Non-uniform Thermal Loads Research Articles

Temperature field of a double squirrel-cage motor during startup

During startup an electric motor can be subject to severe electrical and thermal loads. These loads, despite their relatively short durations, significantly affect motor's lifetime and reliability. The use of the double squirrel-cage arrangement has resulted in the improvement of the startup coefficients for induction motors. However, the cage is still subject to non-uniform thermal loads and, in consequence, to overheating. These transient loads are particularly heavy during a prolonged startup, routinely encountered under tough industrial operating conditions, for example when attempting to start a motor with a locked rotor. Typical examples are starting a motor powering a longwall shearer buried under a collapsed coal face or an overloaded coal mill. A methodology is presented to compute the temperature field of a double squirrel-cage and the core of an induction motor. The procedure employs a three-dimensional model of the motor heating obtained using the control volume method. The model provides the basis for calculating the stress field within the cage. The input data to the model can be obtained from the motor windings specification sheet. The thermomechanical analyses can be performed during the design and construction phases, and may facilitate motor performance optimisation.

Analytical solution for bending of cross-ply laminated plates under thermo-mechanical loading

The static thermo-elastic response of symmetric and anti-symmetric cross-ply laminated plates has been investigated by the use of a unified shear deformation plate theory. The present plate theory enables the trial and testing of different through-the-thickness transverse shear-deformation distributions and, among them, strain distributions that do not involve the undesirable implications of the transverse shear correction factors. The validity of the present theory is demonstrated by comparison with solutions available in the literature. A wide variety of results is presented for the static response of simply supported rectangular plates under non-uniform sinusoidal mechanical and/or thermal loadings. The influence of material anisotropy, aspect ratio, side-to-thickness ratio, thermal expansion coefficients ratio and stacking sequence on the thermally induced response is studied.

Boundary element analysis of interface cracks subjected to non-uniform thermal loading

This work applies the method of multi-region boundary element to analyze the thermal stress intensity factor (TSIF) of the bi-material interface cracks subjected to linear and quadratic temperature distribution. An attempt is also made to resolve the problem containing body force which is caused by the inhomogeneous thermal loading by, initially, separating the solution of the inhomogeneous problem of each material into homogeneous and particular solutions, as proposed by Sung. The particular solution can be obtained by expanding the body force into Fourier series and, then, solving each term of the Fourier series. Next, inserting the obtained particular solutions into the boundary conditions of the original problem allows us to reduce the inhomogeneous problem to a homogeneous one. Moreover, the program of thermal multi-region BEM (TMBEM), which neither requires a domain integral nor changes the kernel functions, is established by imposing the continuity conditions on the interfaces. Finally, the applications of TMBEM are illustrated by evaluating the TSIFs of the interface cracks of bi-material subjected to linear and quadratic temperature distributions.

Nonlinear thermoelastic analysis of composite panels under non-uniform temperature distribution

The response of moderately thick laminated panels experiencing large displacements and rotations under non-uniform thermal loading is investigated through a nonlinear finite element analysis. The present nonlinear thermoelastic analysis incorporates an anisoparametric, doubly curved, shallow shell element that is free of the `locking' phenomenon. The effects of large displacements and rotations, transverse shear deformations, the coupling between stretching and bending due to shallow geometry, and Duhamel–Neumann-type thermoelastic material anisotropy are included in the element formulation. The equations of equilibrium are derived from the virtual work principle, along with the co-rotational form of the total Lagrangian formulation. A non-uniform temperature field across the shell surface is approximated by piecewise-uniform temperature distributions over individual elements. In the thickness direction, the temperature distribution is approximated linearly. Accuracy of the present analysis is established by comparison with benchmark solutions. The numerical results are presented for various configurations, including cutouts under uniform and non-uniform temperatures. The numerical results demonstrate that the present finite element analysis is computationally robust and efficient.

Analysis of Metal Matrix Laminated Cylindrical Panels Subjected to Nonuniform Temperature Loading

The moderately large deflection response of metal matrix composite (MMC) cylindrical panels to nonuniform thermal loading is addressed. Temperature dependence of both elastic and viscoplastic properties of the metallic matrix is taken into account; this suggests that a nonuniformly heated panel should be considered as a nonhomogeneous structure. At each loading increment, a micromechanical analysis is performed to establish the instantaneous thermoinelastic constitutive law at each point of the panel. This is followed by a structural analysis that yields quasi-static thermal response of antisymmetrically laminated MMC panels. Results are presented for simply supported and clamped graphite-aluminum panels and for two types of in-plane boundary conditions. The effects of boundary conditions, lamination angle, panel's curvature, length-to-thickness ratio, and different types of spatial temperature distributions are illustrated. Comparisons with results obtained using an approach that treats the effect of temperature-dependent material properties in a simplified manner are shown. Comparisons with the corresponding elastic solutions (which neglect the inelastic effects in the metallic matrix) are given.

Shearing Deformation in Partial Areal Arrays: Analytical Results

Simple, closed-form expressions, based on elasticity theory, are derived for determining the location and magnitude of the maximum shearing displacement in a partial areal array of solder joints. Both uniform and nonuniform thermal loadings are considered, as is the heterogeneity of the component, which often arises due to different values of coefficient of thermal expansion (CTE) and elastic properties among the module’s constituent materials. The model is based on the following assumptions: (a) the square geometry of the array and component may be replaced with an equivalent axisymmetric geometry; and (b) the stiffness of the solder joints is negligible with respect to that of the component and substrate. The “soft joint” assumption corresponds to low-modulus solders or to thermal excursions occurring at high temperatures or low frequencies, for which significant stress relaxation occurs in the solder. For arrays exhibiting higher stiffness characteristics, the model yields conservative estimates of shearing displacement. Results indicate that, unlike homogeneous-component models under uniform temperature changes, the critical joints are not necessarily at the outer corners of the array. Other candidate locations predicted by the model (and observed in experimental and numerical studies) include the inner corner joints and any joints positioned beneath the die corners. The analytical results, also presented graphically, are found to depend on only three dimensionless parameters: the ratio of inner to outer array dimension, the ratio of die size to outer array dimension, and a “mismatch parameter,” which depends on the material, geometry, and loading characteristics of the problem. The results can be used to quickly determine the location and magnitude of peak shearing displacement in the array, possibly minimizing or eliminating the need to perform expensive and time-consuming finite element macroanalyses on entire assemblies involving hundreds of joints. Thus, the analyst may proceed directly to a detailed finite element microanalysis of the critical joint for fatigue life estimation, using the calculated shearing displacement as a required boundary condition in the finite element model.

Thermal Post-buckling Analysis of Imperfect Laminated Plates on Two-Parameter Elastic Foundations

This study deals with simply supported, perfect and imperfect, composite laminated plates subjected to uniform or parabolically nonuniform thermal loading and resting on two parameter elastic foundations. The analysis uses a mixed Gakerkin perturbation technique to determine the required thermal buckling loads and the post buckling equilibrium paths, with the material properties assumed to be independent of temperature

The effect of temperature-dependent material properties on elasto-viscoplastic buckling behaviour of non-uniformly heated MMC plates

An inelastic bifurcation buckling of symmetrically laminated metal matrix composite (MMC) plates under non-uniform thermal loading is analyzed. The metallic matrix is modeled as a thermoelasto-viscoplastic material with temperature-dependent properties (both elastic and viscoplastic). This suggests that, in the prebuckling state, a MMC plate should be considered as a statistically non-homogeneous thermoelasto-viscoplastic structure. To treat the problem, a method based on a combination of micromechanical and structural analyses is used. As a result, a buckling criterion, incorporating the effective instantaneous constitutive behaviour at every point of the plate at each increment of thermal loading, is obtained. Results are presented for simply supported and clamped SiC/Ti plates. The effects of length-to-thickness and aspect ratios, lamination angle, fiber volume fraction, and different types of spatial temperature distributions on the critical buckling temperature are illustrated. Comparisons with the results obtained using an approach that treats the effect, of temperature-dependent material properties in a simplified manner, are presented. Comparisons with the corresponding elastic solutions, obtained by neglecting the inelastic effects in the metallic matrix, are given.

Internal, Shellside Heat Transfer and Pressure Drop Characteristics for a Shell and Tube Heat Exchanger

Per-tube heat transfer coefficients and per-compartment and intracompartment pressure drops were measured on the shell side of a shell and tube heat exchanger. The main focus of the work was to determine the response of these quantities to variations in the size of the baffle window; the Reynolds number was also varied parametrically. The pressure measurements showed that the fluid flow is fully developed downstream of the first compartment of the heat exchanger and that the per-compartment pressure drop is constant in the fully developed regime. Within a compartment, the pressure drop in the upstream half is much larger than that in the downstream half. The per-tube heat transfer coefficients vary substantially within a given compartment (on the order of a factor of two), giving rise to a nonuniform thermal loading of the tubes. Row-average and compartment-average heat transfer coefficients were also evaluated. The lowest row-average coefficients were those for the first and last rows in a compartment, while the highest coefficient is that for the row just upstream of the baffle edge. It was demonstrated that the per-tube heat transfer coefficients are streamwise periodic for a module consisting of two consecutive compartments.

Elastic buckling of heated doubly curved thin shells

Equations are presented to describe the large deflection behavior of doubly curved shallow thin shells under nonuniform thermal loading. Approximate solutions are obtained by means of the Galerkin method for temperature distributions which a) vary over the surface of the shell and b) vary over the surface and linearly through the thickness of the shell. Load-deflection curves are plotted for simply supported shell panels. The results are used to study buckling and post-buckling behavior of the panels. It is shown, that the buckling temperature is a function of the sum of the curvature parameters, dimensions of the shell and its material properties.

The Elastically Clamped Rectangular Plate With Arbitrary Lateral and Thermal Loading

Within the limits of classical thin-plate theory a variety of elementary problems have been solved for the rectangular plate3,4,5. In particular, the rectangular plate with edges simply supported or clamped has been dealt with at length and the solution to different loading cases given either in the form of a doubly infinite series or a single infinite series. In this paper a rapidly convergent series solution is outlined for the uniformly elastically clamped plate which is subjected to nonuniform lateral and thermal loading. The solution converges in the limit to those corresponding to the simply supported and rigidly clamped plate.