckling temperature change of an imperfect functionally graded plate. The influence of transverse shear on thermal buckling load is discussed.

Thermoelastic stability of functionally graded truncated conical shells

In this study, the thermal buckling loads of truncated conical shells of functionally graded material are considered. The material properties of functionally graded shells are assumed to vary continuously through his thickness of the shell, according to a power law distribution of the volume fractions of the constituents. The fundamental relations, the modified Donnell type stability and compatibility equations of functionally graded truncated conical shells are obtained first. Then applying Galerkin’s method, the closed form solutions are presented for the truncated conical shell with simply supported boundary conditions subjected to three types of thermal loading. Using the obtained results, the effects of the variations of the gradient index of materials, the semi-vertex angle and the ratio radius to thickness in the critical buckling temperature expression are studied through pertinent computations. Comparing results with those in the literature validates the present analysis.

Thermal buckling of imperfect functionally graded plates

Thermal buckling analysis of rectangular functionally graded plates (FGPs) with geometrical imperfections is presented in this paper. The equilibrium, stability, and compatibility equations of an imperfect functionally graded plate are derived using the classical plate theory. It is assumed that the nonhomogeneous mechanical properties of the plate, graded through thickness, are described by a power function of the thickness variable. The plate is assumed to be under three types of thermal loading as uniform temperature rise, nonlinear temperature rise through the thickness, and axial temperature rise. Resulting equations are employed to obtain the closed-form solutions for the critical buckling temperature change of an imperfect FGP. The results are reduced and compared with the results of perfect functionally graded and imperfect isotropic plates.

Thermal buckling of functionally graded circular plates based on higher order shear deformation plate theory

In this research, thermal buckling of circular plates compose of functionally graded material (FGM) is considered. Equilibrium and stability equations of a FGM circular plate under thermal loads are derived, based on the higher order shear deformation plate theory (3rd order plate theory). Assuming that the material properties vary as a power form of the thickness coordinate variable z and using the variational method, the system of fundamental partial differential equations is established. A buckling analysis of a functionally graded circular plate (FGCP) under various types of thermal loads is carried out and the result are given in closed-form solutions. The results are compared with the critical buckling temperature obtained for FGCP based on first order (1st order plate theory) and classical plate theory (0 order plate theory) given in the literature. The study concludes that higher order shear deformation theory accurately predicts the behavior of FGCP, whereas the first order and classical plate theory overestimates buckling temperature.

Thermoelastic stability of functionally graded cylindrical shells

In this paper, the problems of thermal buckling in axial direction of cylindrical shells made of functionally graded materials are discussed. Based on the Donnell’s shell theory, the equilibrium and stability equations of the cylindrical shell subjected to thermal loads are derived firstly. Then the closed form solutions are presented for the shell with simply supported boundary conditions subjected to three types of thermal loading. The material properties are assumed varying as a power form of thickness coordinate variable. The influences of the aspect ratio, the relative thickness and the functionally graded index on the buckling temperature difference are carefully discussed.

Thermal buckling of a simply supported moderately thick rectangular FGM plate

Equilibrium and stability equations of a moderately thick rectangular plate made of functionally graded materials under thermal loads are derived based on the first order shear deformation theory. It is assumed that the material properties vary as a power form of thickness coordinate variable z. The derived equilibrium and buckling equations are then solved analytically for a plate with simply supported boundary conditions. Two types of thermal loading, uniform temperature rise and gradient through the thickness are considered, and the buckling temperatures are derived. The influences of the plate aspect ratio, the relative thickness, the gradient index and the transverse shear on buckling temperature difference are all discussed.

Functionally Graded Cylindrical Shell Thermal Instability Based on Improved Donnell Equations

The thermal instability of cylindrical shells of functionally graded material is considered. The derivation of equations is based on first-order shell theory and the complete Sanders kinematic equations. The resulting equilibrium and the stability equations contain the rotations in the x and θ directions and the transverse shear force in the θ direction, in addition to the conventional Donnell equations. When it is assumed that the material properties vary linearly through the thickness direction, the system of fundamental partial differential equations in terms of the displacement components is is established. Instability analysis of functionally graded cylindrical shells under two types of thermal loads with simply supported boundary conditions is carried out. Results are obtained in analytical form. The results are validated with the known data in the literature.

THERMAL BUCKLING OF FUNCTIONALLY GRADED CYLINDRICAL SHELL

In this article, the thermal buckling loads of cylindrical shells of functionally graded material are considered. Derivation of equations are based on the first-order shell theory and the Sanders kinematic equations. The derived equilibrium and stability equations for the functionally graded cylindrical shell are identical with the equations for homogeneous shells expressed in the form of forces and moments per unit length. Assuming that the material properties vary linearly through the thickness direction, the system of fundamental partial differential equations in terms of the displacement components is established. Buckling analysis of functionally graded cylindrical shells under two types of thermal loads with simply supported boundary conditions are carried out. Results are obtained in the analytical form. The results are validated with the known data in the literature.

THERMAL BUCKLING OF FUNCTIONALLY GRADED PLATES BASED ON HIGHER ORDER THEORY

Equilibrium and stability equations of a rectangular plate made of functionally graded material (FGM) under thermal loads are derived, based on the higher order shear deformation plate theory. Assuming that the material properties vary as a power form of the thickness coordinate variable z and using the variational method, the system of fundamental partial differential equations is established. The derived equilibrium and stability equations for functionally graded plates (FGPs) are identical to the equations for laminated composite plates. A buckling analysis of a functionally graded plate under four types of thermal loads is carried out and results in closed-form solutions. The critical buckling temperature relations are reduced to the respective relations for functionally graded plates with a linear composition of constituent materials and homogeneous plates. The results are compared with the critical buckling temperatures obtained for functionally graded plates based on classical plate theory given in the literature. The study concludes that higher order shear deformation theory accurately predicts the behavior of functionally graded plates, whereas the classical plate theory overestimates buckling temperatures.

Temperature field in a microperiodic two-layered composite caused by a circular laser heat source

The paper is connected with the determination of␣temperature field in a periodically layered half-space caused by a laser heating. Two types of thermal loadings distributed on a boundary of the body is considered: uniform and normal (Gaussian). The influence of geometrical and thermal parameters of the layered composite on the temperature field is analyzed.

Effect of thermal singularities on stress intensity factors: edge crack in rectangular and circular plate

Thermoelastic solutions for cracked bodies under some types of thermal loading exhibit a thermal singularity at the crack tip as well as the familiar stress singularities. A quarter-point crack tip-element is presented which permits the accurate evaluation of these thermal singularities. They are important, since they affect the values of the stress intensity factors. These effects are accounted for by developing a new formulation for the calculation of the stress intensity factors. Several crack problems are solved and the results are compared where possible, with existing solutions.

Thermal Stresses and Their Singularities due to Temperature Discontinuity on the Interface of Dissimilar Materials.

A thermal stress problem of a coated half-space due to a temperature discontinuity on the interface is solved exactly using the two-dimensional thermoelastic theory. Stress singularities at the point of discontinuity of temperature are obtained in closed form. The results show that the normal stresses have jumps of the inverse tangent type and the shear stress has singularity of the logarithmic type. From the comparison with the singularities of the corresponding problem of a point heat source at the interface, the important result is obtained that the types of singularities for the two problems are different but the intensities are the same. In other words, the types of singularities depend on the type of loading but their intensities depend only on the combinations of materials and do not depend on the type of thermal loading.

Failure of thermal coatings of various structures and thicknesses

The main functions of multilayer thermal coatings (TC) are determined, and the separation of these functions between the various layers is established. The influence of the TC structure on the creep resistance of alloy EI868 at constant temperature and during thermal cycling was investigated. It was established that the creation of a heat resistant layer in the form of a multilayered component increases the creep resistance in both types of thermal loading. An increase in the thickness of the ceramic layer changes the failure mechanism of the heat resistant NiCrAlY layer and the total composite overall. The mechanism of crack formation in the ceramic layer of the TC was studied, and a quantitative description of this in the form of an exponential dependency is presented. An association between the indicated parameters and the endurance of the composites studied is noted.

Generalized Kirchhoff-Love assumptions for thick shells: Application to thermal stresses in rectilinear tubes

Asymptotic expansions of displacements in powers of a small parameter related to the shell thickness are re-derived with a view to investigating the way in which the leading terms depend on the thickness coordinate. The outcome of this preliminary study gives a hint concerning possible kinematic assumptions to be used as starting points for constructing thick shell theories. Then the problem of reducing the number of independent generalized displacements by enforcing all or part of the traction boundary conditions on the shell outer and inner surfaces is studied. Several thick shell theories are proposed and compared; the superiority of a certain generalized Kirchhoff-Love assumption is brought out in the particular case of circular cylindrical shells subjected to several types of thermal loadings.

A note on standard methods of investigating the hygro-thermal microclimate (subjective and objective evaluation of the indoor climate).

The methods described for investigating the microclimate are based on the so-called complex system of evaluation of the microclimate, according to which the response of man, induced by the environment, is decisive, i.e. the microclimate being assessed on the basis of the thermal load on man. The methods are applied in two stages. The first stage, the so-called methods of anamnestic examination, is based on the subjective data, provided by persons, on the microclimate which they experience; the second stage, the objective methods of examination establish guidelines on where, when, what and by what methods to measure the environment under examination in relation to the type of thermal load on man.