最佳準則法於結構輕量化設計之應用

Application of Optimality Criteria to Minimum Weight Design of Structures

陳冠華(Kuan-Hua Chen)

指導教授 ： 莊德興

國立中央大學/工學院/土木工程學系/碩士(2008年)

摘要

本文主要是採用兩階段的最佳準則(Optimality Criteria)設計程序來進行結構輕量化問題，限制條件包括位移、應力及挫屈載重因子等限制。進行設計之前，先以Fully Stressed Design(FSD)程序對含有應力限制的問題調整設計變數。兩階段的最佳準則法設計程序是在第一階段採用較大更新因子快速搜尋近似最佳解，並於第二階段藉由降低更新因子以減緩移動步幅，來找出較佳之輕量化設計結果。數個桁架與剛構架的設計例的輕量化設計結果顯示，本研究建議之兩階段設計程序具備快速而穩定收斂的特性，求解品質亦相當接近文獻的結果，甚至更佳。

關鍵字

最佳準則法 ； 輕量化設計 ； 兩階段設計程序 ； 位移限制 ； 應力限制 ； 挫屈載重因子限制

並列摘要

In this report, the minimum weight design of trusses and rigid frames by using a two-stage design procedure based on the optimality criteria method is studied. The behavior constraints considered in this study include the constraints on displacement, stress, and buckling load factor. In this study, the independent variables of a structure with stress constraints are adjusted by using the fully stressed design procedure first. Then, the variables are designed by using the two-stage design procedure. In the two-stage design procedure, a larger exponent of the recursive relation is used to search for a near optimal solution first, and a smaller exponent is then used in the second stage to slow down the moving velocity and to fine tune the solution quality. Several trusses and rigid frames studied in the literature are used to demonstrate the efficiency and the solution quality of the proposed design procedures. Comparative results show that the proposed optimality criteria method can efficiently find good quality solutions for the designed structures.

並列關鍵字

optimality criteria method ； minimum weight design ； two-stage design procedure ； displacement constraints ； stress constraints ； buckling load factor constraint

參考文獻

[5] Gallagher, R.H., “Fully-stressed design,” In Optimum Structural Design, Theory and Applications, Chapter 3, R. H. Gallagher and O.C. Zienkiewicz(Eds.) John Wiley and Sons (1973).

[2] Michell, A.G.M., “The limits of economy of material in framed structures,” Phil. Mag. (series 6), Vol. 8, pp.589-597 (1904).

[6] Venkayya, V. B., “Design of Optimum Structure,” Computers and Structures, Vol. 1, pp. 265-309 (1971).

[7] Khot, N. S., Venkayya, V. B., and Berke, L., “Optimum Design of Composite Structures with Stress and Displacement Constraints,” AIAA 13th Aerospace Sciences Meeting, Pasadena, California, USA, Vol. 2, No. 28, pp.75-141 (1975).

[12] Dobbs, M. W., and Nelson, R. B., “Application of Optimality Criteria to Automated Structural Design,” AIAA Journal, Vol. 14, pp. 1436-1443 (1976).