A unified approach to various problems of structural optimization, based on approximation concepts, is presented. The approach is concerned with the development of the iterative technique, which uses in each iteration the information gained at several previous design points (muttipoi~*t approximations) in order to better fit constraints and/or objective functions and to reduce the total number of FE analyses needed to solve the optimization problem. In each iteration, the subregion of the initial region in the space of design variables, defined by move limits, is chosen. In this subregion, several points (designs) are selected, for which response analyses and design sensitivity analyses are carried out using FEM. The explicit expressions are formulated using the weighted least-squares method. The explicit expressions obtained then replace initial problem functions. They are used as functions of a particular mathematical programming problem. Several particular forms of the explicit expressions are considered. The basic features of the presented approximations are shown by means of classical test examples, and the met]~Lod is compared with other optimization techniques.

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.

No abstract