Structural Optimization Methods for Large Scale Problems: Status and Limitations, International Design Engineering Technical Conferences (IDETC)
Structural Optimization Methods for Large Scale Problems: Status and Limitations, International Design Engineering Technical Conferences (IDETC)
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DOI：
10.1115/detc2007-34326
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发表时间：
2007-09
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影响因子：
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通讯作者：
C. Fleury
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文献类型：
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作者：
C. Fleury
本文介绍了从最近的数值实验的结果支持的理论论据表明，目前的优化方法的局限性时，涉及大量的设计变量以及大量的约束条件，其中许多是积极的问题。这是典型的局部应力约束的最优尺寸问题，特别是当复合材料。它示出，在原始和对偶方法的CPU时间花费在优化器是有关的数值工作需要反转大小为JACT的对称正定矩阵，JACT是有效的活动约束，即与正拉格朗日乘数的约束数。此CPU时间随jact3而变化。当约束的数量m增加时，jact有增长的趋势，但有一个极限。事实上，另一个众所周知的理论性质是，活动约束jact的数量不应超过自由原始变量iact的数量，即未达到下限或上限的变量的数量。这个数iact本身当然小于设计变量的真实的数n。这导致了这样的结论，对于具有许多活动约束的问题，CPU时间可以以n3的速度增长。相对于m，CPU时间的增加保持近似线性。将简要介绍该方法在真实的工业问题中的一些实际应用：飞机复合材料机翼的局部屈曲约束设计优化和发动机挂架的拓扑优化。
This paper presents results from recent numerical experiments supported by theoretical arguments which indicate where are the limits of current optimization methods when applied to problems involving a large number of design variables as well as a large number of constraints, many of them being active. This is typical of optimal sizing problems with local stress constraints especially when composite materials are employed. It is shown that in both primal and dual methods the CPU time spent in the optimizer is related to the numerical effort needed to invert a symmetric positive definite matrix of size jact, jact being the effective number of active constraints, i.e. constraints associated with positive Lagrange multipliers. This CPU time varies with jact3 . When the number m of constraints increases, jact has a tendency to grow, but there is a limit. Indeed another well known theoretical property is that the number of active constraints jact should not exceed the number of free primal variables iact, i.e. the number of variables that do not reach a lower or upper bound. This number iact is itself of course smaller than the real number of design variables n. This leads to the conclusion that for problems with many active constraints the CPU time could grow as fast as n3 . With respect to m the increase in CPU time remains approximately linear. Some practical applications to real life industrial problems will be briefly shown: design optimisation of an aircraft composite wing with local buckling constraints and topology optimization of an engine pylon.Copyright © 2007 by ASME