具有加工限制之結構最佳化雙向演進法

Bi-Directional Evolutionary Structural Optimization Method with Manufacturing Constraints

王嘉霈(Jia-Pei Wang)

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(2013年)

https://doi.org/10.6342/NTU.2013.00070

摘要

本文針對演化率相依問題與加工限制，修正篩選機制與元素增減準則，提出修正式結構最佳化雙向演進法。修正式篩選機制隨著演化過程逐漸縮小篩選半徑，而非選用固定長度的篩選半徑。此修正有助於抑制演化率相依問題，進而提升結構最佳化雙向演進法之穩定性。另一方面，由所需的加工方式而決定的拉拔方向限制，可藉由修正元素增減準則來實現。修正式元素增減準則從拉拔方向的表面往設計區域的內部逐漸移除元素。有拉拔方向限制的最佳設計可避免出現中空或封閉孔洞等難以加工的幾何形狀，因此提升結構最佳化雙向演進法的實用性。本文整合修正式結構最佳化雙向演進法與有限元素分析軟體，發展出一套結構拓樸最佳化軟體。其結果驗證本文所提出的修正方法在結構拓璞最佳化中之可行性及實用性。

關鍵字

結構最佳化 ； 結構最佳化演進法 ； 網格獨立篩選機制 ； 加工限制

並列摘要

This thesis proposes a modified bi-directional evolutionary structural optimization (BESO) method which combines a modified filter scheme and a modified element removal/addition criterion for evolution ratio dependence problem and manufacturing constraints. Instead of selecting a fixed length of filter radius, the modified filter scheme decreases the length of filter radius through the evolution process. Such modification contributes to the suppression of evolution ratio dependence problem, and therefore enhances the stability of BESO method. On the other hand, draw direction constraints, defined by required manufacturing process, are achieved by modifying the element removal/addition criterion. Modified element removal/addition criterion gradually removes elements from top surface of the draw direction to the inner design domain. The optimal designs with draw direction constraints are free from hollow or closed cavity geometries which are infeasible for manufacturing, and therefore the practicability of BESO method is enhanced. A structural topology optimization program which combines the proposed modified BESO method and ANSYS is developed. The results prove the validity and practicability of the proposed modifications in structural topology optimization.

並列關鍵字

structural optimization ； evolutionary structural optimization ； mesh-independency filter ； manufacturing constraints

參考文獻

[3] Mitchell, A. G. M. (1904). The limits of economy of material in framed structures. Philosophical Magazine, Series 6, 8(47), 589-597.

[5] Kirsch, U. (1989). Optimal topologies of truss structures. Computer Methods in Applied Mechanics and Engineering, 72(1), 15-28.

[6] Bendsoe, M. P., & Kikuchi, N. (1988). Generating optimal topologies in structural design using a homogenization method. Computer methods in applied mechanics and engineering, 71(2), 197-224.

[7] Mlejnek, H. P. (1993). Some explorations in the genesis of structures. In Topology design of structures (pp. 287-300). Springer Netherlands.

[8] Bendsoe, M. P. (1989). Optimal shape design as a material distribution problem. Structural Optimization, 1(4), 193-202.