| 隋允康,宣东海,叶红玲,铁军.阶跃函数高精度逼近的结构拓扑优化方法[J].计算力学学报,2010,27(6):959~967 |
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| 阶跃函数高精度逼近的结构拓扑优化方法 |
| Structural topology optimization method using high accuracy approximation of the step function |
| 投稿时间：2009-10-13 修订日期：2010-01-17 |
| DOI：10.7511/jslx20106002 |
| 中文关键词: 阶跃函数 指数型函数 ICM方法 结构拓扑优化 |
| 英文关键词:step function exponential type function ICM method structural topology optimization |
| 基金项目:国家自然科学基金(10872012);北京自然科学基金(3093019);大连理工大学工业装备结构分析国家重点实验室基金(GZ0819)资助项目. |
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| 摘要点击次数: 2542 |
| 全文下载次数: 1565 |
| 中文摘要: |
| 为了提高ICM(Independent Continuous and Mapping,即独立、连续及映射)方法求解结构拓扑优化问题的效率,本文改进了阶跃函数及其反函数的近似逼近函数——磨光函数和过滤函数。首先,分别对ICM方法的磨光函数和过滤函数按其近似性质进行了分类,分别提出了左磨函数及上磨函数和快滤函数、慢滤函数诸概念。然后得到了区分左磨函数和上磨函数、快滤函数和慢滤函数的两个判别定理;并得到了上磨函数、快滤函数、左磨函数及慢滤函数的对应定理。进而给出了磨光函数和过滤函数的使用准则及构造方法。采用高精度逼近阶跃函数的指数类函数做左磨函数,建立近似程度更高的结构拓扑优化模型。上述策略带来了模型非线性程度的提高,增加了求解难度。为此,针对该模型给出了精确对偶映射下的序列二次近似解法。最后,以位移约束下结构重量最轻化问题为例,叙述了相应的算法。与以往采用幂函数做磨光函数时算例结果的比较表明,该模型的提法合理,算法更加有效。由于提高了对阶跃函数及其反函数的逼近程度,从而显著减少了优化迭代的次数。 |
| 英文摘要: |
| To increase efficiency of solving problems of structural topology optimization by using the ICM (Independent Continuous and Mapping) method, some functions are improved to approximate the step function and its inverse function in this paper. Firstly, the polish function and filter function in ICM method are classified by their properties of approximation, and the concepts of left polish function, upper polish function, fast filter function and slow filter function are presented respectively. Then two discriminant theorems, which distinguish two types of polish functions and two types of filter functions respectively, are derived. Two corresponding theorems, which represent the corresponding relationships between upper polish function and fast filter function, left polish function and slow filter function, are also proposed. Furthermore, a use criterion and construction method of the polish function and filter function are given in the paper. A new structural topology optimization model, which approximates the original model with higher precision, is formulated by using exponential type function as left polish function to approximate the step function. Above mentioned strategies bring the nonlinear degree of optimization model higher, so it can solve the optimization model with increased difficulties. In order to overcome the difficulties, a sequential quadratic approximate algorithm is proposed based on exact dual mapping. Finally, an algorithm is formulated by taking weight minimization with displacement constraints as an example. Compared with the past results when a power function is used as the polish function, it indicates that our optimization model is more rational and the corresponding algorithm is more efficient. Moreover, since the accuracy of approximating the step function is increased by taking a fast filter function as the filter function, number of iterations of optimization solution is greatly reduced. |
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