A Method to Compute Koiter’s b-Factor of Anisotropic Panels

Abstract

In his pioneering work W.T. Koiter drew attention to the initial postbuckling behaviour as a means to explain and quantify the discrepancy between the theoretical buckling load of thin shells and their much lower load carrying capacity observed in reality. That discrepancy is attributed to imperfections of various kind, and the so-called b-factor resulting from Koiter’s theory may be considered a measure of the sensitivity to such imperfections. Following a presentation of the variational problem needed to define the b-factor, and its transformation to algebraic equations, the solution of the latter is discussed in this paper. The crucial problem is the solution of a system of linear equations that is ill-conditioned. The difficulty is overcome by utilising the knowledge of several bifurcation loads and the corresponding mode shapes. The method was implemented as a supplement to the computer program BEOS, a finite element based software for buckling of anisotropic plane or curved panels. It admits calculation of the b-factor for a variety of panel configurations, including ones with skew planform and various boundary conditions subjected to uni-axial or bi-axial compression and shear.