本文關(guān)鍵詞： 拓?fù)鋬?yōu)化 拓?fù)涿枋龊瘮?shù) NURBS插值 等幾何分析 自重載荷　出處：《力學(xué)學(xué)報(bào)》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(jié)構(gòu)中,結(jié)構(gòu)的自重是初始設(shè)計(jì)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(jié)構(gòu)拓?fù)鋬?yōu)化設(shè)計(jì)問(wèn)題具有十分重要的意義.針對(duì)考慮自重載荷作用的拓?fù)鋬?yōu)化問(wèn)題所面臨的主要困難,總結(jié)了現(xiàn)有處理考慮自重載荷的拓?fù)鋬?yōu)化問(wèn)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(shù)插值的拓?fù)涿枋龊瘮?shù)方法,基于此方法研究了考慮設(shè)計(jì)依賴自重載荷作用的2D/3D結(jié)構(gòu)優(yōu)化設(shè)計(jì)問(wèn)題.在列式下,高階NURBS基函數(shù)被同時(shí)用于三維NURBS實(shí)體片中的幾何場(chǎng)、位移場(chǎng)及設(shè)計(jì)變量場(chǎng)插值,實(shí)現(xiàn)了幾何模型、分析模型和優(yōu)化模型的有效統(tǒng)一,確保了位移場(chǎng)及設(shè)計(jì)變量場(chǎng)的高階連續(xù)性;詳細(xì)推導(dǎo)了基于NURBS基函數(shù)插值的考慮自重載荷作用的三維結(jié)構(gòu)拓?fù)鋬?yōu)化模型及其靈敏度列式,并采用移動(dòng)漸進(jìn)線方法(method of moving asymptotes,MMA)進(jìn)行了優(yōu)化求解;多個(gè)算例驗(yàn)證了方法的有效性和穩(wěn)定性,結(jié)果表明,優(yōu)化迭代過(guò)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(jié)構(gòu)拓?fù)鋬?yōu)化中經(jīng)常遇到的低密度區(qū)域材料的寄生效應(yīng)及目標(biāo)函數(shù)的非單調(diào)性等問(wèn)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(xué)汽車工程學(xué)院;大連理工大學(xué)工業(yè)裝備結(jié)構(gòu)分析國(guó)家重點(diǎn)實(shí)驗(yàn)室;
【基金】：國(guó)家自然科學(xué)基金(11272075,11302041) 中央高校基本科研業(yè)務(wù)費(fèi)專項(xiàng)(DUT15RC(4)36)資助項(xiàng)目
【分類號(hào)】：O302
【正文快照】： 引言 e3二目速的i 酬 h material—penalization,SIMP)?和漸進(jìn)結(jié)構(gòu)優(yōu)化方化結(jié)果和迭代過(guò)程的影響,而且對(duì)“沒(méi)有材料就沒(méi)有慣性”的理論最優(yōu)解問(wèn)題進(jìn)行了闡述和研究.張陣胃[19]針對(duì)自重載荷作用下連續(xù)體結(jié)構(gòu)拓?fù)鋬?yōu)化+遇到的常見問(wèn)題,提出了一種將_p插值模型與平均敏度過(guò)濾，

本文編號(hào)：1477406