采用指数类函数为快滤函数的高精度逼近ICM(independent continuous and mapping)方法,建立了以结构重量为目标,应力和位移共同约束下的连续体结构拓扑优化模型.利用结构畸变比能的方法全局化应力约束,单位虚载荷法显式化位移约束,归一...采用指数类函数为快滤函数的高精度逼近ICM(independent continuous and mapping)方法,建立了以结构重量为目标,应力和位移共同约束下的连续体结构拓扑优化模型.利用结构畸变比能的方法全局化应力约束,单位虚载荷法显式化位移约束,归一化约束以解决约束限数量级不一致的问题.针对不同性态的过滤函数,给出了指数类快滤函数参数的取值方法.单工况和多工况的算例表明了高精度逼近的ICM方法处理多种约束下连续体结构拓扑优化的可行性与有效性.展开更多
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...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。展开更多
Based on the Independent Continuous Mapping method （ICM）, a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable s...Based on the Independent Continuous Mapping method （ICM）, a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable stress and element stiffness, which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1. Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements： the weak material element method and the tiny section element method. Three criteria （no structural singularity, no violated constraints and no change of structural weight） are introduced to judge iteration convergence. These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure. To improve the efficiency, the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space. By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform, a topological optimization software of frame structures is accomplished. Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.展开更多
在传统拓扑优化设计中,随着结构单元增加,迭代计算过程消耗了大量的时间。本文提出了一种基于深度学习的方法来加速拓扑优化设计过程,缩短了结构拓扑优化设计的迭代过程,并生成了高分辨率拓扑优化结构。利用深度学习方法,在低分辨率中...在传统拓扑优化设计中,随着结构单元增加,迭代计算过程消耗了大量的时间。本文提出了一种基于深度学习的方法来加速拓扑优化设计过程,缩短了结构拓扑优化设计的迭代过程,并生成了高分辨率拓扑优化结构。利用深度学习方法,在低分辨率中间构型与高分辨率拓扑构型之间创建高维映射关系,利用独立、连续和映射(ICM)方法建立深度学习网络所需要的数据集,训练神经网络以实现加速过程,将结构拓扑优化设计问题转化为图像处理中的风格迁移问题。通过引入条件生成对抗式神经网络CGAN(Conditional Generative and Adversarial Network)解决了跨分辨率拓扑优化问题,实验验证了优化过程效率的提高,该方法具有良好的泛化性能,研究模型在其他结构优化设计中具有可推广性。展开更多
文摘采用指数类函数为快滤函数的高精度逼近ICM(independent continuous and mapping)方法,建立了以结构重量为目标,应力和位移共同约束下的连续体结构拓扑优化模型.利用结构畸变比能的方法全局化应力约束,单位虚载荷法显式化位移约束,归一化约束以解决约束限数量级不一致的问题.针对不同性态的过滤函数,给出了指数类快滤函数参数的取值方法.单工况和多工况的算例表明了高精度逼近的ICM方法处理多种约束下连续体结构拓扑优化的可行性与有效性.
文摘为了提高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。
基金The project supported by the National Natural Science Foundation of China (10472003)Beijing Natural Science Foundation (3042002)
文摘Based on the Independent Continuous Mapping method （ICM）, a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable stress and element stiffness, which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1. Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements： the weak material element method and the tiny section element method. Three criteria （no structural singularity, no violated constraints and no change of structural weight） are introduced to judge iteration convergence. These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure. To improve the efficiency, the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space. By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform, a topological optimization software of frame structures is accomplished. Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.
文摘在传统拓扑优化设计中,随着结构单元增加,迭代计算过程消耗了大量的时间。本文提出了一种基于深度学习的方法来加速拓扑优化设计过程,缩短了结构拓扑优化设计的迭代过程,并生成了高分辨率拓扑优化结构。利用深度学习方法,在低分辨率中间构型与高分辨率拓扑构型之间创建高维映射关系,利用独立、连续和映射(ICM)方法建立深度学习网络所需要的数据集,训练神经网络以实现加速过程,将结构拓扑优化设计问题转化为图像处理中的风格迁移问题。通过引入条件生成对抗式神经网络CGAN(Conditional Generative and Adversarial Network)解决了跨分辨率拓扑优化问题,实验验证了优化过程效率的提高,该方法具有良好的泛化性能,研究模型在其他结构优化设计中具有可推广性。
