Optimum shapes of bar cross-sections

In this paper, the problems of optimization of cylindrical bar cross sections are formulated. The functional considered characterizes rigidities, maximum stress and the areas of the cross-section of the bar. The shape of the boundary of the cross-section is taken as a design variable and is found in the case of regular polygonal contours. Using minimax approaches optimal designs have been obtained for simply connected and doubly connected cross-sections having given convex holes. Investigations performed and complete solutions derived from the cross-sectional area minimization under rigidity and strength constraints show the changes of the optimal shapes as functions of the problem parameter.