本文關鍵詞： 拓撲優(yōu)化 拓撲描述函數 NURBS插值 等幾何分析 自重載荷　出處：《力學學報》2016年06期 　論文類型：期刊論文

【摘要】：在許多如大壩、橋梁等大型土木工程結構中,結構的自重是初始設計階段必須考慮的重要載荷之一,因此研究自重載荷作用下的結構拓撲優(yōu)化設計問題具有十分重要的意義.針對考慮自重載荷作用的拓撲優(yōu)化問題所面臨的主要困難,總結了現有處理考慮自重載荷的拓撲優(yōu)化問題的三類主要方法;提出一種基于非均勻有理B樣條(non-uniform rational B-splines,NURBS)基函數插值的拓撲描述函數方法,基于此方法研究了考慮設計依賴自重載荷作用的2D/3D結構優(yōu)化設計問題.在列式下,高階NURBS基函數被同時用于三維NURBS實體片中的幾何場、位移場及設計變量場插值,實現了幾何模型、分析模型和優(yōu)化模型的有效統一,確保了位移場及設計變量場的高階連續(xù)性;詳細推導了基于NURBS基函數插值的考慮自重載荷作用的三維結構拓撲優(yōu)化模型及其靈敏度列式,并采用移動漸進線方法(method of moving asymptotes,MMA)進行了優(yōu)化求解;多個算例驗證了方法的有效性和穩(wěn)定性,結果表明,優(yōu)化迭代過程穩(wěn)健,收斂快,能夠有效地克服自重載荷作用下連續(xù)體結構拓撲優(yōu)化中經常遇到的低密度區(qū)域材料的寄生效應及目標函數的非單調性等問題.
[Abstract]:In many large civil engineering structures such as dams and bridges, the weight of the structure is one of the important loads that must be considered in the initial design stage. Therefore, it is of great significance to study the structural topology optimization problem under the action of deadweight load. Three main methods to deal with topology optimization problems considering deadweight load are summarized. A topological description function method based on non-uniform rational B-splines (NURBS) basis function interpolation for nonuniform rational B-spline is proposed. Based on this method, the optimal design problem of 2D / 3D structure with design dependent on deadweight load is studied. High order NURBS basis function is used to interpolate geometric field, displacement field and design variable field in 3D NURBS solid chip at the same time, realizing the effective unification of geometric model, analytical model and optimization model. The high order continuity of displacement field and design variable field is ensured. Based on NURBS basis function interpolation, the topological optimization model and sensitivity formula of 3D structure considering deadweight load are derived in detail. The method of moving progressive line is used to solve the problem. The effectiveness and stability of the method are verified by several numerical examples. The results show that the iterative optimization process is robust and convergent. It can effectively overcome the parasitic effect of low density regional materials and the non-monotonicity of objective function in topology optimization of continuum structure under self-weight load.
【作者單位】： 大連理工大學汽車工程學院;大連理工大學工業(yè)裝備結構分析國家重點實驗室;
【基金】：國家自然科學基金(11272075,11302041) 中央高�；究蒲袠I(yè)務費專項(DUT15RC(4)36)資助項目
【分類號】：O302
【正文快照】： 引言 e3二目速的i 酬 h material—penalization,SIMP)?和漸進結構優(yōu)化方化結果和迭代過程的影響,而且對“沒有材料就沒有慣性”的理論最優(yōu)解問題進行了闡述和研究.張陣胃[19]針對自重載荷作用下連續(xù)體結構拓撲優(yōu)化+遇到的常見問題,提出了一種將_p插值模型與平均敏度過濾，

本文編號：1477406