發(fā)布時(shí)間：2018-06-30 16:47

  本文選題：沖擊荷載 + 結(jié)構(gòu)優(yōu)化設(shè)計(jì)　； 參考：《大連理工大學(xué)》2016年博士論文

【摘要】：沖擊荷載下結(jié)構(gòu)優(yōu)化設(shè)計(jì)受到學(xué)者與工程師的廣泛關(guān)注。這是因?yàn)?對于許多結(jié)構(gòu),沖擊荷載下的結(jié)構(gòu)響應(yīng)將直接影響其性能,而結(jié)構(gòu)優(yōu)化設(shè)計(jì)可以有效的改善沖擊荷載下的結(jié)構(gòu)性能。然而,相較于其他類型的結(jié)構(gòu)優(yōu)化設(shè)計(jì)問題,沖擊荷載下的結(jié)構(gòu)優(yōu)化設(shè)計(jì)的研究較少。這是因?yàn)?沖擊荷載下的結(jié)構(gòu)優(yōu)化設(shè)計(jì)問題需考慮時(shí)間因素,有時(shí)還需考慮材料非線性與幾何非線性等非線性效應(yīng)。這一方面增加了結(jié)構(gòu)分析的困難,使得結(jié)構(gòu)分析耗時(shí)增加,另一方面也使得計(jì)算結(jié)構(gòu)響應(yīng)關(guān)于設(shè)計(jì)變量的靈敏度難以解析的實(shí)現(xiàn)。這些困難促使沖擊荷載下的結(jié)構(gòu)優(yōu)化設(shè)計(jì)成為最具挑戰(zhàn)的結(jié)構(gòu)優(yōu)化設(shè)計(jì)問題之一。本文致力于研究沖擊荷載下的結(jié)構(gòu)優(yōu)化設(shè)計(jì)問題,提出了一系列的方法用于克服前文中提到的沖擊荷載下結(jié)構(gòu)優(yōu)化設(shè)計(jì)問題面臨的困難。本文重點(diǎn)關(guān)注了兩類有代表性的沖擊荷載下的結(jié)構(gòu)優(yōu)化設(shè)計(jì)問題,分別為殘余振動(dòng)最小化結(jié)構(gòu)優(yōu)化設(shè)計(jì)問題和結(jié)構(gòu)耐撞性拓?fù)鋬?yōu)化設(shè)計(jì)問題。殘余振動(dòng)最小化結(jié)構(gòu)優(yōu)化設(shè)計(jì)問題中,本研究采用二次型積分形式的性能指標(biāo)衡量結(jié)構(gòu)的殘余振動(dòng)大小。該結(jié)構(gòu)性能指標(biāo)可以總體的衡量結(jié)構(gòu)的殘余振動(dòng),但需要通過耗時(shí)的時(shí)程響應(yīng)分析計(jì)算。基于李雅普諾夫方法,研究中首先將上述性能指標(biāo)的表達(dá)式大幅簡化,從而避免了時(shí)程響應(yīng)分析。對于上述的性能指標(biāo),若殘余振動(dòng)階段的初始激勵(lì)與設(shè)計(jì)變量無關(guān),計(jì)算其關(guān)于設(shè)計(jì)變量的靈敏度將更為方便。因此,本文在研究中把殘余振動(dòng)響應(yīng)最小化結(jié)構(gòu)優(yōu)化設(shè)計(jì)問題分為：初始激勵(lì)作用結(jié)構(gòu)的殘余振動(dòng)最小化結(jié)構(gòu)優(yōu)化設(shè)計(jì)問題；沖擊荷載作用結(jié)構(gòu)的殘余振動(dòng)最小化結(jié)構(gòu)優(yōu)化設(shè)計(jì)問題。對于初始激勵(lì)作用結(jié)構(gòu)的殘余振動(dòng)最小化結(jié)構(gòu)優(yōu)化設(shè)計(jì)問題,本研究提出了殘余振動(dòng)響應(yīng)的二次型積分形式性能指標(biāo)關(guān)于設(shè)計(jì)變量的靈敏度分析的伴隨法。無論優(yōu)化問題中包含多少個(gè)設(shè)計(jì)變量,提出的伴隨法均僅需求解兩個(gè)李雅普諾夫方程便可以獲得全部的靈敏度結(jié)果。這不僅實(shí)現(xiàn)了解析的計(jì)算靈敏度還大幅的減少了靈敏度分析過程的計(jì)算耗時(shí)�；谔岢龅陌殡S法,研究中采用拓?fù)鋬?yōu)化方法,分別研究了以殘余振動(dòng)最小化為目標(biāo)的阻尼器／阻尼彈簧和有阻尼材料的最優(yōu)分布問題。數(shù)值算例顯示,基于提出的方法獲得的優(yōu)化設(shè)計(jì)有效的改善了結(jié)構(gòu)性能。對于沖擊荷載作用結(jié)構(gòu)的殘余振動(dòng)最小化結(jié)構(gòu)優(yōu)化設(shè)計(jì)問題,殘余振動(dòng)階段的初始激勵(lì)是與設(shè)計(jì)變量相關(guān)的。為了在靈敏度計(jì)算中考慮初始激勵(lì)與設(shè)計(jì)變量的相關(guān)性,本文提出了第二種計(jì)算衡量殘余振動(dòng)的二次型積分形式的性能指標(biāo)關(guān)于設(shè)計(jì)變量的靈敏度的伴隨法,從而極大的拓寬了本文工作的適用范圍。本文中基于提出的第二種靈敏度計(jì)算方法,研究了以殘余振動(dòng)最小化為目標(biāo)受沖擊荷載作用板結(jié)構(gòu)中的阻尼材料最優(yōu)分布問題。數(shù)值算例結(jié)果顯示,本節(jié)提出的方法是高效且可靠的。之后,本文考慮了約束不完全結(jié)構(gòu)中的殘余彈性振動(dòng)最小化結(jié)構(gòu)優(yōu)化設(shè)計(jì)問題。李雅普諾夫方法無法直接應(yīng)用于約束不完全結(jié)構(gòu)的殘余振動(dòng)優(yōu)化設(shè)計(jì)問題。這是因?yàn)?約束不完全結(jié)構(gòu)的總體剛度陣奇異,導(dǎo)致李雅普諾夫方程無法求得唯一解。研究中提出了兩種分別基于剛體運(yùn)動(dòng)模態(tài)與彈性變形模態(tài)的模型降階法,提出的方法即實(shí)現(xiàn)了消除結(jié)構(gòu)剛體位移而又不影響結(jié)構(gòu)彈性變形。基于上述方法,研究中考慮了將單諧振器微結(jié)構(gòu)系統(tǒng)用于減小結(jié)構(gòu)的殘余振動(dòng)的最優(yōu)參數(shù)與最優(yōu)分布問題。所關(guān)注的單諧振器微結(jié)構(gòu)系統(tǒng),在特定的參數(shù)取值下可以等效為一個(gè)具有負(fù)的質(zhì)量系數(shù)的質(zhì)量塊。最后,本文研究了較高沖擊荷載下結(jié)構(gòu)耐撞性拓?fù)鋬?yōu)化設(shè)計(jì)問題。耐撞性問題需要考慮多種非線性效應(yīng),這使得考慮耐撞性的結(jié)構(gòu)優(yōu)化設(shè)計(jì)變得十分困難,而采用拓?fù)鋬?yōu)化方法獲得耐撞性概念設(shè)計(jì)則更困難。針對耐撞性拓?fù)鋬?yōu)化設(shè)計(jì),本文提出了一種新的混合優(yōu)化法。新的混合法基于修改的慣性釋放法構(gòu)造的等效靜力荷載,并基于該等效荷載可以構(gòu)造等效靜力分析,從而將非線性瞬態(tài)動(dòng)力分析和優(yōu)化問題轉(zhuǎn)化為非線性靜力優(yōu)化問題。對于該非線性靜力優(yōu)化問題,研究中采用混合元胞自動(dòng)機(jī)法求解。新的混合法采用雙層迭代的優(yōu)化流程,其中,內(nèi)層迭代采用混合元胞自動(dòng)機(jī)法求解構(gòu)造的非線性靜力優(yōu)化問題,而外層迭代則基于非線性動(dòng)力分析校核優(yōu)化設(shè)計(jì)的結(jié)構(gòu)響應(yīng)并構(gòu)造基于改進(jìn)的慣性釋放法的等效靜力荷載。研究中,通過數(shù)值算例比較了混合法與混合元胞自動(dòng)機(jī)的優(yōu)化結(jié)果與計(jì)算效率。結(jié)果顯示,混合法與混合元胞自動(dòng)機(jī)法得到了相似的優(yōu)化設(shè)計(jì),但前者的計(jì)算效率遠(yuǎn)高于后者。最后,研究中考慮了一個(gè)簡化的整車模型的耐撞性拓?fù)鋬?yōu)化設(shè)計(jì)問題,其優(yōu)化結(jié)果說明了提出的混合法的有效性。
[Abstract]:Structural optimization design under impact loads is widely concerned by scholars and engineers. This is because, for many structures, structural responses under impact loads will directly affect their performance, and structural optimization design can effectively improve the structural performance under impact loads. However, the impact load is compared to other types of structural optimization problems. There are few studies on the structural optimization design under the load. This is because the time factors should be taken into consideration in the structural optimization design under the impact load, and the nonlinear effects of material nonlinearity and geometric nonlinearity should be considered. This increases the difficulty of structural analysis, increases the time-consuming of structural analysis, and also makes the calculation structure on the other. The sensitivity of the response to the design variables is difficult to be resolved. These difficulties have prompted the structural optimization design under the impact load to become one of the most challenging structural optimization problems. This paper is devoted to the study of structural optimization design under impact loads, and a series of square methods are proposed to overcome the impact load mentioned in the previous article. This paper focuses on two types of representative structural optimization problems under impact loads, which are the optimization design problem of residual vibration minimization and structural optimization design of structural crashworthiness. In the optimization design of residual vibration minimization, this study adopts two times. The performance index of the integral form measures the residual vibration size of the structure. The structural performance index can generally measure the residual vibration of the structure, but it needs to be calculated by time-consuming response analysis. Based on Lyapunov method, the expression of the above performance index is greatly simplified in the study, thus avoiding the time history response analysis. For the above performance indicators, if the initial excitation of the residual vibration stage is independent of the design variables, it is more convenient to calculate the sensitivity of the design variables. Therefore, in this paper, the optimal design problem of the minimization of the residual vibration response is divided into the optimization design of the residual vibration minimization of the initial excitation structure. The problem of structural optimization design for the minimization of residual vibration of the impact loading structure. For the optimization design problem of the residual vibration minimization of the initial excitation structure, this study puts forward the adjoint method of the sensitivity analysis of the two type integral form of the residual vibration response on the design variables. Many design variables are included, and the proposed adjoint method only needs two Lyapunov equations to obtain all the sensitivity results. This not only realizes the analytical calculation sensitivity but also greatly reduces the time-consuming of the sensitivity analysis process. Based on the proposed adjoint method, the topology optimization method is used in the study, respectively. The optimal distribution problem of dampers, damped springs and damping materials with the objective of minimizing the residual vibration is investigated. Numerical examples show that the optimized design based on the proposed method improves the structural performance effectively. The residual vibration phase of the residual vibration is the optimal design for the minimization of the residual vibration of the impact load structure. The initial excitation is related to the design variables. In order to consider the correlation between the initial excitation and the design variables in the sensitivity calculation, this paper presents second methods to calculate the performance index of the two type integral form of the residual vibration on the sensitivity of the design variables, which greatly widens the scope of application of this work. Based on the second sensitivity methods proposed in this paper, the optimal distribution of damping materials in the impacted loading plate structure with the objective of minimizing the residual vibration is studied. The numerical example shows that the method proposed in this section is efficient and reliable. After that, the maximum residual elastic vibration in the constrained structure is considered. The Lyapunov method can not be applied directly to the problem of optimal design for residual vibration of incomplete structures. This is because two kinds of rigid body motion modes and elasticity are proposed in this paper, which can not obtain the unique solution of the Lyapunov equation. Based on the above method, the single resonator microstructural system is used to reduce the optimal parameters and optimal distribution of the residual vibration of the structure. The fixed parameters can be equivalent to a mass block with negative mass coefficient. Finally, this paper studies the problem of topological optimization design for structural crashworthiness under high impact load. The problem of Crashworthiness needs to consider a variety of nonlinear effects, which makes it very difficult to consider the structural optimization design with the consideration of crashworthiness, and the topology optimization side is adopted. It is more difficult to obtain the conceptual design of crashworthiness. For the design of Crashworthiness topology optimization, a new mixed optimization method is proposed in this paper. The new hybrid method is based on the modified inertial release method to construct the equivalent static load, and based on the equivalent load, the equivalent static analysis can be constructed, and the nonlinear transient dynamic analysis and optimization problem are made. The hybrid cellular automaton method is used to solve the nonlinear static optimization problem. The new hybrid method uses the two-layer iterative optimization process, in which the inner iteration adopts the hybrid cellular automaton to solve the nonlinear static optimization problem, while the outer iteration is based on the nonlinear dynamic. The structural response of the optimized design is checked and the equivalent static load based on the improved inertial release method is constructed. In the study, the optimization results and calculation efficiency of the hybrid method and the hybrid cellular automata are compared by numerical examples. The results show that the hybrid method and the hybrid cellular automaton method are similar to the optimal design, but the former is calculated. The calculation efficiency is much higher than that of the latter. Finally, the problem of a simplified vehicle model's crashworthiness topology optimization design is considered. The optimization results show the effectiveness of the proposed hybrid method.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：TB12

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