Relativistic Elasticity & The Universal Equation of Elasticity for Next Generation Aircrafts & Spacecrafts
The theory of “Relativistic Elasticity” is proposed for the design of the new generation large aircrafts with turbojet engines and speeds in the range of 50,000 km/h. This theory shows that there is a considerable difference between the absolute stress tensor and the stress tensor of the moving frame even in the range of speeds of 50,000 km/h. For bigger speeds like c/3, c/2 or 3c/4 (c=speed of light), the difference between the two stress tensors is very much increased. Therefore, for the next generation spacecrafts with very high speeds, then 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 very much bigger 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” and results to the “Universal Equation of Elasticity”. For the structural design of the new generation aircrafts and spacecrafts the stress tensor of the airframe will be used in combination to the singular integral equations method. Such a stress tensor is reduced to the solution of a multidimensional singular integral equation and for its numerical evaluation will be used the Singular Integral Operators Method (S.I.O.M.).
