以Python整合有限元素軟體ABAQUS於板殼結構最佳化

Abstract

本研究使用直譯式程式語言Python開發結合有限元素套裝軟體ABAQUS的結構最佳化程式，將設計領域拓展至三維不規則板殼結構的應用。 ABAQUS軟體能簡化繁瑣的有限元素分析過程，本研究將應用此程式於較複雜難解的結構問題，包含積層板的幾何非線性分析、結合梁元素的板殼加勁分析與計算厚度方向差異的連續殼有限元素分析等例題。 本研究主要分為曲面最佳化與拓樸最佳化兩部分，分別撰寫兩套符合設計需求之自動化建模與分析程式，並探討適用之最佳化演算法。曲面最佳化以NURBS曲面的數值建模方法設計，使用Python第三方模組提供之循序二次規劃法(Sequential Quadratic Programming, SQP)進行最佳化分析。 拓樸最佳化演算法採用本研究團隊過去曾使用的最佳化演進法ESO (Evolutionary structural optimization, Xie et al. 1993 1997)、元素交換法EEM (Element Exchange Method, Rouhi et al. 2010)和固體等向性懲罰函數法SIMP (Solid isotropic material with penalization, Bendsøe 1989; Rozvany et al. 1992)三種方法，並比較三種方法應用於板殼拓樸結果的正確性、穩定性與收斂速度。其中，ESO容易落入局域解、EEM所需迭代步數較多；SIMP較為穩定但計算量較大。此外，本研究亦探討不同設計變數之拓樸方法，助於設計較符合現實情況的板殼結構問題。 本程式之板殼模型的最佳化設計結果與文獻結果比較後，結果大致吻合，驗證最佳化設計系統於板、殼問題的正確性與廣用性，以期推廣最佳化設計的運用範圍並吻合真實建築設計的需求。

This thesis integrates structural optimization problem of 3-dimensional irregular geometric plate and shell structure with Python program for iterative calculation and the FEM commercial software ABAQUS as an analysis engine. Since ABAQUS simplifies the difficult and complicated FEM analysis process, it will be of great benefit to several hard-solving structural iterative optimization design problem, including the geometric nonlinear analysis of laminated plates, plates and shells analysis that combine with stifferner of beam-element, and multi-layered plate analysis by using continuum shell element for solving thickness direction behavior, etc. In this thesis, shape optimization and topology optimization problem are classified as two main part, and codes with suitable algorithm for automatic modeling and optimization analysis are designed respectively. Shape optimization uses NURBS surface for modeling and Python third-party optimizing module for sequential quadratic programming(SQP) method. Topology optimization algorithm uses the past designing methods in our research group, including evolutionary structural optimization (ESO; Xie et al. 1993 1997), element exchange method (EEM; Rouhi et al. 2010),and solid isotropic material with penalization (SIMP; Bendsøe 1989; Rozvany et al. 1992). Comparing correctness, stability and rate of convergence of topology result, it can be found that ESO algorithm is easy to fall into locally optimum solutions, while EEM and SIMP algorithm are both easier to perform better results. However, imperfectness of EEM and SIMP still exist. EEM takes more time for a large number of iteration steps; SIMP used to perform stable result but takes more calculation of programming. The Python program in this thesis is tested. That is, most of the plate and shell structure optimization problems lead to the same result as the past research. Verifying the correctness and applicability of this program, it is expected to expand range of application and meet the requirements of architecture design.