摘要
本文根据有限元分析基础,研究薄壁结构在应力、位移、最小尺寸约束下结构最轻重量的优化设计问题。用Kuhn-Tucker(库恩-塔克)必要条件将多个位移约束简化为单一位移约束(称为最临界位移约束),建立位移约束下的优化设计准则.从而避免大批拉格朗日乘子的计算,并结合满应力优化设计准则,形成了在有效约束界面逐步逼近最优设计点的方法——包络法。用某型飞机后机身一段优化设计作为本文的实际应用,得到令人满意的结果。
Based on the finite element method,an optimization design of minimum weight of thin-walled structures under constraints of multiple load conditions and stress (displacement and size is studied in this paper. Using Kuhn-Tucker necessary conditions,a multi-displacement constrained problem is simplified to a single displacement constraint and called the most critical displacement constraint,eliminating the need to calculate a large set of lagrange multipliers for the effective constraints and deriving an optimization criterion. A recursion formula for stress and displacement constraints is incorporated into a designalgorithm——Envelope Method,which apporaches to the optimum design along the mosteffective constraint boundary. The method is applied successfully to optimum design of aft fuselage.
关键词
有限元
位移
飞机
结构设计
optimization,finite element,iteration,displacement constraint,rate of stress