On the Universal Equation of Elasticity and the Universal Equation of Thermo-elasticity for Next-generation Aircrafts and Spacecrafts

Abstract

In the present investigation, the theories of “Relativistic Elasticity” and “Relativistic Thermo-Elasticity” are proposed for the design of the new-generation large aircraft with turbojet engines and speeds in the range of 50,000 km/h and for the new-generation spacecraft of any speed. Such theories show that there is a considerable difference between the absolute stress tensor and the stress tensor of the moving frames even in the range of speeds of 50,000 km/h. For higher speeds of the next-generation spacecraft, like c/3, c/2 or 3c/4 (c = speed of light), the difference between the two stress tensors is very much increased. Consequently, for the next-generation spacecraft with very high speeds, the relative stress tensor will be very much different than the absolute stress tensor. Furthermore, for velocities near the speed of light, the values of the relative stress tensor are much higher than the corresponding values of the absolute stress tensor. The proposed theory of “Relativistic Elasticity” is a combination between the theories of “Classical Elasticity” and “Special Relativity” or “General Relativity” and results in the “Universal Equation of Elasticity”. Also, the proposed theory of “Relativistic Thermo-Elasticity” is a combination between the theories of “Classical Thermo-Elasticity” and “Special Relativity” or “General Relativity” and results in the “Universal Equation of Thermo-Elasticity’’. On the other hand, for the structural design of the new-generation aircraft and spacecraft, the stress tensor of the airframe will be used in combination of the singular integral equations method. Such a stress tensor is reduced to the solution of a multidimensional singular integral equation and the singular integral operators method (SIOM) will be used for its numerical evaluation

Keywords: Relativistic elasticity, relativistic thermo-elasticity, universal equation of elasticity, universal equation of thermo-elasticity, next-generation aircraft, next-generation spacecraft, relative stress tensor, absolute stress tensor, stationary and moving frames, energy-momentum tensor, multidimensional singular integral equations, singular integral operators method (SIOM)