具自由曲面薄殼結構最佳化設計

Optimal Design of Free-Form Thin Shell Structures

林享樑(Hsiang-Liang 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(2018年)

https://doi.org/10.6342/NTU201801727

摘要

近年來，將美學應用於結構工程上的案例逐漸增加，尤以薄殼結構的造型更具多樣化，但往往其幾何不是最佳的設計。因此本研究透過建構自由曲面技術(Free-form surface)模擬薄殼結構，並結合最佳化理論，以獲得一兼具美學外型及力學性質的設計結果。
自由曲面建構方法多樣化，本研究將使用四種建構方法，包含NURBS、貝茲曲線、類貝茲曲線以及P-curve，四種建構方法會以控制點、各自的基底函數及相對應的調整係數或節點向量控制整個曲面的幾何，並結合最佳化方法循序二次規劃法(Sequential Quadratic Programming, SQP)做最佳化設計。
將自由曲面形狀最佳化結合不同的最佳化種類，分別結合拓樸及厚度最佳化，做多層次(Multi-level)結構最佳化設計，並輔以例題演示最佳化結果及其效果，其中拓樸最佳化演算法選擇固體等向性懲罰函數法(Solid Isotropic Material with Penalization)；厚度最佳化以本研究提出的簡易厚度調整方法進行設計。
在世界各地有不同幾何形狀之薄殼結構，本研究將參考著名的案例，對實尺寸薄殼結構做最佳化設計，考慮自重、活載重及風載重對結構的影響，風載重部分以計算流體力學(CFD)模擬結構所受之風壓分布，並結合我國的設計規範，將規範訂為最佳化問題之限制式，透過上述方法，更能準確模擬實際薄殼結構力學行為，其最終設計結果會更有參考價值。
本研究分析工具以Python語言進行程式撰寫，結合有限元素軟體ABAQUS做分析，程式內容包含將上述提到四種曲面建模方法，並於ABAQUS中自動化建模與分析，接著將ABAQUS分析結果進行最佳化分析，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 ； 拓樸最佳化 ； 尺寸最佳化 ； 計算流體力學 ； 薄殼結構 ； 有限元素套裝軟體

並列摘要

Recently, there are more structural engineering examples combined with aesthetics, especially the geometry of thin shell structures. However, these famous shell structures are probably not the optimal designs. Designs of most shell structure are just based on the architects’ experience. Therefore, this thesis focuses on using free-form surface techniques to model thin shell structure and integrates these techniques with optimization theory to obtain a final design considering both aesthetics and mechanical behaviors.
In this thesis, four parametric methods will be chosen as the approaches to construct the free-form surface, including NURBS, Bézier curve, Bézier -like curve and P-curve. Each method contains its own geometric tuning factors, such as control points, knots factors, etc. According to these information, the whole surface can be constructed easily. In the free-form surface shape optimization problems, sequential quadratic programming (SQP) is selected as the optimization method to find the best design.
Besides shape optimization, topology optimization and sizing optimization are also another types of structural optimization. Hence, shape optimization integrated with topology optimization and sizing optimization are demonstrated respectively in this research. Topology optimization algorithm uses solid isotropic material with penalization (SIMP). In sizing optimization part, the simple thickness tuning method is developed to change the element thickness.
Thin shell structures are constructed all over the world. In this research, some famous thin shell structures are taken as examples and utilized these examples as the initial models of the optimization problems. When engineers design the real thin shell structure, some factors that may influence the shell structure must be considered, such as load cases, structural strength, maximum displacement, etc. Self weight, live load and wind load are often considered as the major load cases. In order to acquire the wind pressure among the complicated geometry of shell surface, computational fluid dynamic (CFD) analysis will be used. A distribution of wind pressure in fluid field would be solved by CFD analysis and then be applied on the surface of shell structures. By referring to Taiwan construction specifications, limit conditions specified in the codes, such as limitation of strength and displacement, are defined as the constraints of optimization problems. By applying these tecniques to real shell structure shape optimization problems, much more practical optimal designs will be obtained. Consequently, engineers and architects can take the optimal results as the design reference.
This research develops Python program to connect the finite element analysis commercial software ABAQUS. The Python program allows users to create free-form surface by four mentioned parametric methods and implement finite element analysis in ABAQUS automatically. With the analysis results from ABAQUS, the program can carry out the optimization analysis and find the final optimal results.

並列關鍵字

Free-form surface ； structural optimization ； shape optimization ； topology optimization ； sizing optimization ； computational fluid dynamic ； thin shell structure ； finite element package

參考文獻

Ansola, R., Canales, J., Tarrago, J. A., & Rasmussen, J. (2002). An integrated approach for shape and topology optimization of shell structures. Computers & structures, 80(5-6), 449-458.

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

Andreassen, E., Clausen, A., Schevenels, M., Lazarov, B. S., & Sigmund, O. (2011). Efficient topology optimization in MATLAB using 88 lines of code. Structural and Multidisciplinary Optimization, 43(1), 1-16.

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

Bézier, P. E. (1968). How Renault uses numerical control for car body design and tooling (No. 680010). SAE Technical Paper.