| 追究根基的结构拓扑优化方法 |
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| 引用本文： | 隋允康,叶红玲,刘建信,陈实,宇慧平.追究根基的结构拓扑优化方法[J].工程力学,2008,25(Z2). |
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| 作者姓名： | 隋允康 叶红玲 刘建信 陈实 宇慧平 |
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| 作者单位： | 北京工业大学工程数值模拟中心; |
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| 基金项目： | 国家自然科学基金项目(10472003);;汽车车身先进设计制造国家重点实验室开放基金项目(30715002);;高校博士点基金项目(20060005010) |
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| 摘 要： | 结合作者在结构拓扑优化方面的研究工作,围绕了ICM(独立、连续、映射)方法涉及的基本概念上的突破,叙述了将本质上为0-1离散变量的拓扑优化问题转化为连续变量优化问题的具体做法,其中介绍了若干要点:以阶跃函数把离散问题化为连续问题即完成关键的等价性转换是第一步;定义磨光函数逼近阶跃函数的可操作的近似是第二步;引入作为磨光函数反函数的过滤函数实现映射性建模是第三步;采用某些光滑算法求解连续变量模型则是第四步。通过连续体结构的典型数值算例说明了将结构拓扑优化的模型转化为独立层次的拓扑优化过程。该方法对于纯数学的0-1离散变量优化的求解也适用,方法与数值都表明了这一点。
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| 关 键 词： | 结构拓扑优化 ICM方法 0-1离散变量数学规划 优化模型的建立 磨光函数 过滤函数 |
A STRUCTURAL TOPOLOGICAL OPTIMIZATION METHOD BASED ON EXPLORING CONCEPTUAL ROOT |
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| SUI Yun-kang,YE Hong-ling,LIU Jian-xin,CHEN Shi,YU Hui-ping.A STRUCTURAL TOPOLOGICAL OPTIMIZATION METHOD BASED ON EXPLORING CONCEPTUAL ROOT[J].Engineering Mechanics,2008,25(Z2). |
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| Authors: | SUI Yun-kang YE Hong-ling LIU Jian-xin CHEN Shi YU Hui-ping |
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| Affiliation: | Numerical Simulation Center for Engineering;Beijing University of Technology;Beijing 100124;China |
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| Abstract: | This paper introduces the transformation of the 0-1 discrete variables into continuous variables in topological optimization problem by ICM (Independence, continuous and Mapping) method. The first step is to convert equivalently the discrete problem into continuous problem taking advantages of the step-up function; The second step is to define the polish function to approach the step-up function; The third step is to establish the mapping model by introducing the filter function which is the inverse functio... |
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| Keywords: | structural topological optimization ICM method mathematical programming about 0-1 discrete variables establishment of optimal model polish function filter function |
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