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A control volume finite element method for the thermoelastic problem in functional graded material with one relaxation time
Abstract
In this paper, a new direct vertex-centred finite volume method (CV-FEM) has been developed for the thermoelastic problem in functional graded material (FGM) based on Lord-Shulman theory. The heat conduction equation in Lord-Shulman theory is modified by considering the product term of spatial gradient of relaxation time and the heat flux rate, and it makes the present method more accurate to capture characteristics of a thermoelastic wave in inhomogeneous and FGM compared with previous methods. Some benchmark examples are used to demonstrate the capability of the present method for hyperbolic heat conduction and thermoelastic coupled problems. The effects of the ‘product-term’ on the wave propagation are studied by a heat conduction problem in inhomogeneous material and a thermoelastic problem in FGM. The FGM results show that its effect on the thermoelastic response is significant even for a linear variation of material properties.
... The idea of this model arose from the attempts to improve the Green-Naghdi type III version by introducing the concept of relaxation time or phase delay. In the last few years, a lot of studies related to the MGT theory and other types of generalized thermoelastic models have been conducted in a wide range of disciplines including fluid dynamics, elasticity, viscoelasticity, and thermoelasticity Singh 2022, 2023;Aboueregal and Sedighi 2021;Abouelregal et al. 2023;Fahmy 2021;Singh et al. 2022;Liu et al. 2021;Peng et al. 2022;Tiwari et al. 2022;Moaaz et al. 2023). ...
The main objective of the present paper is to investigate the relationship between the thermal processes and diffusion in thermoelastic solids. For this reason, a new model of thermo-diffusion interactions has been derived, which, unlike the traditional models, allows the thermo-diffusion waves to propagate at finite speeds. The Moore–Gibson–Thompson (MGT) equation is an essential part of the proposed model, as it is included in the mass diffusion and thermal conductivity equations by adding two relaxation times. The introduced model is then used to investigate a one-dimensional thermodiffusion problem for a homogeneous spherical shell. In the field of the Laplace transform, the analytical expressions for different transformed thermophysical fields are found. Moreover, a numerical inversion algorithm is used to obtain the physical domain solutions. The differences between the presented model and previous theories are graphically presented and discussed in detail. It is exhibited that depending on the relaxation time taken into account, the magnitude of the mass flow rate and heat waves can meaningfully change.
... To address this shortcoming that contradicts the physical phenomena, different non-Fourier theories such as the Cattaneo-Vernotte heat wave model [42,43], dual-phase lag (DPL) theory [44] and three-phase lag models suggested by Choudhuri [45] have emerged. Among the most well-known generalized thermoelastic theories, the Lord and Shulman (LS) model [46], the Green and Lindsey model (G-L) [47], in addition to the Green and Naghdi (GN) [48,49] theories becomes more popular in the field. ...
Thermal behavior of a moving viscoelastic nanobeam under the influence of periodic thermal load is considered in the framework of Kelvin-Voigt viscoelastic model with fractional operators. The equation of motion for axially moving nanobeam is modeled by employing the Eringen's nonlocal elastic theory in conjunction with the couple stress hypothesis and the conventional Euler-Bernoulli beam model. The thermoelastic features is then established by employing the generalized dual phase-lag heat conduction model. After utilizing the Laplace transform, the thermomechanical equations are coupled and solved. The current results are validated by presenting numerical examples and comparing with previous solutions obtained by traditional theories in the literature. According to the provided numerical simulations, the deflection of the axially moving nanobeam as well as its temperature change reduce with the axial velocity and the influences of small scale and nonlocal parameters are also revealed and discussed.
... (4 and 5) to known physical quantities, it is sufficient to compare these two equations to the well-known standard forms of the evolution equations for the heat flux (C.f. 10,21 ): ...
A 2D first order linear system of partial differential equations of plane strain thermoelasticity within the frame of extended thermodynamics is presented and analyzed. The system is composed of the equations of classical thermoelasticity in which displacements are replaced with velocities, complemented with Cattaneo evolution equation for heat flux. For a particular choice of the characteristic quantities and for positive thermal conductivity, it is shown that this system may be cast in a form that is symmetric t-hyperbolic without further recurrence to entropy principle. While hyperbolicity means a finite speed of propagation of heat waves, it is known that symmetric hyperbolic systems have the desirable property of well-posedness of Cauchy problems. A study of the characteristics of this system is carried out, and an energy integral is derived, that can be used to prove uniqueness of solution under some boundary conditions. A numerical application for a finite slab is considered and the numerical results are plotted and discussed. In particular, the wave propagation nature of the solution is put in evidence.
... Qi Liu et al., 3 indeed, in their paper have developed a new direct vertex-centred finite volume method for the thermoelastic problem in functional graded material based on Lord-Shulman theory. Some benchmark examples are used to demonstrate the capability of the present method for hyperbolic heat conduction and thermoelastic coupled problems. ...
The transient displacement, temperature, and stress fields in a functionally graded ceramic/metal layer under uniform thermal shock conditions at the upper surface are numerically studied based on the Lord-Shulman model, employing a direct finite element method. The Newmark method is employed for the time integration of the problem. A Matlab finite element code is developed for the numerical analysis of the one-dimensional problem under consideration. The Voigt model (rule of mixture) is used for the estimation of the effective properties inside the functionally graded layer and the variation of the volume fraction of the materials follows the sigmoid function in terms of the introduced parameter p . Furthermore, a parametric study with respect to the parameter p follows, where three different combinations of ceramic/metal materials are considered. It is concluded that the value p=1 , which corresponds to a linear variation of the properties, minimizes the maximum (tensile) stress applied at the middle of the functionally graded layer.
A two-dimensional model of the generalized thermoelasticity with one relaxation time is established. The resulting nondimensional coupled equations together with the Laplace and Fourier transform techniques are applied to a specific problem of multilayered structures considering thermal resistance subjected to thermal shock and traction-free surface. The solutions in the transformed domain are obtained by a direct approach. Numerical inversion techniques are used to obtain the inverse double transform. Numerical results are represented graphically to estimate the effects of the thermal resistance and thermal conductivities on the temperature, displacement, and stress distributions.
Thermal shock describes the way that a material exposed to a sudden change in temperature. These conditions usually take place in aerospace industry, when aircraft encounter the atmosphere layers. It also happens in combustion chamber of engines when mixture of fuel and air ignite in cylinder. Classical thermoelasticity is not capable to analyze such a problem. Therefore, generalized coupled thermoelasticity theories arose. In this article, the dynamic coupled thermoelastic response of a rectangular plate made of functionally graded material subjected to a thermal shock based on Lord-Shulman theory is studied. Using state space approach, the state equations of the problem are obtained. The plate’s boundary condition is simply support on the edges and the variation of mechanical properties is assumed to change along the thickness of the plate. The Laplace transform is applied to transform governing equations from time domain to the Laplace domain. Then by using a numerical method, the equations are solved and the results are inversed to the time domain displacement and temperature field are acquired. Results are presented for different power law indices and they are validated by previous reported literature.
By using the principle of virtual work, the finite element equations corresponding to the generalized thermoelasticity with two relaxation times (i.e., the G–L theory) are derived. In order to improve the accuracy of integral transform method, especially in two/three-dimension, the equations are solved directly in time-domain. As numerical examples, the developed method is used to investigate the generalized thermoelastic behavior of a slim strip and a semi-infinite plate subject to thermal shock loading. The results demonstrate that the developed method can faithfully predict the deformation of the structure and most importantly the delicate second sound effect of heat conduction in both one and two-dimensional solids whilst it is usually difficult to model, especially in two-dimensional, by using the transform method. This method can also be used to study generalized piezothermoelastic and magnetothermoelastic problems.
The generalized thermoelasticity based on the Lord-Shulman (LS), Green-Lindsay (GL), and Green-Naghdi (GN) theories admit the second sound effect. By introducing some parameters all these theories are combined and a unified set of equations is rendered. These equations are then solved for a layer of isotropic and homogeneous material to study the thermal and mechanical wave propagations. The disturbances are generated by a sudden application of temperature to the boundary. The non-dimensionalized form of the governing equations are solved utilizing the Laplace transform method in time domain. Closed form solutions are obtained for the layer in Laplace transform domain, and a numerical inverse Laplace transform method is used to obtain the temperature, displacement, and stress fields in the physical time domain. The thermo-mechanical wave propagations and reflections from the layer boundaries are investigated.
The dynamic treatment of one-dimensional generalized thermoelastic
problem of heat conduction is made for a layered thin plate which
is exposed to a uniform thermal shock taking into account variable
thermal conductivity. The basic equations are transformed by
Laplace transform and solved by a direct method. The solution was
applied for a plate of sandwich structure, which is thermally
shocked, and is traction-free in the outer sides. The inverses of
Laplace transforms are obtained numerically. The temperature, the
stress, and the displacement distributions are represented
graphically.
This work focuses on basic research into a P/M processed, porous-surfaced and functionally graded material (FGM) destined for a permanent skeletal replacement implant with improved structural compatibility. Based on a perpendicular gradient in porosity the Young's modulus of the material is adapted to the elastic properties of bone in order to prevent stress shielding effects and to provide better long-term performance of the implant-bone system. Using coarse Ti particle fractions the sintering process was accelerated by silicon-assisted liquid-phase sintering (LPS) resulting in a substantial improvement of the neck geometry. A novel evaluation for the strength of the sinter contacts was proposed. The Young's modulus of uniform non-graded stacks ranged from 5 to 80 GPa as determined by ultrasound velocity measurements. Thus, the typical range for cortical bone (10-29 GPa) was covered. The magnitude of the Poisson's ratio proved to be distinctly dependent on the porosity. Specimens with porosity gradients were successfully fabricated and characterized using quantitative description of the microstructural geometry and acoustic microscopy.
This paper describes a new two-dimensional (2-D) control volume finite element method (CV-FEM) for transient heat conduction in multilayer functionally graded materials (FGMs). To deal with the mixed-grid problem, 9-node quadrilateral grids and 6-node triangular grids are used. The unknown temperature and material properties are stored at the node. By using quadratic triangular grids and quadratic quadrilateral grids, the present method offers greater geometric flexibility and the potential for higher accuracy than the linear CV-FEM. The properties of the FGMs are described by exponential, quadratic and trigonometric grading functions. Some numerical tests are studied to demonstrate the performance of the developed method. First, the present CV-FEM with mixed high-order girds provides a higher accuracy than the linear CV-FEM based on the same grid size. Second, the material properties defined location is proved to have a significant effect on the accuracy of the numerical results. Third, the present method provides better numerical solutions than the conventional FEM for the FGMs in conjunction with course high-order grids. Finally, the present method is also capable of analysis of transient heat conduction in multilayer FGM.
In this article, a new two-dimensional control volume finite element method has been developed for thermoelastic analysis in functionally graded materials. A nine-node quadrilateral element and a six-node triangular element are employed to deal with the mixed-grid problem. The unknown variables and material properties are defined at the node. The high-order shape functions of six-node triangular and nine-node quadrilateral element are employed to obtain the unknown variables and their derivatives. In addition, the material properties in functionally graded structure are also modeled by applying the high-order shape functions. The capabilities of the presented method to heat conduction problem, elastic problem, and thermoelastic problem have been validated. First, the defined location of material properties is found to be important for the accuracy of the numerical results. Second, the presented method is proven to be efficient and reliable for the elastic analysis in multi-phase materials. Third, the presented method is capable of high-order mixed grids. The memory and computational costs of the presented method are also compared with other numerical methods.
A new three-dimensional (3-D) control volume finite element method (CV-FEM) has been developed for transient heat conduction in multilayer functionally graded materials (FGMs). A 10-node tetrahedral grid is chosen for spatial discretization and a backward difference scheme is adapted for time discretization. By using quadratic tetrahedral grids, the present CV-FEM offers greater potential for enhanced geometric flexibility and for improved numerical accuracy over the linear CV-FEM. The temperature and material properties are defined at the node. Three different types of material variation (exponential, quadratic and trigonometric) are considered in the analysis. Several test cases are provided to verify the numerical implementation. The results of the test cases are in good agreement with analytical solutions and other numerical simulation results.
In this article, a model concerning free vibrations of spherically symmetric, thermoelastic, isotropic, and functionally graded sphere has been developed and analyzed in the context of linear theory of generalized thermoelasticity with one relaxation time. Laplace transform has been used to solve the problem which yields natural frequencies of free vibrations without performing inversion of the transform. The analytical results for coupled, uncoupled, and homogeneous spheres have been deduced as special cases of the general case. Natural frequencies of first 10 modes of vibrations have been obtained for different values of grading index of cobalt material regarding coupled thermoelastic, generalized thermoelastic, and elastic functionally graded spheres. The frequency shift and thermoelastic damping for Fourier and non-Fourier processes of heat propagation, temperature change, radial, and hoop stresses have been presented graphically. It has been analyzed here that grading index parameter helps in detecting the strength of signals in such material devices and the thermal relaxation time contributes in improving the quality of signals. The analysis also leads to the fact that grading index parameter is useful from design point of view and it can be tailored to specific applications for controlling the stress.
Finite volume method that has been shown to be an effective tool for the study of non-Fourier conduction in one-dimensional heterogeneous material is extended to two-dimensional (2D) heterogeneous materials. The accuracy of 2D numerical formulation is examined by comparing the numerical results with the exact solutions for a homogeneous material with constant thermal properties. The effects of temperature-dependent properties due to both heating and cooling of the medium on the wave propagation are investigated. Transient energy balance shows significant effects of finite thermal wave speed on the transient behavior of internal and wave energy changes in the system. The effects of finite thermal wave speed on the entropy production for the cooling case are examined by invoking the second law of thermodynamics. The 2D transient temperature distributions in a heterogeneous medium show the expected effects of flux lagging constant on the thermal wave propagations through heterogeneous material.
In this study, the nonlinear vibration and dynamic buckling of eccentrically stiffened functionally graded toroidal shell segments surrounded by an elastic medium in thermal environment are presented. The governing equations of motion of eccentrically stiffened functionally graded toroidal shell segments are derived based on the classical shell theory with the geometrical nonlinear in von Karman-Donnell sense and the smeared stiffeners technique. Furthermore, the dynamical characteristics of shells as natural frequencies, nonlinear frequency–amplitude relation, nonlinear dynamic responses and the nonlinear dynamic critical buckling loads evaluated by Budiansky-Roth criterion are considered. The effects of characteristics of functionally graded materials, geometrical ratios, elastic foundation, pre-loaded axial compression and temperature on the dynamical behavior of shells are investigated.
A one-dimensional hyperbolic conduction equation written in primitive variables is solved by a numerical method based on a finite volume formulation. Accuracy of the proposed formulation is verified by exact solutions for homogeneous medium and then applied to composite materials with different conductivity, specific heat, and heat flux lagging constant. Results show quite distinct wave penetration through and reflection at interfaces of dissimilar materials even though the wave speed in the second medium remains identical in all cases. Effect of non-uniform cross-sectional area on wave propagation is also examined. The formulation is straightforward and can be easily extended to multidimensional problems for heterogeneous media with temperature-dependent properties since no special treatments are needed at the interfaces.
In this paper, a new numerical method for prediction of stresses and displacements in thermo-elasto-plastic material is presented. The method is based on the direct solution of the governing equations for thermal energy and momentum balance, expressed in terms of temperature and displacements (as dependent variables) via corresponding constitutive relations, and discretized by the finite volume technique. As a result, the unsteady fields of temperature, displacements and stresses, as well as residual stresses in a solid body subjected to a non-uniform temperature and/or external loads are obtained. The method has been applied to a number of test cases and the results are compared with the analytical solution, calculations obtained by another numerical method or experimental data. Results show that the method is accurate, stable and efficient and that it can be used as a useful tool for predicting thermo-mechanical deformation processes in a solid body.
A new approach based on cell vertex finite volume method (CV-FVM) has been developed by the introduction of the staggered grid technique for thermoelastic analysis in functionally graded materials (FGMs). The 4-node quadrilateral grid and the 3-node triangular grid are employed to deal with mixed-grid problems. The performance of the developed method has been demonstrated by four numerical tests. First, the consideration of the bilinear quadrilateral grid is found to be important for the elimination of artificial numerical oscillation in the displacement field. Second, the staggered grid technique is proved (within the considered test cases) to be efficient and reliable for thermoelastic analysis in FGMs without any undesirable discontinuous distribution. Third, the present method requires small computational and memory costs compared to the method adopting graded elements or higher-order theory.
Two-dimensional hyperbolic heat conduction (HHC) problems with temperature-dependent thermal properties are investigated numerically. The present numerical method involves the hybrid application of the Laplace transform and control-volume methods. The Laplace transform technique is used to remove time-dependent terms, and then the transformed equation is discretized in the space domain by the control-volume formulation. Nonlinear terms induced by temperature-dependent thermal properties are linearized by using the Taylor's series approximation. In general, the numerical solution of the HHC problem has the phenomenon of the jump discontinuity in the vicinity of the thermal wave front. This phenomenon easily causes numerical oscillations in this region. In order to suppress these numerical oscillations, the selection of shape functions is an important task in the present study. The bi-hyperbolic shape function is introduced in the present control-volume formulation. Three examples involving a problem with an irregular geometry are illustrated to demonstrate the accuracy and stability of the present numerical method for such problems.
A SiC/(W,Ti)C ceramic nozzle with gradient structures was produced by hot pressing. The purpose is to reduce the tensile stress at the entry region of the nozzle in abrasive air-jet. The sand erosion performance of this kind gradient ceramic nozzle caused by abrasive particle impact was investigated by abrasive air-jets in comparison with the common one. Results showed that the gradient ceramic nozzles exhibited an apparent increase in erosion wear resistance over the common ceramic nozzles. The mechanism responsible was explained as the formation of compressive residual stresses in nozzle entry region in fabricating process of the gradient ceramic nozzles, which may partially counteract the tensile stresses resulting from external loadings. It is indicated that gradient structures in ceramic nozzles is an effective way to improve the erosion wear resistance of common ceramic nozzles.
A thin coating made of linear elastic functionally graded material (FGM) perfectly bonded to an elastic substrate is considered. This work which is of particular interest to tribological community is devoted to the determination of the thermal and mechanical stresses due to mixed normal and tangential Hertzian surface pressure. The thermomechanical properties of the FGM coating are assumed to vary exponentially through the thickness. Solutions for temperature rise and stresses are obtained by use of Fourier transform technique. The influences of coating thickness, Peclet number and friction coefficient on temperature rise and stresses in the FGM coating are investigated. Comparative studies on FGM versus homogeneous surface coating under thermomechanical loading confirms that use of FGM coating could result in considerable reduction of surface temperature rise. The results also reveal that flexural tensile stresses in the FGM coating are significantly reduced.
A new hybrid numerical method based on the Laplace transform and control volume methods is proposed to analyze transient coupled thermoelastic problems with relaxation times involving a nonlinear radiation boundary condition. The dynamic thermoelastic model of Green and Lindsay is selected for the present study. The following computational procedure is followed for the solution of the present problem. The nonlinear term in the boundary condition is linearized by using the Taylor's series approximation. Afterward, the time-dependent terms in the linearized equations are removed by the Laplace transform technique, and then the transformed field equations are discretized using the control volume method with suitable shape functions, The nodal dimensionless temperature and displacement in the transform domain are inverted to obtain the actual physical quantities, using the numerical inversion of the Laplace transform method. It is seen from various illustrative problems that the present method has good accuracy and efficiency in predicting the wave propagations of temperature, stress, and displacement. However, it should be noted that the distributions of temperature, stress, and displacement can experience steep jumps at their wavefronts. In the present study, the effects of the relaxation times on these thermoelastic waves are also investigated.
The present study is devoted to propose a hybrid Green’s function method to investigate the hyperbolic heat conduction problems. The difficulty of the numerical solutions of hyperbolic heat conduction problems is the numerical oscillation in the vicinity of sharp discontinuities. In the present study, we have developed a hybrid method combined the Laplace transform, Green’s function and ε-algorithm acceleration method for solving time dependent hyperbolic heat conduction equation. From one- to three-dimensional problems, six different examples have been analyzed by the present method. It is found from these examples that the present method is in agreement with the Tsai-tse Kao’s solutions [Tsai-tse Kao, Non-Fourier heat conduction in thin surface layers, J. Heat Transfer 99 (1977) 343–345] and does not exhibit numerical oscillations at the wave front. The propagation of the two- and three-dimensional thermal wave becomes so complicated because it occur jump discontinuities, reflections and interactions in these numerical results of the problem and it is difficult to find the analytical solutions or the result of other study to compare with the solutions of the present method.
This paper presents a review of the principal developments in functionally graded materials (FGMs) with an emphasis on the recent work published since 2000. Diverse areas relevant to various aspects of theory and applications of FGM are reflected in this paper. They include homogenization of particulate FGM, heat transfer issues, stress, stability and dynamic analyses, testing, manufacturing and design, applications, and fracture. The critical areas where further research is needed for a successful implementation of FGM in design are outlined in the conclusions.
In this paper, the response of a circular cylindrical thin shell made of the functionally graded material based on the generalized theory of thermoelasticity is obtained. The governing equations of the generalized theory of thermoelasticity and the energy equations are simultaneously solved for a functionally graded axisymmetric cylindrical shell subjected to thermal shock load. Thermoelasticity with second sound effect in cylindrical shells based on the Lord–Shulman model is compared with the Green–Lindsay model. A second-order shear deformation shell theory, that accounts for the transverse shear strains and rotations, is considered. Including the thermo-mechanical coupling and rotary inertia, a Galerkin finite element formulation in space domain and the Laplace transform in time domain is used to formulate the problem. The inverse Laplace transform is obtained using a numerical algorithm. The shell is graded through the thickness assuming a volume fraction of metal and ceramic, using a power law distribution. The effects of temperature field for linear and non-linear distributions across the shell thickness are examined. The results are validated with the known data in the literature. Copyright © 2006 John Wiley & Sons, Ltd.
This paper deals with thermoelastic material behavior without energy dissipation; it deals with both nonlinear and linear theories, although emphasis is placed on the latter. In particular, the linearized theory of thermoelasticity discussed possesses the following properties: (a) the heat flow, in contrast to that in classical thermoelasticity characterized by the Fourier law, does not involve energy dissipation; (b) a constitutive equation for an entropy flux vector is determined by the same potential function which also determines the stress; and (c) it permits the transmission of heat as thermal waves at finite speed. Also, a general uniqueness theorem is proved which is appropriate for linear thermoelasticity without energy dissipation.
In this paper we consider an alternative generalization of classical thermoelasticity to those already available. Restrictions on constitutive equations are discussed with the help of an entropy production inequality proposed by Green and Laws [4]. The work is closely related to that of Mller [3] but the final results are somewhat more explicit. The theory is linearized and a uniqueness theorem is stated. In agreement with Mller [3] it is shown that the linear heat conduction tensor is symmetric and that the theory allows for second sound effects.In diesem Schreiben berlegen wir eine alternative Verallgemeinerung klassischer Thermo-Elastizitt mit denjenigen schon vorhanden. Vorgeschlagen von Green und Laws [4]. Einschrnkungen der konstitutiven Gleichungen sind diskutiert mit hilfe einer Entropie Produktions-Ungleichung. Die Arbeit ist eng im Zusammenhang mit derjenigen Mller's [3] jedoch das Ergebniss ist deutlicher. Die Theorie ist linearisiert und ein einzigartiges Theorem festgestellt. Es wird gezeigt, in bereinstimmung mit Mller, [3] dass der lineare Wrmeleitung Tensor symmetrisch its und dass die Theorie second-sound Wirkungen bercksichtigt.
A unified treatment is presented of thermoelasticity by application and further developments of the methods of irreversible thermodynamics. The concept of generalized free energy introduced in a previous publication plays the role of a ``thermoelastic potential'' and is used along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement. The general laws of thermoelasticity are formulated in a variational form along with a minimum entropy production principle. This leads to equations of the Lagrangian type, and the concept of thermal force is introduced by means of a virtual work definition. Heat conduction problems can then be formulated by the methods of matrix algebra and mechanics. This also leads to the very general property that the entropy density obeys a diffusion‐type law. General solutions of the equations of thermoelasticity are also given using the Papkovitch‐Boussinesq potentials. Examples are presented and it is shown how the generalized coordinate method may be used to calculate the thermoelastic internal damping of elastic bodies.
Functionally graded coatings are coating systems used to increase performances of high temperature components in diesel engines. These coatings consist of a transition from the metallic bond layer to cermet and from cermet to the ceramic layer. In this study, thermal behavior of functional graded coatings on AlSi and steel piston materials was investigated by means of using a commercial code, namely ANSYS. Thermal analyses were employed to deposit metallic, cermet and ceramic powders such as NiCrAl, NiCrAl + MgZrO3 and MgZrO3 on the substrate. The numerical results of AlSi and steel pistons are compared with each other. It was shown that the maximum surface temperature of the functional graded coating AlSi alloy and steel pistons was increased by 28% and 17%, respectively.
A robust and accurate control volume procedure for solving the elastic stress-strain equations for two-dimensional arbitrarily complex geometries is described. The method is implemented for triangular and/or quadrilateral irregular meshes as well as rectangular regular meshes and is thus a control volume-unstructured mesh (CV-UM) procedure. The procedure is compared favorably to conventional finite element (FE) approaches with regard to accuracy on a number of standard test problems that demonstrate the ability of the CV-UM procedure to model constraints on the boundary and within the domain, boundary loads, body forces throughout the domain induced by a temperature distribution, multimaterial problems, and irregular geometries. For static problems the CV-UM algorithm requires about twice as much CPU time as the conventional FE analysis to achieve convergence on the same mesh. However, it is expected that as the solution procedure is optimized, this overhead will reduce by a further factor of 2.
In this work a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of the heat flow. The theory takes into account the coupling effect between temperature and strain rate, but the resulting coupled equations are both hyperbolic. Thus, the paradox of an infinite velocity of propagation, inherent in the existing coupled theory of thermoelasticity, is eliminated. A solution is obtained using the generalized theory which compares favourably with a known solution obtained using the conventional coupled theory.