結構最佳設計力學於對應系統動力尖峰反應之極限載重研究

載重反應關聯法（Load response correlation method，簡記為LRC法)是將結構承受之外力載重歷時等值為其極限靜力載重分佈，對應於此載重分佈之靜力位移場域，即為結構系統之動力尖峰變形反應。因此，由LRC力學理論，結構系統承載其外力載重歷時之特定等值極限靜力載重分佈下，以靜力結構分析結果即可得系統之動力尖峰位移反應，因而能較為便捷地求得結構系統於動力載重下的極值反應行為。本論文研究成功地融合了LRC法與結構最佳化設計演算法，藉由本研究成果，靜力結構最佳化問題與設計方法，可通用地推廣至結構承受動力荷載的情況。另一方面，本論文之各結構最佳化演示例題中，除以靜力環境下的情況進行最佳化設計，且與其相對應文獻之分析與設計結果一一比較，以檢核本研究所提出融合LRC理論之最佳計算力學方法外，並使用有限元素套裝軟體ABAQUS對於結構設計進行動力分析，以驗證系統最佳設計結果之動力尖峰變形反應均符合設計限制條件。綜合而論，本研究提出一創新之結構最佳設計方法，期能將計算力學於結構動力最佳化設計問題推展至新的層面。

關鍵字

結構最佳化；載重反應關聯法； Newmark分析

並列摘要

Load response correlation (LRC) method is used to transform dynamic load distributions applied on structures into equivalent extreme static loads. Structural responses correlated to such equivalent static load distribution are called the dynamic peak responses of the structures. Hence, through LRC method, dynamic peak responses of structural system under the distribution of equivalent extreme static loads, which are transformed from loading history, are thus simply obtained by static analysis. This study successfully integrated LRC method with structural optimization algorithm. With the proposed design scheme, static structural optimization problems can be extended to another scenario which structures are subjected to dynamic loads. In this thesis, for each optimization example, optimization was not only performed under static loading condition, but the result was compared with references to examine the effectiveness of the proposed method for integrating LRC method and optimization algorithm. In addition, a finite element analysis package- ABAQUS was applied to execute dynamic analysis on optimized structures in order to identify that the peak dynamic responses of the optimized structures meet the design constraints. To sum up, this research proposed an innovative structural optimization method, anticipating it could provide computational mechanics with a new avenue toward engineering design problems.

並列關鍵字

Structural Optimization ； Load-Response-Correlation Method ； Newmark Analysis

參考文獻

Wang, M. Y., Wang, X., & Guo, D. (2003). A level set method for structural topology optimization. Computer Methods in Applied Mechanics and Engineering, 192(1–2), 227-246. doi:https://doi.org/10.1016/S0045-7825(02)00559-5

Adeli, H., & Kamal, O. (1986). Efficient optimization of space trusses. Computers and Structures, 24(3), 501-511. doi:10.1016/0045-7949(86)90327-5

Adeli, H., & Kumar, S. (1995). Distributed genetic algorithm for structural optimization. Journal of Aerospace Engineering, 8(3), 156-163. doi:10.1061/(ASCE)0893-1321(1995)8:3(156)

Arora, J. S. (1989). Introduction to optimum design. Singapore: McGraw-Hill.

Atkinson, K. E. (1989). An introduction to numerical analysis (2nd ed ed.) Wiley. Retrieved from http://ci.nii.ac.jp/ncid/BA06815441

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結構最佳設計力學於對應系統動力尖峰反應之極限載重研究

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