Free-form optimization method for buckling of shell structures under out-of-plane and in-plane shape variations

In the present work, in order to tackle the linear elastic buckling problem, we develop a shape optimization process based on a free-form optimization method to optimize a shell structure under out-of-plane and in-plane shape variations. The free-form optimization method is a node-based method in which mesh regularity can be maintained and shape design parameterization is not required. It has the advantages of sufficient efficiency for treating large-scale problems and the ability to realize a smooth shape. The buckling coefficient in buckling mode 1 is set as the objective function in the shape optimization problem. We consider repeated eigenvalues and volume constraint for the whole optimization process. Three numerical examples are presented in this work to illustrate the shape optimization algorithm and to show that it can increase the buckling strength substantially, especially under shape variation in the out-of-plane direction.