Relaxation methods applied to engineering problems - The elastic stability of plane frameworks and of flat plating

Abstract

Methods propounded in Part VI of this series, for computing normal modes and the associated frequencies of vibration, are here developed and extended to investigate ‘critical loadings’, and the associated modes of distortion, for plane frameworks and for flat plating in circumstances of ‘neutral elastic stability’. The extension to plane frameworks is straightforward. For flat plating, on the other hand, it is difficult to conjecture even approximately the mode associated with the gravest critical loading, and to meet this difficulty a special technique has been developed. This has proved successful in a case which by orthodox methods seems quite intractable for the reason that the mode is not expressible in terms of known functions.