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Some problems of multipurpose analysis and optimization of deformed structures and thin-walled structural elements are studied in this paper under some constraints including incomplete data. The first problem is the multipurpose optimization of layered plate made from given set of materials in context of optimization of ballistic limit velocity. Incomplete data concerning the thickness of layers of optimized multilayered shield structure are taken into account. The Pareto-approach and numerical evolutionary method (genetic algorithm) are used for solving of the considered multipurpose problem. The second problem studied in the paper is the shape optimization problem for rigid punch moving on the surface of elastic half-space, which is solved analytically in multipurpose formulation taking into account friction of contacted surfaces, wear of materials and arising pressure distributions. The relative movement is considered in frame of quasi-static formulation. Formulated optimization problem is studied analytically using the developed decomposition approach and exact solutions are obtained for the punch which has a rectangular contact region and moves translationally with a constant velocity.

The problem of contact pressure optimization is formulated for the case of rigid punch interacted with elastic medium. Coupling of the punch penetration and action of external loads at the outside regions is taken into account. The shape of the punch is considered as an unknown design variable. The minimized integral functional characterizes the discrepancy between the actual contact pressure and the required pressure distribution. The problem is studied under condition that the total forces and moments applied to the punch and the loads acted at the outside regions are given. It is shown that the considered optimization problem can be splitted and transformed to two successively solved problems. Optimal shapes are found analytically for the punches having rectangular contact domains.

The optimization problems taken into consideration consist in finding the shape and thickness distribution of brittle or quasibrittle elastic shells with cracks, loaded by fixed statical forces in such a way that the cost functional (volume of the shell material or weight) reaches a minimum, while satisfying some fracture mechanics constraints. As constraints we use bounds on stress intensity factors or structural longevity. In the case of cycling loadings we consider the number of cycles before fracture as the constraint for optimization problem. Considered optimization problems are characterized by incomplete information concerning initial crack size, crack location and its orientation. In this context the paper presents some possible formulations of optimal structural design problems, based on guaranteed (minimax) and probabilistic approaches. Some examples of analytical and numerical solutions are presented.