最佳化演算法應用於薄殼結構之主應力線加勁設計

Abstract

近年來隨著設計與分析工具的進步，建築師擁有更為多樣的設計選擇，其中形狀複雜且承載能力佳的薄殼結構成為了許多建築物的外型首選。本研究透過自由曲面建構技術，結合有限元素分析以及最佳化理論，推出一系列薄殼結構最佳化設計流程，供予建築師以及結構工程師們參考，以利設計出兼顧力學性質以及視覺美感之最佳薄殼結構。 對於大跨度之薄殼結構，為提高結構勁度，除了幾何形狀最佳化設計之外，須給予其額外之加勁輔助結構，因此加勁方式的設計至關重要。本研究著重於薄殼結構附屬加勁梁之最佳化設計，尤其以加勁梁之配置為重。以主應力線之走向作為加勁梁之分布依據，透過多種最佳化演算法，結合整體結構之尺寸最佳化，於固定體積下設計出具有最高勁度之薄殼結構。 於眾多聞名的薄殼結構中，選擇位於美國新澤西州 (New Jersey) 的聖阿洛伊修斯教堂 (The Church of St. Aloysius) 作為案例，根據本研究之薄殼結構最佳化設計流程進行設計以及探討。將現行規範之限制以及載重組合納入考量。比較該案例之初始結構與最佳化設計之結果，應證了本研究之薄殼結構最佳化設計確實能於兼顧現行規範以及美學觀感的同時，大幅提升結構之力學表現。

In recent years, thin-shell structures with complex shapes are extensively used in civil and architectural engineering due to the efficient load-carrying capacity. However, most of the thin-shell structures are designed on the basis of architects’ aesthetic point of view, rather than the mechanical performance. Therefore, this research demonstrates an optimal thin-shell structure design method that integrates free-form surface technology with finite element method and optimization theory in considering of both aesthetics and mechanical behaviors. Large-span shells generally require not only optimal geometric design but also additional support to improve the stiffness of the structures. Hence, it is crucial to decide the way to fortify the structures. This research focuses on the optimization of the ribs attached to the thin-shell structures, with particular emphasis on the layout of the ribs. The distribution of the ribs is based on the orientation of the principal stress lines which demonstrate the paths of stress flow. In the optimization process, a variety of optimization algorithms are combined to retrieve the optimal thin-shell structures with the highest stiffness. To verify the optimization method, this research chooses The Church of St. Alioysius in New Jersey, USA, as a case study. Comparing the analysis results between the initial structure and the optimal design while taking the limitations of current codes and load combinations into account, the stiffness of the structure has significantly improved. It shows that the optimal thin-shell structure design method by this research can indeed enhance the mechanical performance of the structure while considering both aesthetics and the limitations of the current codes.