【摘要】： 本文利用ANSYS平臺(tái)的二次開發(fā)功能,并依據(jù)“相對(duì)差商法”思想,開發(fā)了一種在ANSYS平臺(tái)下的桁架結(jié)構(gòu)離散變量?jī)?yōu)化算法;編制了相應(yīng)的ANSYS二次開發(fā)程序。通過諸多實(shí)例的論證,本程序計(jì)算效率高,優(yōu)化結(jié)果收斂性好,也證實(shí)了按本文思想在ANSYS平臺(tái)下桁架結(jié)構(gòu)離散變量?jī)?yōu)化設(shè)計(jì)的可行性和有效性。 另外,本文對(duì)幾何大變形大跨度桁架結(jié)構(gòu)的計(jì)算分析提出了一種新的數(shù)值算法。在工程中,某些大跨度結(jié)構(gòu),由于其結(jié)構(gòu)構(gòu)造或形狀的特殊及工作荷載的特點(diǎn),工作時(shí)常常產(chǎn)生相對(duì)較大的幾何變形,但其絕對(duì)量仍然不大;而且要保證正常工作的使用,須要求應(yīng)力—應(yīng)變保持線性關(guān)系。對(duì)這類結(jié)構(gòu)的分析計(jì)算,必須應(yīng)用幾何大變形非線性理論。計(jì)算分析這種問題的傳統(tǒng)方法是應(yīng)用最小勢(shì)能原理,將大變形的非線性幾何方程的近似表達(dá)式和線性的應(yīng)力—應(yīng)變關(guān)系代入總勢(shì)能的泛函中,且經(jīng)離散化處理得到關(guān)于節(jié)點(diǎn)位移的泛函表達(dá)式,再根據(jù)總勢(shì)能的極小化條件可得到關(guān)于節(jié)點(diǎn)位移的歐拉方程,即關(guān)于節(jié)點(diǎn)位移的非線性平衡方程。因?yàn)樵摲匠淌且宰冃魏蟮墓?jié)點(diǎn)位移列出的,所以它與變形狀態(tài)是統(tǒng)一的、協(xié)調(diào)的;但因該平衡方程是位移的非線性函數(shù),求解的難度很大,尤其對(duì)多自由度的復(fù)雜結(jié)構(gòu)更難。而本文基于ANSYS平臺(tái)的二次開發(fā),所構(gòu)思的大變形分析思想為:采用兩步交替迭代逐步逼近,使平衡狀態(tài)與變形狀態(tài)協(xié)調(diào)、統(tǒng)一,建立并求出變形后的平衡方程及其解;也就是說,首先由已知桿件內(nèi)力建立計(jì)算節(jié)點(diǎn)位移的連續(xù)方程并求解,然后由已知節(jié)點(diǎn)位移建立計(jì)算桿件內(nèi)力的平衡方程并求解,通過多次迭代求得平衡狀態(tài)與變形狀態(tài)協(xié)調(diào)統(tǒng)一的非線性大變形結(jié)構(gòu)分析的精確解。 由于本文方法在幾何大變形分析的過程中僅需做一次結(jié)構(gòu)分析,此點(diǎn)尤其在幾何大變形的結(jié)構(gòu)優(yōu)化設(shè)計(jì)中優(yōu)點(diǎn)顯著;故據(jù)此提出了幾何大變形桁架結(jié)構(gòu)離散變量?jī)?yōu)化設(shè)計(jì)的思想,并針對(duì)扁桁架、大跨度桁架作了相應(yīng)分析。通過編制相應(yīng)的ANSYS二次開發(fā)程序,并由數(shù)值算例驗(yàn)證了本文方法的有效性,計(jì)算精確和計(jì)算效率。值得一提的是,本文對(duì)大變形的分析思想可蛻化分析桁架結(jié)構(gòu)的幾何小變形問題。
[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.
【學(xué)位授予單位】：同濟(jì)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2008
【分類號(hào)】：TU323.4

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