應用不同有限元素於改進雙向演進法之拓樸結構最佳化

A Modified Bi-directional Structural Topological Optimization Using Various Finite Elements

朱嘉榮(Ka-Weng Chu)

指導教授 ： 鍾添東

國立臺灣大學/工學院/機械工程學研究所/碩士(2015年)

https://doi.org/10.6342/NTU.2015.02089

摘要

本文針對應用不同有限元素於雙向結構最佳化演進法進行研究及探討。由於結構最佳化演進法只容許元素的刪除，因此往往在一些邊界條件中未能完成整個演進法，為了解決這些問題，容許補回元素的雙向結構最佳化演進法被提出，並結合了投影的概念使元素的敏感度分佈更平滑改良結構最佳化演進法。本研究利用不同有限元素於雙向結構最佳化演進法，通過範例說明不同元素在演進過程的穩定性、演進率相依及元素類型相依問題進行說明。同時提出改良之加工方向限制使雙向結構最佳化演進法可配合及解決更多之機械加工問題。本文通過結合程式語言及有限元素分軟體，建立出一套結構拓樸最佳化演進法軟體，使用者可以通過參數簡單地應用。而結合了不同元素類型及改良的加工方向限制之雙向結構最佳化演進法及軟體之應用及可行性已通過範例進行驗證。

關鍵字

拓樸最佳化 ； 結構最佳化演進法 ； 有限元素類型 ； 加工限制

並列摘要

This thesis studies bi-directional evolutionary structural optimization method (BESO) by using various finite elements. Evolutionary Structural Optimization method (ESO) fails in some boundary condition cases because of its simple procedure in removing elements. To solve this problem, BESO method is modified by filling back element with combing the concept of smoothing and projection. The research of using different finite elements in BESO method is proposed in this thesis. Several examples are illustrated against the stability of evolution process, evolution rate and structural element dependence problems, etc. At the same time, the modified draw direction constraints can be applied to solve more situations the machining problem. A BESO program which integrates Visual Studio and ANSYS is developed, and the parametric parameters make the users easily to apply. The feasibility and the application of BESO method applying to different element types and the modified draw direction constraints are proved in this thesis through the numerical examples.

並列關鍵字

Topology optimization ； Evolutionary structural optimization ； finite element types ； Manufacturing constraints

參考文獻

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