The matrix methods of structural analysis developed specifically for use on modern digital computers have now become universally accepted in structural design. These methods provide a means for rapid and accurate stress and deflection analysis of complex structures under static and dynamic loading conditions and they can also be used very effectively for the stability analysis. In the conventional stability analysis two possible approaches are normally used; either the differential equations describing the structural deflections are formulated and the lowest eigenvalue representing the buckling load condition is found for a given set of boundary conditions, or alternatively, if the differential equations are too difficult to prescribe, approximate deflection shapes are used in the strain energy expression for large deflections which is subsequently minimised, leading to the stability determinant whose lowest root represents the instability condition. When designing complex structures the conventional methods of finding buckling load conditions are extremely difficult to apply, and therefore in such cases we have to rely on the matrix methods of stability analysis.

It is well known that the performance of the practical gas turbine cycle, in which compression and expansion are non-isentropic, is critically dependent upon the maximum temperature of the working fluid. In engines in which shaft-power is produced the thermal efficiency and the specific power output rise steadily as the turbine inlet temperature is increased. In jet engines, in which the gas turbine has so far found its greatest success, similar advantages of high temperature operation accrue, more particularly as aircraft speeds increase to utilise the higher resultant jet velocities. Even in high by-pass ratio engines, designed specifically to reduce jet efflux velocities for application to lower speed aircraft, overall engine performance responds very favourably to increased turbine inlet temperatures, in which, moreover, these more severe operating conditions apply continuously during flight, and not only at maximum power as with more conventional cycles.