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As a continued treatment of a previous article (1) by the same author, this paper presents an iterative algorithm for seeking the global weight optimum, the convergent conditions of the algorithm being established using M. Edlestein's contraction mapping theorem. 本文是工作的深入.文中给出求全局最优解的迭代算法,并用M.Edlestein收缩映射定理建立收敛条件. The present paper is a s ummary of our recent research works [1-5] on optimum design of thin, solid, elastic plates. Within the context of thin plate theory, we first study the traditional formulation for optimal design, and then proceed to a new formulation, which is based on a densely, integrally stiffened plate model. Both numerical and analytical results reveal that a global optimal thickness ful1ction for thin, solid, elastic plates does genera- lly not exist within the class of continuous functions, or... The present paper is a s ummary of our recent research works [1-5] on optimum design of thin, solid, elastic plates. Within the context of thin plate theory, we first study the traditional formulation for optimal design, and then proceed to a new formulation, which is based on a densely, integrally stiffened plate model. Both numerical and analytical results reveal that a global optimal thickness ful1ction for thin, solid, elastic plates does genera- lly not exist within the class of continuous functions, or continuous functions with a finite number of discontinuities, and shou1d instead be sought within the class of functions with an infinite number of discontinuities. In cases where smooth(or partially smooth) designs are possible, a now necessary condition for optimality should be applied. 本文是我们最近关于实心弹性薄板最优设计[1-5]的一个扼要总结。在薄板理论内,我们先研究传统提法,然后讨论新的、以密级加肋板模型为基础的提法。数值和解析结果两者揭示了实心弹性薄板的全局最优解在连续函数类和只有有限个问断的连续函数内并不存在,而应在只有无限间断的函数类内寻找。当光滑解可能时,本文给出一个新的最优化必要条件. The present paper studies the problem of optimizing thin, solid elastic plates with limited slope of thickness functions. Starting from randomly ge- nerated initial designs, an algorithm based on optimality criterion leads to different, locally optimal designs. It is further discovered that the compliance functional is not a convex functional, and the existence of locally optimal de- signs is inevitable. But it is also observed that in cases that the load wave number n is small or the constraints on slope are... The present paper studies the problem of optimizing thin, solid elastic plates with limited slope of thickness functions. Starting from randomly ge- nerated initial designs, an algorithm based on optimality criterion leads to different, locally optimal designs. It is further discovered that the compliance functional is not a convex functional, and the existence of locally optimal de- signs is inevitable. But it is also observed that in cases that the load wave number n is small or the constraints on slope are moderate, design obtained from initial design of uniform thickness destribution seems to be a globally optimal one. 本文研究在对板的厚度函数斜率加上限制的条件下实心弹性环板的最小柔顺性 (或最大刚度)设计。从随机地产生的不同初始设计出发,以最优准则为基础的叠代 算法收敛到不同的局部“最优”设计,进一步发现,柔顺性(Compliance)泛函不 是一个凸泛函.必然存在多个局部极值。但当外荷载沿环向变化较慢时,或对板的厚 度变化斜率加上比较严的限制时(这种限制在工程上是比较合理的),从均匀厚度的 初始设计出发进行叠代收敛到的最后设计极可能是一个全局最优解。
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