Critical initial imperfection of structures

A method is introduced for determining the critical initial imperfection of discretized structures that decreases the load-bearing capacity most rapidly. The effects of imperfections on simple critical points, such as limit points of loads and simple bifurcation points, are theoretically investigated based on the idea of the Lyapunov-Schmidt decomposition developed in bifurcation theory. Imperfection sensitivity varies with the types of points. Nonetheless critical imperfection pattern is expressed in the same formula regardless of the types. Among various imperfections, the most influential can be found in a quantitative manner. The validity and the usability of the proposed method are illustrated through its application to simple example structures.