Fields In Multilayered Structures Research Articles

Thermoelasticity of multilayered plates with imperfect interfaces

Three-dimensional exact solutions for temperature and thermoelastic stresses in multilayered anisotropic plates are derived for advanced boundary-value problems with general boundary conditions. The extended Stroh formalism is formulated to include the thermal coupling with the Eringen nonlocal elasticity theory that captures small scale effects. The simply supported structures are subjected to time-harmonic distributions of temperature, combined with tractions, which are represented by means of Fourier series expansions. In particular, the prescribed loads on both the bottom and top surfaces include the uniformly and heterogeneously distributed normal stresses, while imperfect thermal and mechanical contacts between constituents are incorporated at the internal interfaces. Recursive field relations for multilayered plates with imperfect interfaces are consistently articulated by virtue of the traditional propagation matrix method, which is further completed by the dual variable and position technique to overcome numerical instability issues. Three application examples are proposed to throw light on various effects of the externally applied loads and internal imperfections on the thermoelastic fields in multilayered structures. The residual stress fields in graphite fiber-reinforced epoxy matrix composites are shown to be drastically different from those predicted by the classical elasticity theory when nonlocal effects are significant. The stacking sequence and the number of copper and molybdenum in laminated anisotropic plates are of great importance in tailoring interfacial properties, especially if the thermally conducting boundaries are taken into account. The forced vibration analysis of thermal barrier coatings on nickel based superalloys is investigated, including interfacial bonding effects between adjoining layers. Depending on the input frequency amplitude, severe oscillating displacements and stresses take place in the single crystal superalloys that can endanger the safety-related stability and integrity of aircraft engines. Overall, the present formalism should be utilized in the optimal design of sophisticated multilayered structures with desired steady-state and time-harmonic thermoelastic responses.

DETERMINATION OF NON-STATIONARY TEMPERATURE FIELD IN THE SYSTEM OF TWO SPHERICAL SHELL

The main classification indicator, in terms of fire safety, is the degree of fire resistance of the house. Depending on this indicator normalize its surface, the area of development and distance to other buildings and structures. The de-gree of fire resistance of the house is determined by the limit of fire resistance of its building structures and the limit of the fire spread by these structures. Therefore, the value of the fire resistance limit of building constructions, which con-sists of a house, significantly affect its architectural solution and the parameters of construction in general. On this ba-sis, taking into account the approaches to ensuring normalized fire resistance limits of the design and the features of their behavior under high-temperature (fire) influence is very relevant.Most research on building constructions. The proposed work is devoted to the application of the direct method to the study of heat transfer processes in the system of two embedded spherical bodies – a ball in a sphere. It is assumed that there is an ideal thermal contact between the balls, and the law of temperature change on the outer surface is an arbitrary function of time, and evenly distributed over the surface of the ball. Consequently, isotherms inside this construction are concentric fields, that is, the problem is symmetric and is solved for the first time in such a statement. To solve such a problem, in parallel, the auxil-iary problem of determining the distribution of a non-stationary temperature field in a two-layer hollow spherical structure with a "extracted" sphere of sufficiently small radius is raised. In this case the symmetry condition of the original problem is replaced by the condition of the second kind on the inner surface of this construction. The implementation of the solution of the auxiliary problem is carried out by applying a reduction method using the concept of quasiderivatives. In the future, the Fourier scheme is used with the use of the modified eigenfunctions method. To find the solution of the original problem, the idea of the boundary transition is used by passing the radius of the withdrawn bullet to zero. It is established that in this approach all the eigenfunctions of the corresponding problem on the eigenvalues have no singularities at zero, which means that the solutions of the original problem are constrained throughout the design. The solution of this problem at zero temperature on the outer surface coincides with those known in the literature. To illustrate the proposed method, a model example of finding the temperature field distribution in a system of two spherical bodies with different thermophysical properties of materials is solved. The results of the calcu-lations are presented in the form of a table and a three-dimensional graph of temperature change, depending on the time and spatial coordinates. The generalization of the results obtained in the event of any finite number of nested balls is a purely technical problem, and not a fundamental one. Note that while changing the boundary condition of the first kind to any other boundary condition (for example, the third kind) does not affect the scheme of solving similar tasks. Since the general scheme of studying the distribution of temperature fields in multi-layered structures with an arbitrary number of layers in the presence of internal sources of heat is studied in detail, the setting and solving of such problems for the system of nested balls does not cause any difficulty.

DETERMINATION OF THE NON-STATIONARY TEMPERATURE FIELD IN THE SYSTEM OF TWO CYLINDRICAL SHELL UNDER THE FIRE CONDITIONS

The proposed work is devoted to the application of the direct method to the study of heat transfer processes in the system "solid cylinder inside a cylindrical shell". It is assumed that there is an ideal thermal contact between them, and the law of changing the ambient temperature, which rinses the surface of the structure, is an arbitrary function of time, and evenly distributed over the surface. Consequently, isotherms inside this construction are concentric circles, that is, the problem is symmetric and is solved for the first time in such a statement. To solve such a problem, the auxiliary problem of determining the distribution of a non-stationary temperature field in a two-layer hollow cylindrical structure with a "withdrawn" cylinder of sufficiently small radius is raised in parallel. In this case the symmetry condition of the original problem is replaced by the condition of the second kind on the inner surface of this construction. The implementation of the solution of the auxiliary problem is carried out by applying a reduction method using the concept of quasi-derivatives. In the future, the Fourier scheme is used with the use of the modified eigenfunctions method. To find the solution of the original problem, the idea of the boundary transition is used by passing the radius of the withdrawn cylinder to zero. It is established that in this approach all the eigenfunctions of the corresponding problem on the eigenvalues have no singularities at zero, which means that the solutions of the original problem are constrained throughout the design. In order to illustrate the proposed method, a model example of finding the temperature field distribution in a column of a circular cross-section (concrete in a steel shell) is solved under the influence of the standard temperature regime of the fire. The results of the calculations are presented in a bulk schedule of temperature changes, depending on time and spatial coordinates. The generalization of the results obtained in the case of any finite number of cylindrical shells is a purely technical problem, and not a fundamental one. Note that while changing the boundary condition of the third kind to any other boundary condition (for example, the first kind) does not affect the scheme of solving similar tasks. Since the general scheme of studying the distribution of temperature fields in multi-layered structures with an arbitrary number of layers in the presence of internal sources of heat is studied in detail, the setting and solving of such problems for the system of "solid cylinder inside a cylindrical shell" is not without difficulty.

Thermal analysis of layered electronic circuits with Green's functions

This paper presents a method for thermal simulation of electronic circuits using an analytical solution of the three-dimensional heat equation resulting from an appropriate circuit thermal model. The temperature fields in multilayered structures are computed analytically employing the Green's functions solution method. The entire solution methodology is illustrated in detail on the particular examples of electronic circuits containing multiple heat sources. Compared to the previous papers published by the authors, the method has been extended by including the possibility of simulating imperfect layer contacts. The simulation results are validated with infra-red measurements and results obtained using other methods. Additionally, the discussion of simulation errors caused mainly by different non-linear phenomena is included.

Electromagnetic wave propagation in inhomogeneous multilayered structures of arbitrarily varying thickness-Generalized field transforms

To provide a suitable basis for the expansion of electromagnetic fields in multilayered structures of arbitrarily varying thickness we derive, in this paper, the appropriate transform pairs for the transverse electric and magnetic field components. Applying the technique utilized earlier for two semi-infinite media, we first derive the transform pairs for the three-medium problem. Building on these expressions for the transform pairs, we systematically extend our results for structures with an arbitrary number of layers. The generalized transforms derived consist of two infinite integrals (continuous spectrum) which correspond to the radiation and the lateral wave terms as well as a finite number of terms (discrete spectrum) which correspond to the surface waves. Exact boundary conditions are employed rather than surface impedance boundary conditions. In the analysis, the sources and the observation point may be located in any of the structure's layers. Thus for instance, the derived field expressions are suitable for the study of antennas embedded in the earth's crust or submerged underwater.