Optimization of geometrically nonlinear thin-walled structures using the multipoint approximation method

Abstract

The present study concentrates on the optimization of geometrically nonlinear shell structures using the multipoint approximation approach. The latter is an iterative technique, which uses a succession of approximations for the implicit objective and constraint functions. These approximations are formulated by means of multiple regression analysis. In each iteration the technique enables the use of results gained at several previous design points. The approximate functions obtained are considered to be valid within a current subregion of the space of design variables defined by move limits. A geometrically nonlinear curved triangular thin shell element with the corner node displacements and the mid-side rotations as degrees of freedom is used for the FE analysis. The influence of initial shape imperfections on the optimum designs is investigated. Imperfections are considered as a shape distortion proportional to the lowest buckling modes of the perfect structure. Displacement, stress, and stability constraints are taken into account. To prevent finite element solutions from becoming unstable during the optimization process, a simple strategy for avoiding passage of stability points is applied. Some numerical examples are solved to show the practical use and efficiency of the technique presented.