Optimization of geometrically non-linear symmetric systems with coincident critical points

A new formulation is presented for optimum design of an elastic symmetric structure for specified non-linear buckling load factor. It is shown that the method of sensitivity analysis of bifurcation load factor developed in Ohsaki and Vetani (Int. J. Numer. Methods Engng. 1996; 39: 1707–1720) can also be applied for the case where the structure reaches coincident critical points including a limit point. Based on the method of sensitivity analysis, an algorithm is presented for finding optimum designs for specified coincident critical points. The well-known danger of designing a structure that exhibits coincident buckling is discussed in detail. It is shown in the examples of trusses that the structural volume may be successfully reduced as a result of optimization even if the reduction of the maximum load factor due to possible asymmetric initial imperfection is considered.