Introduction to shape optimization : shape sensitivity analysis
Introduction to shape optimization : shape sensitivity analysis
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发表时间：
1992
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通讯作者：
J. Sokołowski;J. Zolésio
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作者：
J. Sokołowski;J. Zolésio
本书介绍了现代泛函分析方法，用于对某些由偏微分方程控制的无限维系统进行灵敏度分析。主要主题以一般性和系统性的方式进行处理。它们包括许多经典应用，例如 Signorini 问题、弹塑性扭转问题和粘弹塑性问题。定义了可以导出成本函数的任何形状导数的“材料导数”。本书还包含了关于波动方程和单边问题的新结果，旨在作为形状优化问题的算法方法的基础参考书。
This book presents modern functional analysis methods for the sensitivity analysis of some infinite-dimensional systems governed by partial differential equations. The main topics are treated in a general and systematic way. They include many classical applications such as the Signorini problem, the elastic-plastic torsion problem and the visco-elastic-plastic problem. The "material derivative" from which any kind of shape derivative of a cost functional can be derived is defined. New results about the wave equation and the unilateral problem are also included in this book, which is intended to serve as a basic reference work for the algorithmic approach to shape optimization problems.