Computational procedures for a matrix analysis of the stability and vibration of thin flat-walled structures in compression

Abstract This paper is concerned with computational problems arising in the application of a previously published matrix analysis of the stability and vibration of structures consisting entirely of a series of thin flat rectangular plates connected together along longitudinal edges. The theory requires that the conditions at the ends of the structure permit a mode which varies sinusoidally in the longitudinal direction, and it is then possible to consider each individual flat plate as one element having four degrees of freedom at each of its two longitudinal edges. The corresponding stiffness matrices are essentially exact within the spirit of thin plate theory. The main computational problem is that of testing whether or not, for a specified wavelength of buckle, any chosen value of the compressive stress is less than or greater than the lowest buckling stress of the structure. This problem is discussed in detail, and a systematic test procedure is derived. Examples of panels with integral unflanged stiffeners, bonded Z-section stiffeners, bonded top-hat stiffeners and corrugated-core sandwich panels are discussed.