【摘要】：本文基于剛度擴(kuò)散法提出了若干處理多組件系統(tǒng)協(xié)同優(yōu)化設(shè)計的新型優(yōu)化模型，為多組件系統(tǒng)的協(xié)同優(yōu)化設(shè)計提供了新的思路和方法。 首先，本文詳細(xì)介紹了剛度擴(kuò)散方法的基本原理，主要包括徑向基函數(shù)插值模型、數(shù)學(xué)公式推導(dǎo)和靈敏度分析方法，通過若干數(shù)值算例說明了徑向基函數(shù)插值的特點(diǎn)及剛度擴(kuò)散方法在處理桁架結(jié)構(gòu)布局優(yōu)化及組合結(jié)構(gòu)優(yōu)化設(shè)計問題時的合理性及有效性。 其次，針對桿件與連續(xù)體結(jié)構(gòu)的協(xié)同優(yōu)化設(shè)計問題，本文首先基于剛度擴(kuò)散法提出了尺寸固定桿件與連續(xù)體結(jié)構(gòu)的協(xié)同優(yōu)化設(shè)計模型，通過剛度擴(kuò)散方法把桿件的剛度擴(kuò)散到連續(xù)體結(jié)構(gòu)的剛度矩陣中，推導(dǎo)了靈敏度分析公式，數(shù)值算例驗(yàn)證了所提出模型的有效性。然后在此基礎(chǔ)上提出了同時考慮桿件尺寸優(yōu)化設(shè)計的尺寸可變桿件與連續(xù)體的協(xié)同優(yōu)化設(shè)計模型，同時實(shí)現(xiàn)了桿件的布局優(yōu)化、尺寸優(yōu)化及連續(xù)體結(jié)構(gòu)的拓?fù)鋬?yōu)化。 第三，針對彈性體組件與連續(xù)體結(jié)構(gòu)的協(xié)同優(yōu)化設(shè)計問題，本文首先提出了拓?fù)涔潭◤椥泽w組件與連續(xù)體結(jié)構(gòu)協(xié)同優(yōu)化設(shè)計模型，對彈性體組件劃分有限元網(wǎng)格，通過網(wǎng)格節(jié)點(diǎn)坐標(biāo)利用徑向基函數(shù)插值模型建立彈性體組件位移場與支撐結(jié)構(gòu)位移場之間的聯(lián)系，通過剛度擴(kuò)散方法把組件的剛度擴(kuò)散到支撐結(jié)構(gòu)的剛度陣中。然后在此基礎(chǔ)上提出了同時考慮彈性體組件拓?fù)鋬?yōu)化設(shè)計的組件與連續(xù)體的協(xié)同優(yōu)化設(shè)計模型，數(shù)值算例表明，本文所提方法同時實(shí)現(xiàn)了組件的拓?fù)鋬?yōu)化、布局優(yōu)化及連續(xù)體結(jié)構(gòu)的拓?fù)鋬?yōu)化。 第四，通過把支撐視為在特殊位置移動的彈性體組件，利用本文提出的彈性體組件與連續(xù)體結(jié)構(gòu)協(xié)同優(yōu)化設(shè)計模型，實(shí)現(xiàn)了結(jié)構(gòu)支撐位置與拓?fù)涞膮f(xié)同優(yōu)化設(shè)計。另外，考慮到實(shí)際工程中施工的難易程度，，在優(yōu)化模型中加入了支撐的成本約束，得到了不同成本約束下的優(yōu)化結(jié)果，表明成本約束對支撐的位置及結(jié)構(gòu)拓?fù)溆泻艽蟮挠绊�，�?shù)值算例驗(yàn)證了剛度擴(kuò)散方法在處理此類問題的有效性和靈活性。 最后，對全部工作進(jìn)行了總結(jié)，并對未來工作提出了展望。
[Abstract]:In this paper, based on stiffness diffusion method, several new optimization models dealing with collaborative optimization design of multi-component systems are proposed, which provide new ideas and methods for collaborative optimization design of multi-component systems. Firstly, the basic principle of stiffness diffusion method is introduced in detail, including radial basis function interpolation model, mathematical formula derivation and sensitivity analysis method. Some numerical examples are given to illustrate the characteristics of radial basis function interpolation and the rationality and effectiveness of the stiffness diffusion method in dealing with the optimization of truss structure layout and the optimal design of composite structures. Secondly, aiming at the problem of cooperative optimization design of member and continuum structure, this paper first presents a collaborative optimization design model of fixed member and continuum structure based on stiffness diffusion method. The stiffness of the member is diffused into the stiffness matrix of the continuum structure by the method of stiffness diffusion. The sensitivity analysis formula is derived and the validity of the proposed model is verified by a numerical example. On the basis of this, the cooperative optimization model of variable rod and continuum is proposed, and the optimization of the layout, size and topology of the continuum structure is realized at the same time. Thirdly, aiming at the problem of cooperative optimization design of elastomer and continuum structure, this paper proposes a cooperative optimization design model of topological fixed elastomer component and continuum structure, and divides the elastomer component into finite element meshes. The relation between displacement field of elastic body component and displacement field of braced structure is established by using radial basis function interpolation model in grid node coordinates, and stiffness of component is diffused into stiffness matrix of braced structure by means of stiffness diffusion method. Then, a cooperative optimization design model of component and continuum considering the topology optimization of elastomer components is proposed. Numerical examples show that the proposed method realizes the topology optimization of components at the same time. Layout optimization and topology optimization of continuum structure. Fourthly, by considering the bracing as an elastomer component moving in a special position, the cooperative optimization design of the structure support position and topology is realized by using the cooperative optimization design model of the elastomer component and the continuum structure proposed in this paper. In addition, considering the difficulty of construction in practical engineering, the cost constraints of support are added to the optimization model, and the optimization results under different cost constraints are obtained, which show that cost constraints have a great influence on the position and structure topology of the support. Numerical examples demonstrate the effectiveness and flexibility of the stiffness diffusion method in dealing with such problems. Finally, the whole work is summarized, and the prospect of future work is put forward.
【學(xué)位授予單位】：華南理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：TU318

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