As contemporary aerostructural research for aircraft design trends toward high-fidelity computational methods, aerostructural solutions based on theory are often neglected or forgotten. In fact, in many modern aerostructural wing optimization studies, the elliptic lift distribution is used as a reference in place of theoretical aerostructural solutions with more appropriate constraints. In this paper, the authors review several theoretical aerostructural solutions that could be used as reference cases for wing design studies, and these are compared to high-fidelity solutions with similar constraints. Solutions are presented for studies with 1) constraints related to the wing integrated bending moment, 2) constraints related to the wing root bending moment, and 3) structural constraints combined with operational constraints related to either wing stall or wing loading. It is shown that, under appropriate design constraints, theoretical solutions for the optimum lift distribution may capture aerostructural coupling sufficiently to serve as appropriate reference cases for higher-fidelity solvers. A comparison of theoretical and high-fidelity solutions for the optimum wingspan and corresponding drag reveals important insights into the effects of certain aerodynamic and structural parameters and constraints on the aerodynamic and structural coupling involved in aerostructural wing design and optimization.

随着当代飞机设计的航空结构研究趋向于高保真计算方法，基于理论的航空结构解决方案经常被忽视或遗忘。事实上，在许多现代航空结构机翼优化研究中，椭圆升力分布被用作参考，而不是具有更合适约束的理论航空结构解决方案。在本文中，作者回顾了几种可用作机翼设计研究参考案例的理论航空结构解决方案，并将这些解决方案与具有类似约束的高保真解决方案进行了比较。针对以下研究提出了解决方案：1) 与机翼综合弯矩相关的约束，2) 与翼根弯矩相关的约束，3) 结构约束与与机翼失速或机翼载荷相关的操作约束相结合。结果表明，在适当的设计约束下，最佳升力分布的理论解决方案可以充分捕捉航空结构耦合，以用作更高保真度求解器的适当参考案例。最佳翼展和相应阻力的理论和高保真解决方案的比较揭示了对某些空气动力学和结构参数的影响以及对空气结构机翼设计和优化中涉及的空气动力学和结构耦合的约束的重要见解。最佳升力分布的理论解决方案可以充分捕获航空结构耦合，以用作更高保真度求解器的适当参考案例。最佳翼展和相应阻力的理论和高保真解决方案的比较揭示了对某些空气动力学和结构参数的影响以及对空气结构机翼设计和优化中涉及的空气动力学和结构耦合的约束的重要见解。最佳升力分布的理论解决方案可以充分捕获航空结构耦合，以用作更高保真度求解器的适当参考案例。最佳翼展和相应阻力的理论和高保真解决方案的比较揭示了对某些空气动力学和结构参数的影响以及对空气结构机翼设计和优化中涉及的空气动力学和结构耦合的约束的重要见解。