本文關(guān)鍵詞：含自重載荷桁架結(jié)構(gòu)若干函數(shù)的特性及桁架結(jié)構(gòu)優(yōu)化算法研究　出處：《廣西大學(xué)》2015年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 桁架結(jié)構(gòu)優(yōu)化 自重載荷 頻率約束 KKT乘子的求解 直接迭 代求解的拋物線法 優(yōu)化迭代求解的拋物線法 步長因子的自動確定

【摘要】：含自重載荷作用桁架結(jié)構(gòu)函數(shù)及其敏度的特性分析還較為缺乏,不能有效保證結(jié)構(gòu)優(yōu)化算法的收斂性。同時(shí)含應(yīng)力、位移和禁用頻率帶等約束的桁架結(jié)構(gòu)優(yōu)化還未成熟,難以獲得其最優(yōu)解。本文在研究含自重載荷作用桁架結(jié)構(gòu)若干函數(shù)及其敏度特性的基礎(chǔ)上,以約束優(yōu)化問題的極值必要條件為依據(jù),針對含自重載荷作用桁架結(jié)構(gòu)拓?fù)�、尺寸與幾何及其同時(shí)優(yōu)化的需要,研制桁架結(jié)構(gòu)優(yōu)化的算法及其算法實(shí)現(xiàn)和算例驗(yàn)證。(1)分別以各桿橫截面積和各節(jié)點(diǎn)坐標(biāo)做等比變化,討論含白重載荷作用桁架結(jié)構(gòu)的節(jié)點(diǎn)位移、桿內(nèi)軸向應(yīng)力、軸向應(yīng)變能和固有頻率及其敏度的特性。依據(jù)受橫向均布載荷梁的理論,討論等截面桿單元的最大彎曲應(yīng)力的特性,以及控制其最大彎曲應(yīng)力和防止壓桿屈曲的方法。(2)在分析KKT條件的基礎(chǔ)上,依據(jù)對偶目標(biāo)函數(shù)的極值必要條件,討論KKT乘子尋優(yōu)方向和最優(yōu)步長因子的確定,以直接求解含單性態(tài)約束界信息的乘子或在乘子空間優(yōu)化迭代求解多性態(tài)約束的乘子。依據(jù)本文導(dǎo)出的含自重載荷作用桁架結(jié)構(gòu)若干函數(shù)的敏度特性,討論拋物線法直接迭代求解式和優(yōu)化迭代求解式的構(gòu)造原理及其收斂條件,以及優(yōu)化迭代步長因子的自動確定方法。(3)針對用于含節(jié)點(diǎn)自重載荷作用下桁架拓?fù)鋬?yōu)化的軸向應(yīng)變能約束結(jié)構(gòu)重量最小化問題,結(jié)合本文導(dǎo)出的軸向應(yīng)變能函數(shù)及其敏度的特性,討論本文提出的單性態(tài)約束桁架結(jié)構(gòu)優(yōu)化算法原理的運(yùn)用,即：依據(jù)其KKT條件和對偶規(guī)劃的原理,討論功—重量分配準(zhǔn)則的建立與應(yīng)用、射線比例因子的解析求解與乘子非負(fù)要求的保證、含約束界信息乘子的直接求解、拋物線法直接迭代求解式的建立及其特性、以及程序?qū)崿F(xiàn)與算例驗(yàn)證等。(4)針對含自重載荷作用桁架結(jié)構(gòu)尺寸與拓?fù)涞淖詣觾?yōu)化設(shè)計(jì),結(jié)合本文導(dǎo)出的節(jié)點(diǎn)位移、軸向應(yīng)力和固有頻率的敏度特性,討論本文提出的多性態(tài)約束桁架結(jié)構(gòu)優(yōu)化算法原理的運(yùn)用,即：依據(jù)其KKT條件和對偶規(guī)劃的原理,討論乘子的優(yōu)化迭代求解及其最優(yōu)步長因子的自動確定,各桿橫截面積的拋物線法優(yōu)化迭代求解及其步長因子的自動確定,以及程序?qū)崿F(xiàn)、算例驗(yàn)證與單元?jiǎng)h除準(zhǔn)則討論等。(5)針對含自重載荷作用桁架結(jié)構(gòu)尺寸、幾何與拓?fù)涞淖詣觾?yōu)化設(shè)計(jì),結(jié)合本文導(dǎo)出的節(jié)點(diǎn)位移、軸向應(yīng)力和固有頻率的敏度特性,討論本文提出的多性態(tài)約束桁架結(jié)構(gòu)優(yōu)化算法原理的運(yùn)用,即：依據(jù)其KKT條件和對偶規(guī)劃的原理,討論乘子的優(yōu)化迭代求解及其最優(yōu)步長因子的自動確定,各節(jié)點(diǎn)坐標(biāo)的拋物線法優(yōu)化迭代求解及其步長因子的自動確定,以及程序?qū)崿F(xiàn)與算例驗(yàn)證等。以上論點(diǎn)均用含自重載荷作用下平面與空間桁架結(jié)構(gòu)的拓?fù)�、尺寸與幾何優(yōu)化算例進(jìn)行了驗(yàn)證,優(yōu)化過程自動高效,優(yōu)化結(jié)果好。
[Abstract]:The characteristic analysis of truss structure function and its sensitivity with deadweight load is still lacking, which can not effectively guarantee the convergence of structural optimization algorithm and contain stress. The optimization of truss structures with displacements and forbidden frequency constraints is still immature, so it is difficult to obtain its optimal solution. In this paper, some functions and their sensitivity characteristics of truss structures with deadweight loads are studied. Based on the extremum necessary condition of constrained optimization problem, the topology, dimension and geometry of truss structure with self-weight load are considered. The algorithm of truss structure optimization and its implementation and example verification. (1) the joint displacement of truss structure with white heavy load is discussed by changing the cross-sectional area of each bar and the coordinate of each node respectively. The characteristics of axial stress, axial strain energy, natural frequency and their sensitivity in the bar. Based on the theory of the beam subjected to transverse uniform load, the characteristics of the maximum bending stress of the bar element with equal section are discussed. The method of controlling the maximum bending stress and preventing the buckling of the compression bar is given. Based on the analysis of the KKT condition, the necessary conditions for the extreme value of the dual objective function are obtained. The optimization direction and the optimal step factor of KKT multiplier are discussed. Based on the sensitivity properties of some functions of truss structures with self-weight loads derived in this paper, the multipliers with simple state constraint bounds or iterated iterations in multiplier space are used to solve polymorphic constraints directly. The construction principle and convergence conditions of direct iterative solution and optimization iterative solution of parabola method are discussed. And the automatic determination method of optimization iterative step size factor. 3) aiming at the axial strain energy constrained structural weight minimization problem for the topology optimization of truss under the action of nodal deadweight load. Combined with the properties of the axial strain energy function and its sensitivity derived in this paper, the application of the proposed optimization algorithm for single-state constrained truss structures is discussed, that is, according to its KKT condition and the principle of dual programming. This paper discusses the establishment and application of the power-weight distribution criterion, the analytic solution of the ray ratio factor and the guarantee of the non-negative requirement of the multiplier, and the direct solution of the multiplier with the information of the constraint bound. The establishment and characteristic of direct iterative solution of parabola method, program realization and example verification etc.) automatic optimization design for the size and topology of truss structure with self-weight load. Combined with the sensitivity characteristics of node displacement, axial stress and natural frequency derived in this paper, the application of the optimization algorithm for polymorphic constrained truss structures proposed in this paper is discussed. That is, according to its KKT condition and the principle of dual programming, the optimal iterative solution of the multiplier and the automatic determination of the optimal step size factor are discussed. The optimization iterative solution of the cross section area of each bar and the automatic determination of step size factor, as well as the program realization, the example verification and the discussion of the criterion of element deletion, etc.) are aimed at the size of truss structure with self-weight load. The automatic optimization design of geometry and topology, combined with the sensitivity characteristics of node displacement, axial stress and natural frequency derived in this paper, discusses the application of the optimization algorithm of polymorphic constrained truss structures proposed in this paper. That is, according to its KKT condition and the principle of dual programming, the optimal iterative solution of the multiplier and the automatic determination of the optimal step size factor are discussed. The optimization iterative solution of each node coordinate and the automatic determination of step size factor, as well as the program realization and the example verification, etc. All of the above arguments are based on the topology of plane and space truss structures under the action of self-weight load. The example of dimension and geometry optimization shows that the optimization process is automatic and efficient, and the optimization results are good.
【學(xué)位授予單位】：廣西大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2015
【分類號】：TU323.4

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