以整合力法為分析工具之結構離散輕量化設計效率的探討

Discrete optimum design of structures using integrated force method

陳冠廷(Kuan-Ting 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(2011年)

摘要

本文主要是以整合力法(Integrated force method, IFM)搭配和聲搜尋(Harmony Search, HS)與離散拉格朗日法(Discrete Lagraingian Method, DLM)組成之混合演算法進行離散結構之最佳化設計。探討整合力法與傳統贅力法、位移法所需結構分析時間之差異，並利用混合式搜尋法希望藉以提升最佳解之品質，藉以改善最佳解整體之計算效率。本文使用整合力法進行結構分析運算過程中，使用虛擬反矩陣法(Psedo-inverse method)與奇異值分解法(Singular Value Decomposition, SVD)求得諧和矩陣；另外透過有限元分析建立力平衡矩陣，透過諧和矩陣與力平衡矩陣即可直接求得各桿件內力，並藉此反求結構各自由度位移。本文藉由數個結構離散輕量化設計例比較本文方法之優異性，並於部分算例同時考慮LRFD鋼結構設計規範。結果顯示整合力法能夠較位移法節省許多計算時間，並且可有效利用HS-DLM混合搜尋法獲得可能之整體最佳解。

關鍵字

整合力法 ； 和聲搜尋法 ； 離散拉格朗日法 ； 結構輕量化設計

並列摘要

In this article, the discrete structural optimization problem solves by using HS-DLM in conjunction with the integrated force method (IFM) of analysis is presented. In IFM, all the element forces are taken as the independent variables instead of the redundants as the prime unknowns.
The equilibrium matrix is generated automatically through the finite element analysis and the compatibility matrix is obtained directly using the displacement-deformation relations and singular value decomposition (SVD) technique. By combining the compatibility and equilibrium matrix, the structural element forces are obtained directly. And the displacement can de back-calculated through the element forces. The results of the analysis are compared with the results of the redundant force method and displacement method. The design examples have been demonstrated that integrated force method is efficient and equally viable as compared to the displacement method. The results also shows HS-DLM algorithm is reliable, and the solution quality of the optimum design problems studies in the literature is comparable to other optimal method.

並列關鍵字

Harmony search method ； Discrete lagrangian method ； Optimum structural design ； Integrated force method

參考文獻

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