含自重载荷桁架结构若干函数的特性及桁架结构优化算法研究

发布时间：2018-01-10 07:16

本文关键词：含自重载荷桁架结构若干函数的特性及桁架结构优化算法研究　出处：《广西大学》2015年博士论文　论文类型：学位论文

【摘要】：含自重载荷作用桁架结构函数及其敏度的特性分析还较为缺乏,不能有效保证结构优化算法的收敛性。同时含应力、位移和禁用频率带等约束的桁架结构优化还未成熟,难以获得其最优解。本文在研究含自重载荷作用桁架结构若干函数及其敏度特性的基础上,以约束优化问题的极值必要条件为依据,针对含自重载荷作用桁架结构拓扑、尺寸与几何及其同时优化的需要,研制桁架结构优化的算法及其算法实现和算例验证。(1)分别以各杆横截面积和各节点坐标做等比变化,讨论含白重载荷作用桁架结构的节点位移、杆内轴向应力、轴向应变能和固有频率及其敏度的特性。依据受横向均布载荷梁的理论,讨论等截面杆单元的最大弯曲应力的特性,以及控制其最大弯曲应力和防止压杆屈曲的方法。(2)在分析KKT条件的基础上,依据对偶目标函数的极值必要条件,讨论KKT乘子寻优方向和最优步长因子的确定,以直接求解含单性态约束界信息的乘子或在乘子空间优化迭代求解多性态约束的乘子。依据本文导出的含自重载荷作用桁架结构若干函数的敏度特性,讨论抛物线法直接迭代求解式和优化迭代求解式的构造原理及其收敛条件,以及优化迭代步长因子的自动确定方法。(3)针对用于含节点自重载荷作用下桁架拓扑优化的轴向应变能约束结构重量最小化问题,结合本文导出的轴向应变能函数及其敏度的特性,讨论本文提出的单性态约束桁架结构优化算法原理的运用,即：依据其KKT条件和对偶规划的原理,讨论功—重量分配准则的建立与应用、射线比例因子的解析求解与乘子非负要求的保证、含约束界信息乘子的直接求解、抛物线法直接迭代求解式的建立及其特性、以及程序实现与算例验证等。(4)针对含自重载荷作用桁架结构尺寸与拓扑的自动优化设计,结合本文导出的节点位移、轴向应力和固有频率的敏度特性,讨论本文提出的多性态约束桁架结构优化算法原理的运用,即：依据其KKT条件和对偶规划的原理,讨论乘子的优化迭代求解及其最优步长因子的自动确定,各杆横截面积的抛物线法优化迭代求解及其步长因子的自动确定,以及程序实现、算例验证与单元删除准则讨论等。(5)针对含自重载荷作用桁架结构尺寸、几何与拓扑的自动优化设计,结合本文导出的节点位移、轴向应力和固有频率的敏度特性,讨论本文提出的多性态约束桁架结构优化算法原理的运用,即：依据其KKT条件和对偶规划的原理,讨论乘子的优化迭代求解及其最优步长因子的自动确定,各节点坐标的抛物线法优化迭代求解及其步长因子的自动确定,以及程序实现与算例验证等。以上论点均用含自重载荷作用下平面与空间桁架结构的拓扑、尺寸与几何优化算例进行了验证,优化过程自动高效,优化结果好。
[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.
【学位授予单位】：广西大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TU323.4

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