几何大变形桁架结构离散变量优化设计

发布时间：2018-09-06 07:14

【摘要】： 本文利用ANSYS平台的二次开发功能,并依据“相对差商法”思想,开发了一种在ANSYS平台下的桁架结构离散变量优化算法;编制了相应的ANSYS二次开发程序。通过诸多实例的论证,本程序计算效率高,优化结果收敛性好,也证实了按本文思想在ANSYS平台下桁架结构离散变量优化设计的可行性和有效性。另外,本文对几何大变形大跨度桁架结构的计算分析提出了一种新的数值算法。在工程中,某些大跨度结构,由于其结构构造或形状的特殊及工作荷载的特点,工作时常常产生相对较大的几何变形,但其绝对量仍然不大;而且要保证正常工作的使用,须要求应力—应变保持线性关系。对这类结构的分析计算,必须应用几何大变形非线性理论。计算分析这种问题的传统方法是应用最小势能原理,将大变形的非线性几何方程的近似表达式和线性的应力—应变关系代入总势能的泛函中,且经离散化处理得到关于节点位移的泛函表达式,再根据总势能的极小化条件可得到关于节点位移的欧拉方程,即关于节点位移的非线性平衡方程。因为该方程是以变形后的节点位移列出的,所以它与变形状态是统一的、协调的;但因该平衡方程是位移的非线性函数,求解的难度很大,尤其对多自由度的复杂结构更难。而本文基于ANSYS平台的二次开发,所构思的大变形分析思想为:采用两步交替迭代逐步逼近,使平衡状态与变形状态协调、统一,建立并求出变形后的平衡方程及其解;也就是说,首先由已知杆件内力建立计算节点位移的连续方程并求解,然后由已知节点位移建立计算杆件内力的平衡方程并求解,通过多次迭代求得平衡状态与变形状态协调统一的非线性大变形结构分析的精确解。由于本文方法在几何大变形分析的过程中仅需做一次结构分析,此点尤其在几何大变形的结构优化设计中优点显著;故据此提出了几何大变形桁架结构离散变量优化设计的思想,并针对扁桁架、大跨度桁架作了相应分析。通过编制相应的ANSYS二次开发程序,并由数值算例验证了本文方法的有效性,计算精确和计算效率。值得一提的是,本文对大变形的分析思想可蜕化分析桁架结构的几何小变形问题。
[Abstract]:In this paper, a discrete variable optimization algorithm of truss structure based on ANSYS platform is developed by using the secondary development function of ANSYS platform and the idea of "relative difference quotient method", and the corresponding ANSYS secondary development program is worked out. It is proved by many examples that the program has high calculation efficiency and good convergence of optimization results. It also proves the feasibility and validity of the discrete variable optimization design of truss structure under ANSYS platform according to the idea of this paper. In addition, this paper presents a new numerical algorithm for the calculation and analysis of geometric large deformation and large span truss structures. In engineering, some long-span structures often produce relatively large geometric deformation due to the special structure or shape of the structure and the characteristics of the working load, but the absolute amount is still small, and the normal operation should be ensured. A linear relationship between stress and strain should be required. The nonlinear theory of geometric large deformation must be applied to the analysis and calculation of this kind of structures. The traditional method of calculating and analyzing this kind of problem is to apply the principle of minimum potential energy to replace the approximate expression of nonlinear geometric equation with large deformation and the linear stress-strain relation into the functional of total potential energy. The functional expression of node displacement is obtained by discretization, and the Euler equation on node displacement is obtained according to the minimization condition of total potential energy, that is, the nonlinear equilibrium equation of node displacement. Because the equation is listed by the deformed node displacement, it is unified and coordinated with the deformation state, but as the equilibrium equation is a nonlinear function of displacement, it is very difficult to solve, especially for complex structures with multiple degrees of freedom. Based on the secondary development of ANSYS platform, the idea of large deformation analysis in this paper is as follows: the two-step iterative approximation is used to harmonize the equilibrium state with the deformation state, and the equilibrium equation and its solution after deformation are established and solved. That is to say, the continuous equation for calculating the displacement of the node is established and solved by the internal force of the known member, and then the equilibrium equation for calculating the internal force of the member is established and solved by the known displacement of the node. Through multiple iterations, the exact solution of nonlinear large deformation structure analysis is obtained, in which the equilibrium state and the deformation state are coordinated and unified. Since the method in this paper only needs to do one structural analysis in the process of geometric large deformation analysis, this point has obvious advantages in the structural optimization design of geometric large deformation. Therefore, the idea of discrete variable optimization design of geometric large deformation truss structure is put forward, and the corresponding analysis is made for flat truss and large span truss. By compiling the corresponding ANSYS secondary development program, the validity, accuracy and efficiency of the proposed method are verified by numerical examples. It is worth mentioning that the analysis of large deformation in this paper can degenerate and analyze the geometric small deformation of truss structures.
【学位授予单位】：同济大学
【学位级别】：硕士
【学位授予年份】：2008
【分类号】：TU323.4

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