以力法為分析工具之結構離散輕量化設計效率的探討

On the Computational Efficiency of Using Force Method in Discrete Structural Optimization

林俊榮(Jing-Long Lin)

指導教授 ： 莊德興

國立中央大學/工學院/土木工程學系/碩士(2011年)

摘要

本文主要是以矩陣力法配合離散拉格朗日法(Discrete Lagrangian Method, DLM)進行離散結構最佳化設計，並與位移法比較設計所需時間，藉以探討其對最佳化整體計算效率改善情況。一般的最佳化設計研究多數以位移法分析為主，位移法分析時所需求解的方程式數量是系統自由度的數量，而力法所需要求解的方程式數量則是系統贅餘度數，因此當超靜定結構的贅餘度數小於系統自由度數量的情況下，其所需要的分析時間會低於位移法所需的時間；此外，力法分析中的力平衡矩陣不會變更，不需重覆找出對應於贅力的平衡矩陣和基元靜定結構的平衡矩陣，因此應用力法於需要反覆求解之的最佳化問題時，比位移法更具優勢。DLM為一種鄰點搜尋法，其具備非常強健之搜尋能力，由過去的研究結果顯示此法求解能力極佳，本文同時考慮合向量移動策略來改善DLM求解大型結構的效能，並能加快DLM的求解效率。本文最後將以數個傳統結構離散輕量化設計例來展示以力法作為結構分析工具的優點，並比較力法和位移法所需的計算時間。

關鍵字

結構輕量化設計 ； 力法

並列摘要

In this paper, the discrete structural optimization problem solved by using discrete Lagrangian method (DLM) in conjunction with force method of analysis is presented. DLM belongs to the neighborhood searching methods. In the past, the analysis module built in the DLM algorithm is based on the displacement approach. To improve the searching efficiency of the method, the force method of analysis will be considered in this study. Most structural optimization algorithms published in the literature were developed based on the displacement method of analysis which is incorporated inside the optimization routine. In the displacement method, the number of equations needed to be solved is the number of degrees of freedom for the system whereas that for the force method is the number of redundant forces. If the number of degrees of freedom is greater than for the number of redundant in a structural system, the displacement method requires much more computer time than the force method does. Furthermore, the equilibrium matrix in the force method does not change in the redesign process making this method attractive and efficient. The DLM (Discrete Lagrangian Method) is an adaptation of usual Lagrange multiplier method to structural optimization problems using available sections have shown that it is robust and validate. To enhance the efficiency and robustness of the search for optimal larger structural design problems, an enhancing strategy for accelerating the search speed of the DLM. The advantage of using force method and the efficiency improvement of the force method will be discussed for discrete sizing optimization problems of structures.

並列關鍵字

Force Method ； Structural Optimization

參考文獻

1. Arora, J. S., and Govil, A. K., “An Efficient Method for Optimal Structural Design by Substructuring,” Computers and Structures, Vol. 7, No.4?B, pp. 507?515, 1977.

2. Arora, J. S., Introduction to Optimum Design, McGraw?Hill, 1989.

3. Arora, J. S., Huang, M.W., and Hsieh, C. C., “Methods for Optimization of Nonlinear Problems with Discrete Variables: A Review,” Structural Optimization, Vol. 8, pp. 69?85, 1994.

4. Cai, J., and Thierauf , G., “Discrete Optimization of Structures Using an Improved Penalty Function Method,” Engineering Optimization, Vol. 21, pp. 293?306, 1993.

6. Camp, C., Pezeshk, S., and Cao, G., “Optimized Design of Two?Dimensional Structures Using a Genetic Algorithm,” Journal of Structural Engineering, ASCE, Vol. 124, No. 5, pp. 551?559, 1998.