结构拓扑优化变密度法的灰度单元等效转换方法
发布时间：2019-04-24 04:40
【摘要】：在连续体结构优化的经典变密度法中,随着优化模型的复杂化,优化结果中容易出现灰度单元过多的问题.为了在优化后得到一个不存在灰度单元、可直接提取的清晰优化构型,提出了一种基于变密度法的灰度单元等效转换方法.该方法通过2个核心算法步骤来彻底消除灰度单元.首先通过转换规则控制算法将拓扑优化计算结果中的单元密度(密度),将单元密度变量从连续的[0,1]分布转换为{0,1}离散分布,得到全局"满状态"单元构型,彻底消除原优化构型中的灰度单元;其次通过转换等效性评估算法,确保在使用该转换方法前后结构的力学性能具有高度的等效性.将等效转换方法与标准SIMP优化算法相结合,便能在结构优化计算结果中得到可直接提取的清晰优化构型.通过二维与三维优化数值算例,将等效转换方法结合到SIMP优化算法中,并与标准的SIMP优化算法对比.结果表明,结合等效转换方法的SIMP优化算法能彻底消除灰度单元,并且不影响标准SIMP优化算法提升结构力学性能,具有降低体积与重量的作用.
[Abstract]:In the classical variable density method of continuum structure optimization, with the complexity of the optimization model, the problem of too many gray-scale units is easy to appear in the optimization results. In order to obtain a clear optimization configuration which can be extracted directly after optimization, an equivalent transformation method based on variable density method is proposed. In this method, two core algorithm steps are used to completely eliminate the gray-scale units. Firstly, the element density (density) is transformed from the continuous [0,1] distribution to the {0,1} discrete distribution by the transformation rule control algorithm, and the global "full state" element configuration is obtained. The gray-scale units in the original optimized configuration are completely eliminated; Secondly, the equivalence evaluation algorithm is used to ensure that the mechanical properties of the structure are highly equivalent before and after the use of the transformation method. By combining the equivalent transformation method with the standard SIMP optimization algorithm, a clear optimal configuration which can be extracted directly can be obtained from the results of the structural optimization calculation. Through two-dimensional and three-dimensional optimization numerical examples, the equivalent transformation method is combined into the SIMP optimization algorithm and compared with the standard SIMP optimization algorithm. The results show that the SIMP optimization algorithm combined with the equivalent transformation method can completely eliminate the gray-scale elements, and does not affect the standard SIMP optimization algorithm to improve the mechanical performance of the structure, and can reduce the volume and weight of the structure.
【作者单位】： 同济大学航空航天与力学学院;
【基金】：航空科学基金(2015ZA38001)
【分类号】：TP301.6
本文编号：2464111
[Abstract]:In the classical variable density method of continuum structure optimization, with the complexity of the optimization model, the problem of too many gray-scale units is easy to appear in the optimization results. In order to obtain a clear optimization configuration which can be extracted directly after optimization, an equivalent transformation method based on variable density method is proposed. In this method, two core algorithm steps are used to completely eliminate the gray-scale units. Firstly, the element density (density) is transformed from the continuous [0,1] distribution to the {0,1} discrete distribution by the transformation rule control algorithm, and the global "full state" element configuration is obtained. The gray-scale units in the original optimized configuration are completely eliminated; Secondly, the equivalence evaluation algorithm is used to ensure that the mechanical properties of the structure are highly equivalent before and after the use of the transformation method. By combining the equivalent transformation method with the standard SIMP optimization algorithm, a clear optimal configuration which can be extracted directly can be obtained from the results of the structural optimization calculation. Through two-dimensional and three-dimensional optimization numerical examples, the equivalent transformation method is combined into the SIMP optimization algorithm and compared with the standard SIMP optimization algorithm. The results show that the SIMP optimization algorithm combined with the equivalent transformation method can completely eliminate the gray-scale elements, and does not affect the standard SIMP optimization algorithm to improve the mechanical performance of the structure, and can reduce the volume and weight of the structure.
【作者单位】： 同济大学航空航天与力学学院;
【基金】：航空科学基金(2015ZA38001)
【分类号】：TP301.6
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1 周乐;约束阻尼板的结构减振动力学优化方法研究[D];南昌航空大学;2015年
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3 李翔;基于变密度法的结构动响应拓扑优化研究[D];复旦大学;2011年
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