【摘要】：在連續(xù)體結(jié)構(gòu)優(yōu)化的經(jīng)典變密度法中,隨著優(yōu)化模型的復(fù)雜化,優(yōu)化結(jié)果中容易出現(xiàn)灰度單元過(guò)多的問(wèn)題.為了在優(yōu)化后得到一個(gè)不存在灰度單元、可直接提取的清晰優(yōu)化構(gòu)型,提出了一種基于變密度法的灰度單元等效轉(zhuǎn)換方法.該方法通過(guò)2個(gè)核心算法步驟來(lái)徹底消除灰度單元.首先通過(guò)轉(zhuǎn)換規(guī)則控制算法將拓?fù)鋬?yōu)化計(jì)算結(jié)果中的單元密度(密度),將單元密度變量從連續(xù)的[0,1]分布轉(zhuǎn)換為{0,1}離散分布,得到全局"滿狀態(tài)"單元構(gòu)型,徹底消除原優(yōu)化構(gòu)型中的灰度單元;其次通過(guò)轉(zhuǎn)換等效性評(píng)估算法,確保在使用該轉(zhuǎn)換方法前后結(jié)構(gòu)的力學(xué)性能具有高度的等效性.將等效轉(zhuǎn)換方法與標(biāo)準(zhǔn)SIMP優(yōu)化算法相結(jié)合,便能在結(jié)構(gòu)優(yōu)化計(jì)算結(jié)果中得到可直接提取的清晰優(yōu)化構(gòu)型.通過(guò)二維與三維優(yōu)化數(shù)值算例,將等效轉(zhuǎn)換方法結(jié)合到SIMP優(yōu)化算法中,并與標(biāo)準(zhǔn)的SIMP優(yōu)化算法對(duì)比.結(jié)果表明,結(jié)合等效轉(zhuǎn)換方法的SIMP優(yōu)化算法能徹底消除灰度單元,并且不影響標(biāo)準(zhǔn)SIMP優(yōu)化算法提升結(jié)構(gòu)力學(xué)性能,具有降低體積與重量的作用.
[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.
【作者單位】： 同濟(jì)大學(xué)航空航天與力學(xué)學(xué)院;
【基金】：航空科學(xué)基金(2015ZA38001)
【分類號(hào)】：TP301.6

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