曲面結構多層次最佳化

Multilevel Optimization Design of Free-Form Structure

林家萱(Chia-Hsuan Lin)

指導教授 ： 呂良正

國立臺灣大學/工學院/土木工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202003032

摘要

隨著多樣化且具有流線形之大跨度薄殼結構設計成為趨勢，本研究主要探討之結構以自由曲面薄殼結構為主，除了透過自由曲面建模之技術模擬薄殼結構，也導入最佳化理論於設計之過程，並結合多種最佳化設計，目標以結構最大勁度或是結構最輕重量為主，提供設計者設計出兼具較佳力學行為、低成本與美學外型之結構設計結果。
本研究利用NURBS作為主要的自由曲面建模方法以及形狀最佳化時調整形狀的方法，透過控制點、節點向量和基底函數等進行參數化控制曲面形狀和建模，其中利用最佳化方法之循序二次規劃法(Sequential Quadratic Programming, SQP)做為最佳化方法，並結合形狀最佳化、支承位置的調整、薄殼厚度最佳化、鋼結構斷面尺寸最佳化等最佳化設計，提出多種多層次最佳化設計程序，並討論最佳化程序的順序性對最佳化之最終結果之影響。
為使最佳化結構的結果更趨近於真實，本研究在最佳化鋼網柵薄殼結構的部分，在施加載重時考慮活載重、自重及風載重對結構的影響，其中，風載重將以計算流體力學(CFD)模擬風載重在結構不同形狀時，結構上不同位置所受之風壓分布，最佳化程式中結合我國的鋼結構設計規範，設定出最佳化問題之限制式，使得鋼網柵薄殼結構之模擬結果更趨向現實，其分析結果更具參考價值。
本研究分析工具以Python語言進行程式撰寫和控制有限元素軟體ABAQUS進行分析，程式內容將包含上述提到之NURBS曲面建模方法，透過ABAQUS進行最佳化之自動化建模與分析，以獲得最終設計結果。

關鍵字

自由曲面 ； 結構最佳化 ； 形狀最佳化 ； 尺寸最佳化 ； 計算流體力學 ； 薄殼網柵結構

並列摘要

Shell structures are widely used in structure design due to the benefit of their load-carrying capacity or economical material. This thesis focuses on using free-form surface techniques to model thin shell structure. This thesis also integrates optimization theory to maximal the stiffness of structure or minimize weight of material. Therefore, we can obtain a final design considering both aesthetics, mechanical behaviors and cost of material.
In this thesis, we discuss some optimization, including shape optimization, sizing shell thickness optimization, sizing steel section optimization and adjusts the support location to optimization structure. We integrate different types of optimization and suggest different kinds of multilevel optimization. In the both shape and sizing optimization, sequential quadratic programming(SQP) is selected as the optimization method to find the best design of structure. In the free-form surface shape optimization problem, we use NURBS to modeling free-from shell structure and change the shape of structure in shape optimization problem. This method contains geometric tuning factors, such as control points, knots factor, etc.
In order to make the final optimization design results of structure more realistic, this thesis considers the effects of live load, dead load and wind load on the structure when optimization steel grid shell structure. We use Computational fluid dynamics (CFD) to analysis the wind pressure distribution of wind load in different shapes and positions of the structure and mapping them to the surface of structure. Furthermore, the multilevel optimization program of grid shell is combined with the constraint which are defined by Taiwan construction specification and limit conditions specified in the codes, such as limitation of strength and displacement. Through these considerations, the final optimization design results of the steel grid shell structure are more realistic, and the analysis results are more reference value.
This thesis develops Python program to control the finite element software ABAQUS modeling and analysis free-form structure. The Python program allows user to create free-form structure by previous parametric NURBS method. With the analysis results from ABAQUS, the program can carry out the optimization analysis automatically and find the final optimization design.

並列關鍵字

Free-form surface ； Structural optimization ； Shape optimization ； Sizing optimization ； Computational fluid dynamic ； Grid shell structure

參考文獻

李宗豪(2005)，以有限元素套裝軟體為分析引擎之最佳化設計系統架構開發，國立台灣大學土木工程學研究所碩士論文。

郭哲宇(2011)，加入隨機化之拓樸最佳化方法之研究及應用，國立臺灣大學土木工程學研究所碩士論文。

施可葳(2013)，元素交換法於結構拓樸最佳化之改良與應用，國立臺灣大學土木工程學研究所碩士論文。

Ansola, R., Canales, J., Tarrago, J. A., Rasmussen, J. (2004). Combined shape and reinforcement layout optimization of shell structures. Structural and Multidisciplinary Optimization, 27(4), 219-227

Arora, J. S. (2011). Introduction to Optimum Design. London, Academic Press.