Bending of lightweight circular tubes

The concept design (sizing) of thin-walled tubes subject to bending is dealt by resorting to rigorous design principles pertaining to engineering science. Multi-objective optimization is the proper theory that has been exploited. Minimum mass and maximum stiffness (minimum compliance) are the optimization objectives. Safety (admissible stress), stability (buckling), available room (external radius of the tube), and thickness of the tube (arising from technological issues) are introduced as constraints. Linear elastic theory is used. Optimal solutions are given in analytical form for a prompt use by designers. Such optimal solutions refer both to the objectives (mass and compliance) and to the design variables (radius and thickness of the tube). The best attainable lightweight design is discussed as a function of the constraints. In particular, given the upper and lower bounds for radius and thickness respectively, three candidate optimal solutions are addressed in the paper for concept design purposes. The comparative lightweight design of tubes made from different materials is presented. Contrary with respect to the reputation of aluminum for effective lightweight construction, steel can be the best choice, when the available room has to be saturated.