寻找具有随动载荷和可重定位集中质量的最强稳定失重柱
Finding the strongest stable weightless column with a follower load and relocatable concentrated masses
摘要：
本文研究一端固定，自由端受非保守随动力作用的无质量弹性柱的集中质量最优配置问题。目标是找到最大可能的区间，使得在该区间内的载荷参数的变化保持结构的稳定性。稳定性约束是非凸和非光滑的，使得优化问题相当具有挑战性。我们给出了一个详细的分析处理的情况下，两个群众，认为最佳参数配置的颤振和发散边界的稳定区域同时接近。此外，我们推测，这一性质适用于任何数量的群众，这反过来又表明了一个简单的公式为$n$群众的最大负载间隔。这一猜想得到了广泛的计算结果的有力支持，获得使用最近开发的开源软件包GRANSO（基于GRAdient的算法非光滑优化），以最大限度地提高负载区间的非光滑稳定性约束的适当制定。我们希望，我们的工作将提供一个新的方法来解决经典的长期存在的问题，在民用和机械工程中出现的非保守弹性系统的稳定性优化的基础。
英文摘要：
We consider the problem of optimal placement of concentrated masses along a massless elastic column that is clamped at one end and loaded by a nonconservative follower force at the free end. The goal is to find the largest possible interval such that the variation in the loading parameter within this interval preserves stability of the structure. The stability constraint is nonconvex and nonsmooth, making the optimization problem quite challenging. We give a detailed analytical treatment for the case of two masses, arguing that the optimal parameter configuration approaches the flutter and divergence boundaries of the stability region simultaneously. Furthermore, we conjecture that this property holds for any number of masses, which in turn suggests a simple formula for the maximal load interval for $n$ masses. This conjecture is strongly supported by extensive computational results, obtained using the recently developed open-source software package GRANSO (GRadient-based Algorithm for Non-Smooth Optimization) to maximize the load interval subject to an appropriate formulation of the nonsmooth stability constraint. We hope that our work will provide a foundation for new approaches to classical long-standing problems of stability optimization for nonconservative elastic systems arising in civil and mechanical engineering.
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