The lightweight design of a thin-walled tube under torsion is addressed in the paper. A multi-objective optimization approach is adopted to minimize the mass while maximizing the structural stiffness of the thin walled tube. Constraints on available room (maximum diameter), safety (admissible stress), elastic stability (buckling), minimum thickness (forced by manufacturing technologies) are included in the problem. The analytical solution of the multi-objective optimization problem is obtained by applying a relaxed formulation of the Fritz John conditions for Pareto-optimality. Relatively simple analytical expressions of the Pareto-optimal set are derived both in the design variables (tube diameter and wall thickness) and objective functions (mass and compliance) domain. Simple practical formulae are provided to the designer for the preliminary design of thin-walled tubes under torsion. Finally, the comparative lightweight design of tubes made from different materials is presented and an application of the derived formulae to a simple engineering problem is discussed.

中文翻译：

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扭转薄壁管：多目标优化设计

本文探讨了扭转下薄壁管的轻量化设计。采用多目标优化方法来最小化质量，同时最大化薄壁管的结构刚度。问题包括对可用空间（最大直径），安全性（允许应力），弹性稳定性（屈曲），最小厚度（由制造技术强制）的约束。多目标优化问题的解析解是通过对帕累托最优应用弗里茨·约翰条件的宽松公式来获得的。在设计变量（管直径和壁厚）和目标函数（质量和顺应性）域中都可以得出帕累托最优集的相对简单的解析表达式。为设计人员提供了用于扭转下薄壁管的初步设计的简单实用公式。最后，介绍了由不同材料制成的管的比较轻量化设计，并讨论了导出的公式在简单工程问题中的应用。