桁架动力学形状优化的统一设计变量方法

Shape Optimization for Truss Dynamics with Unified Design Variables

研究了具有多种约束 ,特别是动力学约束 (频率约束 )作用下的平面桁架形状优化问题。提出一种将两类不同性质的设计变量 (尺寸变量、节点几何坐标变量 )变换为统一形式的无量纲设计变量的方法 ,解决了不同性质变量耦合引起的收敛困难问题 ,并拓展了设计空间。联合运用内点罚函数法、DFP法 (即变尺度法 )和一维搜索技术 (二次插值法 ) ,将约束优化问题转化为无约束序列优化问题 ,得到了满意的优化结果。算例表明本文方法对桁架形状优化的有效性 。

A shape optimization problem for plane truss subjected to various constraints, especially dynamic constraints (frequency constraints) was investigated. Elastic trusses were designed for minimum weight by varying the areas of themembers and the location of the joints. In order to settle the convergence deterioration caused by the coupling of two different kinds of design variable (sizing and geometry design variables) in optimizing progress, an unified and dimensionless variable formula was put forward. An obvious convergence improvement and extension of the design space were showed in the optimizing progress via a numerical example. Joined with one dimensional searching technology (quadratic interpolation method), interior penalty function method and DFP method (variable metric method ) were used to convert constrained optimization problem into sequence unconstrained optimization problem. The numerical example showed that the method described and proposed in the paper was effective to the shape optimization. A great weight of truss was reduced under the condition that all constraints were met. It also showed the simplicity and practicality of the algorithm for engineering design purpose.