發(fā)布時間：2018-07-02 10:27

  本文選題：變密度法 + 灰度單元�。� 參考：《計算力學學報》2017年01期

【摘要】：在傳統變密度法SIMP(Solid Isotropic Microstructures with Penalization)中,Sigmund靈敏度過濾策略是解決拓撲優(yōu)化結果數值不穩(wěn)定問題的重要方法之一。但在SIMP方法中采用Sigmund靈敏度過濾策略時,有時優(yōu)化結果會有較多的灰度單元。為了減少拓撲優(yōu)化結果中灰度單元的數量,提出了一種基于改進靈敏度過濾策略的SIMP方法。在過濾后單元靈敏度的計算中,增加了一個與中心單元過濾前靈敏度有關的部分,該部分在過濾后靈敏度中所占的比重需要通過過濾權重來調節(jié)。通過對靈敏度過濾需要的分析,確定了過濾半徑和中心單元密度值是影響過濾權重的因素。根據拓撲優(yōu)化實例的優(yōu)化結果給出了過濾半徑影響過濾權重的情況,并基于過濾半徑對過濾權重的影響情況構建了過濾權重的函數。在改進靈敏度過濾策略的基礎上,結合雙重SIMP算法給出了本文SIMP方法的流程。最后,以懸臂梁結構和簡支梁結構為例,驗證了本文方法的有效性。與Sigmund靈敏度過濾策略相比,改進的靈敏度過濾策略能有效地減少灰度單元。與雙重SIMP方法相比,本文SIMP方法能有效地減少數值不穩(wěn)定現象。
[Abstract]:Sigmund sensitivity filtering strategy is one of the most important methods to solve the numerical instability problem of topological optimization results in traditional simp (solid Isotropic structures with Penalization). However, when Sigmund sensitivity filtering strategy is used in SIMP method, sometimes there are more gray units in the optimization results. In order to reduce the number of gray units in topology optimization, a SIMP method based on improved sensitivity filtering strategy is proposed. In the calculation of the sensitivity of the filtered unit, a part related to the sensitivity of the central unit before filtering is added. The proportion of this part in the sensitivity after filtering needs to be adjusted by the filter weight. By analyzing the need of sensitivity filtering, it is determined that the filter radius and the density of the central unit are the factors affecting the filter weight. The influence of filter radius on filter weight is given according to the optimization result of topology optimization example, and the function of filter weight is constructed based on the influence of filter radius on filter weight. Based on the improved sensitivity filtering strategy, the flow chart of the SIMP method is given by combining the dual SIMP algorithm. Finally, the effectiveness of this method is verified by taking cantilever beam structure and simply supported beam structure as examples. Compared with Sigmund's sensitivity filtering strategy, the improved sensitivity filtering strategy can effectively reduce gray level units. Compared with the double SIMP method, the SIMP method in this paper can effectively reduce the numerical instability.
【作者單位】： 桂林電子科技大學機電工程學院;
【基金】：國家自然科學基金(51265006)資助項目
【分類號】：O224
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本文編號：2089823