Multimodal optimization of arches under stability constraints with two independent design functions (Q1119063)

An elastic, plane and funicular circular arch loaded by uniformly distributed radial pressure is considered. Fundamental buckling modes corresponding to two lowest critical loads both for out-of-plane and in- plane buckling of the arch are studied. Both depth and width of a rectangular cross-section are treated as independent control functions. The optimization problem determines these cross-sectional dimensions as the functional design variables in order to minimize the total volume of the arch under given external pressure and geometrical constraints. Suitable optimality conditions are derived using the Pontryagin maximum principle. The solution requires a multimodal, even quadrimodal, formulation of the optimization problem to be introduced. Some detailed numerical results are presented and advantages connected with the assumption of two independent design variables are discussed.