應用多目標粒子群演算法於測力計拓樸最佳化

Topology Optimization of a Load Cell via a Multi-objective Particle Swarm Algorithm

蔡至捷(Chih-Chieh Tsai)

指導教授 ： 盧中仁

國立臺灣大學/工學院/機械工程學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201802867

摘要

優良的測力計需要較高的基頻以及較大的撓性以符合精度要求，這兩個互相衝突的要求很難同時滿足。本研究的目的是尋找適當的拓樸結構使得測力計能滿足這兩個設計規範。本研究設定測力計為桿件組成的平面構架，桿件的節點和截面尺寸為設計變數，目標函數為構架的基頻和自由端的面外靜力位移。在材料性質固定的前提下，在設計空間中，利用多目標粒子群演算法尋找測力計的拓樸最佳化設計。以有限元素法計算所指定的目標函數值。多目標粒子群演算法則參考Coello提出MOPSO[1]，以網格劃分、指定適應性與輪盤選擇，維持粒子的多樣性。本研究嘗試數種不同的構架建構方式，發覺對稱於中心線的基部斜撐補強構架有最好的效能。首先固定截面尺寸，改變節點的位置得到最佳的拓樸形狀；接著再將所得的構架細分，藉由改變各段截面尺寸更進一步優化。最後將所得的最佳設計和前人的設計相比較。

關鍵字

多目標粒子群演算法 ； MOPSO ； 拓樸最佳化 ； 有限元素法 ； 尤拉樑理論

並列摘要

A good load cell should have a wide band-width and large flexibility to meet the demand of high resolution. It’s very difficult to satisfy these two conflicting demands. This research aims to find a proper design, thorough topology optimization, of a load cell possessing both proper band-width and flexibility. The load cell studied in this thesis is a planar frame. The position of every joint and cross-section area of each rod are used as design variables. The objective functions are the fundamental frequency and the static deflection at the free end of the structure. The Pareto solutions in the design space are located by a multi-objective particle swarm optimization (MOPSO) algorithm. The values of the objective functions are determined using an in-house finite element method code. The MOPSO algorithm proposed by Coello [1], which introduces a mutation operator and a roulette-wheel selection scheme for maintaining the diversity of the particles, is employed to find the optimal designs. In this thesis, several schemes for constructing the frame of the load cell are tested. The symmetrical structures with angle braces have the best performance. In order to find proper designs in a feasible time, we first determine the primary frames under the restriction that the every rod has the same cross-sectional area. Then a primary design in the Pareto set is chosen and further optimized. In the final optimization process, the cross-sectional dimensions of each rod as well as the coordinates of each joint are used as design variables. The final optimal designs are compared with previous designs obtained using different topological optimization algorithms.

並列關鍵字

multi-objective particle swarm optimization ； MOPSO ； topology optimization ； finite element analysis ； Euler beam Theory

參考文獻

參考文獻

[1] Coello, C. A. C., Pulido, G. T., and Lechuga, M. S., "Handling Multiple Objectives with Particle Swarm Optimization," IEEE Transactions on Evolutionary Computation, 8(3), pp. 256-279, 2004.

[2] Bendsøe, M. P. and Kikuchi, N., "Generating Optimal Topologies in Structural Design Using a Homogenization Method," Computer Methods in Applied Mechanics and Engineering, 71(2), pp. 197-224, 1988.

[3] Bendsøe, M. P., "Optimal Shape Design as a Material Distribution Problem," Structural Optimization, 1(4), pp. 193-202, 1989.

[4] Zhou, M. and Rozvany, G., "The COC Algorithm, Part II: Topological, Geometrical and Generalized Shape Optimization," Computer Methods in Applied Mechanics and Engineering, 89(1-3), pp. 309-336, 1991.