本文選題：拓?fù)鋬?yōu)化　切入點(diǎn)：參數(shù)化水平集　出處：《華中科技大學(xué)》2016年博士論文　論文類型：學(xué)位論文

【摘要】：結(jié)構(gòu)拓?fù)鋬?yōu)化是指在給定的設(shè)計(jì)空間內(nèi),尋找滿足約束條件并使結(jié)構(gòu)某項(xiàng)或多項(xiàng)性能達(dá)到最優(yōu)的優(yōu)化設(shè)計(jì)方法。結(jié)構(gòu)拓?fù)鋬?yōu)化應(yīng)用領(lǐng)域涵蓋了航空航天、汽車工業(yè)、生物工程、材料工程、土木水利以及能源工業(yè)等,其不僅可以提高結(jié)構(gòu)性能,減輕結(jié)構(gòu)重量,縮短研發(fā)周期,還可以應(yīng)用于傳統(tǒng)設(shè)計(jì)方式無(wú)法解決的復(fù)雜結(jié)構(gòu)的創(chuàng)新性設(shè)計(jì)問題。隨著計(jì)算機(jī)技術(shù)、有限元方法和力學(xué)理論的迅速發(fā)展,結(jié)構(gòu)拓?fù)鋬?yōu)化方法得到了一定的發(fā)展。基于水平集的拓?fù)鋬?yōu)化方法與傳統(tǒng)拓?fù)鋬?yōu)化方法相比,能夠?qū)崿F(xiàn)拓?fù)浜托螤畹耐瑫r(shí)優(yōu)化,且設(shè)計(jì)結(jié)果具有光滑的結(jié)構(gòu)邊界和清晰的幾何信息,因此得到了廣泛的關(guān)注和研究。然而傳統(tǒng)水平集方法存在的一些缺陷,影響其進(jìn)一步應(yīng)用與發(fā)展。本文針對(duì)傳統(tǒng)水平集方法存在的數(shù)值計(jì)算困難,提出相應(yīng)的解決措施,并將所提出的方法推廣并應(yīng)用到多工況結(jié)構(gòu)拓?fù)鋬?yōu)化、結(jié)構(gòu)頻率響應(yīng)拓?fù)鋬?yōu)化、擠壓成型結(jié)構(gòu)拓?fù)鋬?yōu)化以及多孔材料/結(jié)構(gòu)一體化拓?fù)鋬?yōu)化中。首先,研究了基于參數(shù)化水平集的結(jié)構(gòu)拓?fù)鋬?yōu)化方法。為克服傳統(tǒng)水平集方法的數(shù)值計(jì)算困難,提出了基于緊支徑向基函數(shù)(CSRBF)和離散小波分解(DWT)的參數(shù)化水平集方法,構(gòu)建了基于參數(shù)化水平集的結(jié)構(gòu)剛度拓?fù)鋬?yōu)化模型,開展了基于形狀導(dǎo)數(shù)的敏度分析,設(shè)計(jì)了基于優(yōu)化準(zhǔn)則法的優(yōu)化算法,實(shí)現(xiàn)了基于參數(shù)化水平集的結(jié)構(gòu)拓?fù)鋬?yōu)化設(shè)計(jì)。在所提出的方法中,緊支徑向基函數(shù)用于對(duì)水平集函數(shù)進(jìn)行插值,保留了傳統(tǒng)水平集方法的優(yōu)點(diǎn),有效避免了直接求解復(fù)雜的Hamilton-Jacobi偏微分方程所導(dǎo)致的數(shù)值計(jì)算困難,離散小波分解用于壓縮緊支徑向基函數(shù)的插值矩陣,進(jìn)一步提高了求解效率。其次,研究了參數(shù)化水平集方法在多工況結(jié)構(gòu)拓?fù)鋬?yōu)化中的應(yīng)用。針對(duì)該問題的研究現(xiàn)狀,結(jié)合參數(shù)化水平集方法,提出了基于歸一化指數(shù)加權(quán)準(zhǔn)則(NEWC)的多目標(biāo)優(yōu)化建模方法,消除了載荷病態(tài)問題,保證了在Pareto前端非凸時(shí)也能找到Pareto最優(yōu)解。針對(duì)子目標(biāo)權(quán)重的確定,提出了基于模糊多屬性群體決策(FMAGDM)的權(quán)重計(jì)算方法,減少了主觀因素的影響。首次提出了考慮擴(kuò)展最優(yōu)性的多工況結(jié)構(gòu)拓?fù)鋬?yōu)化設(shè)計(jì),實(shí)現(xiàn)了各子工況下結(jié)構(gòu)柔度和結(jié)構(gòu)體積分?jǐn)?shù)的同時(shí)優(yōu)化,得到了重量更輕的結(jié)構(gòu)。第三,研究了參數(shù)化水平集方法在結(jié)構(gòu)頻率響應(yīng)拓?fù)鋬?yōu)化中的應(yīng)用。針對(duì)不同類型的結(jié)構(gòu)頻率響應(yīng),分別提出了基于參數(shù)化水平集的結(jié)構(gòu)全局和局部頻率響應(yīng)拓?fù)鋬?yōu)化方法,保證了光滑的結(jié)構(gòu)邊界,并有效地提升了結(jié)構(gòu)的動(dòng)態(tài)性能。針對(duì)頻帶激勵(lì)下結(jié)構(gòu)頻率響應(yīng)的有限元分析過程,引入了多頻擬靜力Ritz向量(MQSRV)進(jìn)行有限元模型降階,減少了反復(fù)調(diào)用有限元分析所產(chǎn)生的計(jì)算成本。第四,研究了參數(shù)化水平集方法在擠壓成型結(jié)構(gòu)拓?fù)鋬?yōu)化中的應(yīng)用。以結(jié)構(gòu)邊界和截面兩個(gè)方面為切入點(diǎn),研究擠壓成型結(jié)構(gòu)拓?fù)鋬?yōu)化技術(shù)。針對(duì)結(jié)構(gòu)邊界問題,采用所提出的參數(shù)化水平集方法構(gòu)建了面向擠壓成型工藝的結(jié)構(gòu)拓?fù)鋬?yōu)化模型,保證了最優(yōu)拓?fù)浣Y(jié)構(gòu)具有完整的邊界幾何信息。針對(duì)相同截面的設(shè)計(jì)要求,引入了擠壓成型約束,并提出了截面投影法處理擠壓成型約束,確保了優(yōu)化設(shè)計(jì)結(jié)果的可制造性,提高了方法的優(yōu)化效率。第五,研究了參數(shù)化水平集方法在多孔材料/結(jié)構(gòu)一體化拓?fù)鋬?yōu)化中的應(yīng)用。針對(duì)當(dāng)前材料/結(jié)構(gòu)一體化拓?fù)鋬?yōu)化在計(jì)算效率和加工成本方面的問題,提出了一種兩階段的設(shè)計(jì)方法。在宏觀結(jié)構(gòu)布局優(yōu)化階段,采用SIMP材料密度插值模型,獲得了結(jié)構(gòu)域內(nèi)的分層材料密度分布;在材料微結(jié)構(gòu)拓?fù)鋬?yōu)化階段,采用參數(shù)化水平集方法描述微結(jié)構(gòu)邊界,獲得了邊界光滑且宏觀等效性能各異的材料微結(jié)構(gòu)構(gòu)型。通過組合兩階段的優(yōu)化結(jié)果,得到了具有多種功能特性的最優(yōu)材料/結(jié)構(gòu)。第六,將所提出的方法應(yīng)用于兩個(gè)實(shí)際工程案例。結(jié)果表明,所提出方法極大地簡(jiǎn)化了結(jié)構(gòu)設(shè)計(jì)流程,提升了結(jié)構(gòu)性能,實(shí)現(xiàn)了工程產(chǎn)品的輕量化設(shè)計(jì),有效地支持了工程產(chǎn)品的結(jié)構(gòu)優(yōu)化設(shè)計(jì)。最后,總結(jié)了本文的研究成果及主要?jiǎng)?chuàng)新點(diǎn),展望了未來的研究工作。
[Abstract]:Topology optimization refers to the design of a given space, for which satisfy the constraint condition and optimization design method of the structure of one or more to achieve optimal performance. The topology optimization application fields include aerospace, automotive industry, biological engineering, materials engineering, civil water and energy industry, it can not only improve the structure performance and to reduce the structural weight, shorten the development cycle, the innovative design of complex structures can also be used in the traditional design method can not be solved. With the development of computer technology, finite element method and the mechanical theory of the rapid development, structural topology optimization method has been developed. Compared with the traditional topology optimization method for topology optimization of level set method based on the topology and shape optimization can be achieved at the same time, and the design results with smooth boundary structure and clear geometric information, so it is widely Attention and study. However, the traditional level set method has some defects, affecting its further development and application. Based on the traditional level set method in numerical calculation, put forward the corresponding measures, and the proposed method is generalized to multi condition topology optimization, topology optimization of structure response frequency, topology integration optimization of extrusion molding and structure topology optimization of porous materials / structures. Firstly, research the topology optimization method of parameter based on the level set. In order to overcome the traditional level set method for numerical calculation of difficulties, proposed based on compactly supported radial basis function (CSRBF) and discrete wavelet decomposition (DWT) parametric level set method based on the parametric structure level set stiffness topology optimization model, the shape derivative sensitivity analysis based on optimization algorithm is designed based on the method of realizing the optimization criterion. The topology optimization design based on parametric level set. In the proposed method, compactly supported radial basis functions for level set function interpolation, retains the advantages of traditional level set method, effectively avoiding the difficulties caused by the direct numerical calculation for solving complex partial differential equations Hamilton-Jacobi, discrete wavelet decomposition for compression compactly supported radial basis function interpolation matrix, further improve the efficiency of the algorithm. Secondly, the application of the parametric level set method in topology optimization under multiple working conditions in the structure. According to the research status of the problem, combined with the parametric level set method, proposed the normalized weighted index (NEWC) criterion based on multi-objective optimization modeling method that eliminates the problem of load sickness, which can find the optimal solution in the Pareto Pareto front-end. Determine the needle on non convex object weight, is proposed based on fuzzy multiple attribute Group decision making (FMAGDM) method to calculate the weight, reduce the influence of subjective factors is put forward for the first time. Considering the extension of the optimality of the topology optimization design of multi working structure, optimize the volume fraction and structure flexibility sub conditions at the same time, lighter structure is obtained. Third, we study the parametric level set response method application of topology optimization in the structure frequency. According to the structure of different types of frequency response are proposed topology optimization method for structural response of global and local parametric level set based on the frequency, to ensure the smooth boundary structure, and effectively improve the dynamic performance of the structure. According to the finite element structure under frequency response band the incentive analysis process, the introduction of multi frequency quasi static Ritz vector (MQSRV) reduced order finite element model, reduces the computation repeatedly calling the finite element analysis generated by the research. Fourth. The application of the parametric level set method in extrusion molding in structural topology optimization. In the two aspects of structural boundary and cross section as the starting point, to study the structure of extrusion molding technology of topology optimization for structure boundary problem, set method to construct the topology optimization model for extrusion molding process using the proposed parametric level, guarantee the optimal topology structure with geometric boundary information complete. According to the requirement of the same design section, introduced the extrusion molding constraint, and put forward the projection section extrusion molding processing constraints, to ensure that the optimization design results of manufacturability, improves the optimization efficiency of the method. Fifth, the application of the parametric level set method in topology optimization of structure integration in porous materials / materials / structures. In view of the current integration of topology optimization in the computation efficiency and the processing cost of the problem, put forward a The design method of two stages. In the macro structure layout optimization stage, using SIMP material density interpolation model, layered material density distribution domain is obtained; in the material micro structure topology optimization stage, using parametric level set method to describe the micro structure of the boundary, the boundary is smooth and the equivalent performance of different material microstructure configuration the optimization results obtained. Combination of the two stage, the optimal material / has a variety of functional properties of structure are obtained. Sixth, the proposed method is applied to two practical engineering case. The results show that the proposed method greatly simplifies the structure design process, improve the structure performance, realize the lightweight design of engineering products the structure optimization design, and effectively support the engineering products. Finally, this paper summarizes the research achievements and main innovation points, the prospect of future research work.

【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TB21
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本文編號(hào)：1623400