Imperfection sensitivity analysis of hill-top branching with many symmetric bifurcation points

Imperfection sensitivity properties are derived for finite dimensional elastic conservative systems exhibiting hill-top branching at which arbitrary many bifurcation points coincide with a limit point. The critical load at a hill-top branching point is demonstrated to be insensitive to initial imperfections when all the bifurcation points are individually symmetric. Therefore, it is not dangerous to design a frame or truss so that many members buckle simultaneously at the limit point, although the notion of the danger of optimization by compound bifurcation is widespread.