應用拓樸最佳化與B-spline函數於結構外形設計之研究

A Study of Structural Shape Design by Topology Optimization and B-spline Function

顏金田(Chin-Tien Yen)

指導教授 ： 張永康

淡江大學/工學院/航空太空工程學系碩士班/碩士(2007年)

https://doi.org/10.6846/TKU.2007.00743

摘要

本論文是應用拓樸最佳化與B-spline函數於結構外形設計之研究。研究中使用ANSYS做為結構分析的工具，並利用拓樸設計方法中之最佳材料分配法配合逐次線性規劃法以獲得最佳結構外形。在本文中除使用混合法同時保留必要元素與排除非必要元素來減少不合理之情形外，並應用B-spline函數之概念，定義設計參數上下限來平滑結構外形。本研究採用三階段的設計來進行結構最佳化，經過這三個階段拓樸最佳化設計後，可改善傳統拓樸最佳化設計結果不平滑之現象，以達到更具實用性之結構外形設計。

本研究以六個不同結構範例探討結構最佳化設計問題，其結果顯示出所得到的結構外形比只使用傳統拓樸最佳化之結構外形更加的清晰，結構形狀更易於製造加工。期望以本研究之方法應用於工業界實際的結構設計問題上，能有效地達到結構最佳化的需求並增加製造上的便利性。

關鍵字

拓樸最佳化 ； 結構外形設計 ； B-spline函數

並列摘要

A Methodology of structural shape design by topology optimization and B-spline function was developed in this study. The finite element analysis software ANSYS was used for structural analysis. The optimum shape design was obtained by the concept of material distribution borrowed from density method with sequential linear programming. In addition to using the element growth-removal combined method (EGRCM) simultaneously to grow and remove the essential element and the non-essential element, the concept of B-spline curve was used to smooth the design shape.Three stages topology design was employed in this study. After three stages design strategy , the primitive optimum design can be improved to more practical design.
Six examples were discussed in the numerical examples. The results of final design were better than the traditional topology design. We hope the results of this study can provide the convenience of manufacturing to the industry of structural design.

並列關鍵字

Topology Optimization ； Structural Shape Design ； B-spline function

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