结构优化中的建模方法概述  

BRIEF REVIEW ON MODELING METHOD IN STRUCTURAL OPTIMIZATION

作　　者：隋允康[1] 李善坡[1] 

机构地区：[1]北京工业大学工程数值模拟中心,北京100022

出　　处：《力学进展》2008年第2期190-200,共11页Advances in Mechanics

基　　金：国家自然科学基金(10472003);高校博士点基金(20060005010)~~

摘　　要：建立优化模型是结构优化前的最佳选择.由于工程实际问题的复杂性,很难建立显式表达的模型,即使少数问题能够建立显式表达的模型,也难以求解.因此需要借助近似方法建立模型,为了便于求解或提高求解效率,通常还要对模型进行变换.文中列举了结构优化中常用的近似建模方法,并根据建立近似显式的途径和敏度分析的方法对其进行分类,详细介绍了近几年来广泛应用的样本点构造方法,然后描述了它们在结构优化中的应用和具体实现过程,分析了它们的优缺点和应用范围,指出了结构优化建模方法今后的发展方向.It is a good choice to establish an optimization model before a structural optimization, Due to the complexity of engineering problems, it is very difficult to construct an explicit expression of structural response in terms of design variables. Even though an explicit model may be established for some problems, it would be difficult to the problem with the model solve. Therefore, an approximation method is needed to establish an optimization model and convert the model to a solvable one. This paper discusses some frequently used approximate modeling methods and classifies them according to modeling ways and methods of sensitivity analysis. The constructing methods based on sample points, which are widely used in recently years, are introduced in detail. Then the methods are described in applications and concrete realization processes for structural optimizations. Advantage, disadvantage and applicable range of each method are analyzed and the trends of model establishing method for structural optimizations in the future are pointed out.

关 键 词：结构优化 近似方法 数学模型 响应面方法 径向基函数方法 KRIGING方法 

分 类 号：O224[理学—运筹学与控制论] TP391.9[理学—数学]