發(fā)布時(shí)間：2018-03-22 13:17

  本文選題：周期性梁板　切入點(diǎn)：漸近均勻化　出處：《大連理工大學(xué)》2015年博士論文　論文類型：學(xué)位論文

【摘要】：梁板結(jié)構(gòu)是工程中廣泛應(yīng)用的兩大類結(jié)構(gòu),在近代商用飛機(jī)、衛(wèi)星、運(yùn)載火箭、高速列車結(jié)構(gòu)中具有廣闊的應(yīng)用前景。隨著工程技術(shù)的高速發(fā)展,人們對(duì)工程結(jié)構(gòu)的高比剛／強(qiáng)度,輕質(zhì)及多功能等性能提出了更高的要求,出現(xiàn)了越來越多的新型復(fù)合梁板結(jié)構(gòu),對(duì)于先進(jìn)復(fù)合梁板結(jié)構(gòu)的優(yōu)化設(shè)計(jì)需求也越來越強(qiáng)烈。本論文針對(duì)周期性復(fù)合板結(jié)構(gòu)和梁結(jié)構(gòu),利用漸近均勻化方法,拓?fù)鋬?yōu)化技術(shù)以及多尺度分析技術(shù)等多種方法,對(duì)周期性梁結(jié)構(gòu)的等效性能預(yù)測(cè),指定或極值剛度的微結(jié)構(gòu)優(yōu)化設(shè)計(jì)以及周期性板的宏微觀一體化優(yōu)化設(shè)計(jì)等進(jìn)行了深入的研究,并將商用有限元軟件作為黑箱,實(shí)現(xiàn)基于商用軟件高性能計(jì)算的復(fù)合梁板結(jié)構(gòu)均勻化降階及優(yōu)化設(shè)計(jì)。本文研究的主要內(nèi)容包括：(1)基于一維周期性漸近均勻化理論,發(fā)展了一維周期性梁結(jié)構(gòu)漸近均勻化方法的有限元列式,并將基于商業(yè)軟件的均勻化理論求解新方法擴(kuò)展到一維周期性梁結(jié)構(gòu)中,將具有復(fù)雜微結(jié)構(gòu)單胞的一維周期性梁結(jié)構(gòu)等效為宏觀歐拉伯努利梁,實(shí)現(xiàn)了對(duì)其等效剛度的快速預(yù)測(cè)。新方法將商業(yè)軟件作為一個(gè)黑箱,從而充分利用軟件中的各種單元類型和建模技術(shù),減小編程工作量及單胞模型規(guī)模,提高求解效率。上述方法的建立,使得對(duì)三維(二維)周期性材料,二維周期性板殼結(jié)構(gòu)和一維周期性梁結(jié)構(gòu)的均勻化求解都可以統(tǒng)一在相同數(shù)值求解和軟件實(shí)現(xiàn)的框架內(nèi)完成。將一維周期性梁的求解新方法與彎曲能量近似方法和基于三維周期性均勻化的近似方法進(jìn)行了比較,并討論了沿厚度方向的尺度效應(yīng)。結(jié)果表明,基于直法線假定的彎曲能量法忽視了復(fù)合梁結(jié)構(gòu)內(nèi)的三維應(yīng)力狀態(tài),過高地估計(jì)了梁的等效性質(zhì)。而基于三維周期性均勻化的方法引入了截面內(nèi)的周期性假設(shè),在梁截面內(nèi)單胞數(shù)量較少時(shí),與一維均勻化新方法的結(jié)果差別較大,當(dāng)截面內(nèi)單胞數(shù)量足夠多時(shí),二者的結(jié)果趨于一致。(2)作為微結(jié)構(gòu)優(yōu)化設(shè)計(jì)的基礎(chǔ)性研究,對(duì)使用體積守恒的Heaviside函數(shù)密度過濾進(jìn)行優(yōu)化過程中,迭代后期目標(biāo)函數(shù)發(fā)生嚴(yán)重振蕩的原因進(jìn)行了研究。推導(dǎo)了體積守恒的非線性密度過濾的精確靈敏度表達(dá)式,通過有限差分法驗(yàn)證了新公式的正確性,并通過算例比較了采用不同靈敏度求解公式的結(jié)果差別。結(jié)果發(fā)現(xiàn),當(dāng)非線性參數(shù)增大時(shí),原靈敏度公式的結(jié)果與差分結(jié)果嚴(yán)重背離,而精確靈敏度公式的結(jié)果與差分結(jié)果保持一致,進(jìn)而驗(yàn)證了精確靈敏度公式的正確性。此外,當(dāng)固化可調(diào)參數(shù)時(shí),原靈敏度公式仍然是正確的靈敏度公式。這項(xiàng)工作為后期優(yōu)化中得到清晰的微結(jié)構(gòu)拓?fù)涮峁┝擞辛Φ闹С帧?3)在一維周期性梁均勻化新方法的基礎(chǔ)上,研究了在一定材料體積約束下的一維周期性梁結(jié)構(gòu)指定剛度或極值剛度優(yōu)化問題。提出了基于均勻化新方法的解析靈敏度求解方法,通過構(gòu)造復(fù)合位移場(chǎng)并提取相應(yīng)的應(yīng)變能項(xiàng),實(shí)現(xiàn)了基于商業(yè)軟件對(duì)等效剛度及其靈敏度的求解,從而降低了優(yōu)化的門檻,提高了優(yōu)化的效率。將該優(yōu)化方法推廣到了一維周期性桁架梁結(jié)構(gòu),并實(shí)現(xiàn)了對(duì)拉扭耦合剛度的優(yōu)化。討論了單胞數(shù)量較少的短梁的優(yōu)化方法,說明基于變量連接的短梁優(yōu)化可以考慮到橫向剪切的影響。(4)研究了蜂窩板結(jié)構(gòu)的剛度設(shè)計(jì)問題,通過沿法線方向單元的變量連接來模擬蜂窩單胞,并將基于均勻化新方法的解析靈敏度求解方法推廣到了周期性板殼結(jié)構(gòu)。將此方法與基于直法線假設(shè)的二維均勻化和沿法線方向積分的求解方法進(jìn)行比較,發(fā)現(xiàn)蜂窩單胞的長(zhǎng)高比對(duì)于優(yōu)化的最終結(jié)果是有影響的,而基于直法線假設(shè)的求解方法不能區(qū)分這一影響。在此基礎(chǔ)上,研究了以宏觀結(jié)構(gòu)的最小柔順性為目標(biāo)、同時(shí)考慮宏觀板結(jié)構(gòu)與微觀單胞構(gòu)型的雙尺度優(yōu)化方法,給出了基于商業(yè)軟件計(jì)算的目標(biāo)函數(shù)及宏微觀設(shè)計(jì)變量的靈敏度求解方法,從而實(shí)現(xiàn)了對(duì)雙尺度拓?fù)鋬?yōu)化問題的高效求解。(5)作為梁板模型降階方法在工程中的實(shí)際應(yīng)用,研究了MSC.SimXpert軟件平臺(tái)面向ProE的多層次多精度彈體結(jié)構(gòu)分析模板的開發(fā)方法。提出了基于特征命名的CAD與CAE之間的信息傳遞方式,并通過外部XML文件數(shù)據(jù)庫對(duì)屬性自動(dòng)識(shí)別和創(chuàng)建,實(shí)現(xiàn)了MSC.SimXpert模板對(duì)于ProE模型的精確識(shí)別和有限元模型的一鍵式快速轉(zhuǎn)換。通過均勻化方法等模型降階技術(shù),將復(fù)雜精細(xì)實(shí)體模型替換為簡(jiǎn)化模型或一維梁模型,并通過模板平臺(tái)進(jìn)行多級(jí)彈體結(jié)構(gòu)部件的自由替換與組裝,從而建立多層次的有限元分析模型,有效的降低了全彈結(jié)構(gòu)的計(jì)算規(guī)模。此外,通過模板能自動(dòng)生成單元質(zhì)量檢查和結(jié)果文件,提高產(chǎn)品的研發(fā)速度。
[Abstract]:The beam slab structure is two kinds of structures are widely used in engineering, in the modern commercial aircraft, satellites, launch vehicles, and has wide application prospect of high speed train structure. With the rapid development of engineering technology, high specific strength and people of engineering structure, put forward higher requirements of lightweight and multifunctional properties. A new composite beam slab structure more and more, for the optimization design of advanced composite beam slab structure is also more and more strong. This thesis focuses on the periodic composite plate and beam structures, using the asymptotic homogenization method, topology optimization technology and multi-scale analysis methods, prediction of the equivalent properties of periodic beam structure the specified or extreme stiffness of micro structure optimization design and periodic plate optimization integration of macro and micro design are studied, and the finite element software as a black box, realize Composite beam slab structure calculation software of high performance reduction and homogenization based optimization design. The main contents of this paper include: (1) the one-dimensional periodic asymptotic homogenization theory based on finite element formulation developed one-dimensional periodic beam asymptotic homogenization method, and a new method of homogenization theory for business the software based on extended to one-dimensional periodic structure, with complex microstructure cell of the one-dimensional periodic beam structure is equivalent to macro Euler Bernoulli beam, to achieve a rapid prediction of the equivalent stiffness. The new method will be commercial software as a black box, so as to make full use of software in a variety of cell types and modeling technology, reduce the workload of programming and the cell model scale, improve the efficiency of the algorithm. The establishment of the above methods, the three dimensional (2D) periodic material, two-dimensional periodic one-dimensional periodic beam and plate structure. The homogenization solution can be unified in the framework of the same numerical solution and software. The new method for solving the one-dimensional periodic beam and bending energy approximation method and the approximate method of three-dimensional periodic homogenization based on the comparison, the scale effect along the thickness direction are discussed. The results show that the three-dimensional stress the state of the composite beam structure in bending energy method based on the assumption of normal straight neglect, overestimate the equivalent properties of the beam. The three-dimensional periodic homogenization method is introduced based on the hypothesis of periodicity in the cross section, in the section in the number of single cell is small, and the new method of one-dimensional uniform results vary greatly in the section, when the number of single cell is big enough, the two results are consistent. (2) as the basic research on the design of micro structure optimization, Heaviside function of density filtering using volume conservation optimize. In the process, the reason later iterations objective function serious oscillation is studied. The accurate sensitivity expression of nonlinear density filter of volume conservation is deduced and verified the correctness of the new formula by finite difference method, the sensitivity of different solution formula and compare the difference between the results by examples. The results showed that when the nonlinear parameters with the increase of the original sensitivity formula results and the difference results seriously, and accurate results and the sensitivity formula of difference was consistent, and then verify the correctness of the accurate sensitivity formula. In addition, when the solid of adjustable parameters, the sensitivity formula is still the sensitivity formula correct. This work provides a strong the support of micro structure topology obtained for later optimization. (3) based on the new method of homogeneous one-dimensional periodic beam, in the study of the materials under a certain volume constraint Dimensional periodic beam structure specified stiffness or extreme stiffness optimization problem is proposed. The analytic sensitivity method for solving the new method based on homogenization, by constructing a composite displacement field and extract the corresponding strain energy, the solution of the equivalent stiffness and the commercial software based on sensitivity, thus reducing the optimization threshold, improve the efficiency of optimization. The optimization method is applied to one-dimensional periodic truss beam structure, and realize the optimization of the tension torsion coupling stiffness is discussed. The optimization method of short beam cell number, indicating the short beam connection based on the optimization variables can take into account the effect of transverse shear. (4) study stiffness design problem of honeycomb board, through the unit along the normal direction of variables connected to analog cellular cell, and the analytic sensitivity method for solving the new method of homogenization is extended to periodic structure based on the shell. Compare this method with two-dimensional uniform based on the assumption of straight normal and integral along the normal direction of solving method, single celled cellular found taller than the final results for the optimization is influential, but not solving method based on the assumption of straight normal distinguish this effect. On this basis, to study the minimum compliance the macro structure as the goal, considering the two scale optimization method of macro and micro structure in single cell configuration, given the sensitivity calculation method based on the commercial software of objective function and macro design variables, so as to realize the efficient solution of the topology optimization problem of two scale. (5) as a practical application of beam plate model order method in engineering, research the multi precision structure of MSC.SimXpert software platform for ProE analysis of the development method of template. Based on CAD and CAE features named between The transmission of information, and through the external XML file to automatically identify and create database attributes, to achieve the MSC.SimXpert template for a type of accurate identification of ProE model and finite element model of the rapid conversion. Through the model of homogenization method and reduction technique, the complex solid model is replaced with simplified model or one-dimensional beam model, and the multilevel structure of parts through the template free replacement and assembly platform, so as to establish a multilevel finite element analysis model, effectively reduces the computational scale of missile structure. In addition, the template can automatically generate unit quality inspection and result file, improve the speed of product development.

【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類號(hào)】：TB12

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