本文選題：拓?fù)鋬?yōu)化 + 鉸點(diǎn)布局優(yōu)化��； 參考：《大連理工大學(xué)》2012年碩士論文

【摘要】：桁架臂頂節(jié)局部結(jié)構(gòu)的拓?fù)鋬?yōu)化設(shè)計(jì)問題,是當(dāng)前桁架類吊臂設(shè)計(jì)中所面臨的一項(xiàng)關(guān)鍵性問題。合理的頂節(jié)局部結(jié)構(gòu)的材料布局形式,不僅能夠充分發(fā)揮材料的力學(xué)性能、減輕結(jié)構(gòu)重量,還能有效的傳遞載荷、提高桁架臂整體的抗屈曲能力,進(jìn)而提高桁架類起重機(jī)整機(jī)的起重性能。 桁架臂頂節(jié)結(jié)構(gòu)復(fù)雜,工況繁多,直接運(yùn)用常規(guī)的拓?fù)鋬?yōu)化思想很難獲得最佳的結(jié)構(gòu)布局。針對(duì)這一問題文中提出了一種新的優(yōu)化設(shè)計(jì)方法,其總體思路是：首先,基于彈性穩(wěn)定性思想確定滿足臂架最小屈曲儲(chǔ)存應(yīng)變能下合理的受力鉸點(diǎn)位置。其次,運(yùn)用基于灰色理論的改進(jìn)的折中規(guī)劃思想完成多工況下頂節(jié)局部拓?fù)鋬?yōu)化設(shè)計(jì)。最后,針對(duì)拓?fù)鋬?yōu)化中數(shù)值不穩(wěn)定性現(xiàn)象,引入避免灰色材料邊界的非線性密度過濾技術(shù)予以消除。論文的主要研究工作和成果如下： (1)基于彈性穩(wěn)定約束的桁架臂頂節(jié)鉸點(diǎn)布局優(yōu)化。運(yùn)用鐵摩辛柯彈性穩(wěn)定性理論,將桁架臂結(jié)構(gòu)簡化成鐵摩辛柯梁形式；在此基礎(chǔ)上,以最小屈曲儲(chǔ)存應(yīng)變能為目標(biāo)函數(shù)建立數(shù)學(xué)模型,運(yùn)用遺傳算法對(duì)桁架臂頂節(jié)鉸點(diǎn)布局優(yōu)化問題進(jìn)行求解。 (2)基于SIMP法的連續(xù)體結(jié)構(gòu)單工況拓?fù)鋬?yōu)化。在材料密度插值理論的基礎(chǔ)上,建立單工況下變密度插值法最小柔度問題的拓?fù)鋬?yōu)化數(shù)學(xué)模型并推導(dǎo)出優(yōu)化準(zhǔn)則算法。 (3)基于SIMP法的桁架臂頂節(jié)多工況拓?fù)鋬?yōu)化。基于SIMP變密度的拓?fù)鋬?yōu)化思想,運(yùn)用折中規(guī)劃法建立桁架臂頂節(jié)結(jié)構(gòu)靜態(tài)多工況下多剛度拓?fù)鋬?yōu)化數(shù)學(xué)模型。基于灰色理論的專家評(píng)價(jià)思想對(duì)上述算法進(jìn)行改進(jìn),以獲得合理的目標(biāo)函數(shù)權(quán)重消除主觀因素的影響。利用OptiStruct軟件對(duì)優(yōu)化模型進(jìn)行求解,以獲得靜態(tài)多工況下最優(yōu)拓?fù)洹?(4)避免灰色材料邊界的非線性網(wǎng)格過濾技術(shù)。為避免諸如棋盤格式和網(wǎng)格依賴性等數(shù)值不穩(wěn)定現(xiàn)象、確保優(yōu)化結(jié)果的可制造性,常需要在拓?fù)鋬?yōu)化中引入過濾技術(shù)。然而,運(yùn)用常規(guī)的過濾技術(shù)時(shí),拓?fù)浣Y(jié)果中會(huì)出現(xiàn)灰色材料邊界現(xiàn)象以致難以用于加工制造。非線性密度過濾技術(shù)(如基于Heaviside函數(shù)過濾技術(shù)),能有效避免這一現(xiàn)象,但不能保證迭代過程材料體積的守恒性導(dǎo)致震蕩現(xiàn)象。基于Heaviside函數(shù)的體積守恒過濾技術(shù)能夠保證迭代體積守恒性,確保了優(yōu)化的高效性和迭代的穩(wěn)定性。提出了一種體積守恒非線性密度過濾函數(shù),通過工程實(shí)例驗(yàn)證其算法是合理、有效的,較上述體積守恒非線性過濾函數(shù)表達(dá)式更為簡潔、收斂性更好,并可獲得材料邊界清晰的拓?fù)浣Y(jié)果。
[Abstract]:The topology optimization of the local structure of the truss arm top joint is a key problem in the design of the truss boom. The reasonable material layout of the local structure can not only give full play to the mechanical properties of the material, reduce the weight of the structure, but also effectively transfer the load and improve the overall buckling resistance of the truss arm. Thus, the lifting performance of the truss crane is improved. The structure of the top joint of the truss arm is complex and the working conditions are various. It is difficult to obtain the optimal structure layout by using the conventional topology optimization idea directly. A new optimal design method is proposed in this paper. The main ideas are as follows: firstly, based on the elastic stability theory, a reasonable position of the pivot point satisfying the minimum buckling storage strain energy of the boom is determined. Secondly, the local topology optimization design of the top node under multiple working conditions is completed by using the improved compromise planning idea based on the grey theory. Finally, the nonlinear density filtering technique is introduced to eliminate the numerical instability in topology optimization. The main research work and results are as follows: 1) the optimization of the hinge point layout at the top of the truss arm based on elastic stability constraints. In this paper, the truss arm structure is simplified into the form of iron friction beam by using Temocco elastic stability theory, and the mathematical model is established based on the minimum buckling stored strain energy as the objective function. Genetic algorithm (GA) is used to solve the optimization problem of the hinge point layout at the top of the truss arm. 2) Topology optimization of continuum structure under single working condition based on SIMP method. Based on the theory of material density interpolation, the topological optimization mathematical model of minimum flexibility problem of variable density interpolation method under single working condition is established and the optimization criterion algorithm is derived. 3) Topology optimization of truss arm top joint based on SIMP method. Based on the idea of topological optimization of SIMP variable density, a mathematical model of topology optimization of truss arm joints under static condition and multiple working conditions is established by means of compromise programming method. The expert evaluation idea based on grey theory is used to improve the above algorithm in order to get a reasonable weight of objective function to eliminate the influence of subjective factors. The optimization model is solved by OptiStruct software in order to obtain the optimal topology under static and multi-working conditions. (4) Non-linear mesh filtering technique to avoid gray material boundary. In order to avoid numerical instability such as chessboard format and grid dependency and ensure the manufacturability of optimization results filtering techniques are often introduced into topology optimization. However, using conventional filtering techniques, grey material boundary phenomena will occur in topological results, which makes it difficult to be used in processing and manufacturing. The nonlinear density filtering technique, such as filter based on Heaviside function, can effectively avoid this phenomenon, but it can not guarantee the conservation of material volume in the iterative process. The volume conservation filtering technique based on Heaviside function can guarantee the iterative volume conservation and ensure the efficiency of optimization and the stability of iteration. A novel nonlinear density filtering function for volume conservation is proposed. The algorithm is proved to be reasonable and effective by an engineering example, and it is more concise and convergent than the expression of the volume conservation nonlinear filter function mentioned above. The topological results with clear material boundary can be obtained.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：TH21

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