![]() ![]() This concept of similarity law has been explored before by the present author for thin-walled cylinders. The main purpose is to utilize the theory to formulate a law of similarity, whereby the problem of stressing a heated wing can be solved by performing a set of experiments on a properly proportioned and properly loaded wing at room temperature without heating. However, the main purpose of the present paper is not just to construct a theory for heated plates. Thus, the effects of decrease in Young's modulus with increase in temperature can be taken into account in the present theory. Secondly, Young's modulus E of the material is now allowed to vary as a function of temperature. The temperature profile is now arbitrary. The present study generalizes the earlier theory in two directions: Nádai's assumption of linear temperature profile across the plate is no longer necessary. In fact, the problem of thermal stresses in an elastic plate has been treated some time ago by Nádai. This problem in general theory of elasticity is greatly simplified by the fact that the wing is thin, and therefore the Kirchhoff hypothesis for bending of thin plates holds. That is, the stress in the wing at each time instant can be calculated from the temperature distribution at that time instant without the inertia effects from the time variation of the material displacements required by the changing stresses and the thermal expansions. Because the rate of change of temperature is small in comparison to the speed of sound propagation in the material, the stress calculation can be considered as a quasi-steady problem. The starting point of the stress analysis is the temperature distribution in the wing. The purpose of this paper is to suggest a method of stressing such heated wings. ![]() Therefore, concurrent with the severe aerodynamic heating, there is the problem of determining the thermal stresses in the wing. When there are large temperature gradients in the material, there are generally large thermal stresses due to the uneven thermal expansion of the material. For instance, in a recent paper by Kaye, the transient temperature distribution in a wedge-shaped solid wing was calculated for accelerated flight and was found to be rapidly varying both with respect to the space points in the wing and with respect to time instants. The high stagnation temperature for flight of aircraft at supersonic speeds results in severe aerodynamic heating of the surfaces of aircraft. ![]()
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