Shape optimization of nonprismatic rods of circular hollow cross-sections and of variable wall thickness

Within the presented research rods exhibiting the maximum buckling resistance are looked for. It was assumed that they have to possess the same mass and the same length as a solid cylindrical bar treated as the reference one. Nonprismatic rods of circular hollow cross-section and of variable wall thickness were only included into considerations. It was assumed that the external and internal surfaces of revolution were defined by some assumed in advance smooth functions. Three different classes of functions were used in the research, and namely: polynomial of the second order, sine and hyperbolic cosine functions. The classical optimization problem was defined by the objective function which was the buckling force, being maximized with appropriate constraints. Design variables were three independent geometrical parameters defining uniquely the sought bar shape. All derivations were carried out analytically by means of MathematicaTM system. The presented procedure was illustrated by two examples. The obtained increase of the critical force was dependent on the slenderness of the reference bar and reached the value 40 in the case of the longer, considered reference bar.Within the presented research rods exhibiting the maximum buckling resistance are looked for. It was assumed that they have to possess the same mass and the same length as a solid cylindrical bar treated as the reference one. Nonprismatic rods of circular hollow cross-section and of variable wall thickness were only included into considerations. It was assumed that the external and internal surfaces of revolution were defined by some assumed in advance smooth functions. Three different classes of functions were used in the research, and namely: polynomial of the second order, sine and hyperbolic cosine functions. The classical optimization problem was defined by the objective function which was the buckling force, being maximized with appropriate constraints. Design variables were three independent geometrical parameters defining uniquely the sought bar shape. All derivations were carried out analytically by means of MathematicaTM system. The presented procedure was illustrated by two examples. The obtain...