應用多目標基因演算法於測力計拓樸最佳化

Topology Optimization of a Load Cell via a Multi-objective Genetic Algorithm

江倚瑄(Yi-Syuan Jiang)

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(2016年)

https://doi.org/10.6342/NTU201601766

摘要

量測昆蟲振翅力的測力計需要較高的基頻以及較低的剛性以符合精度要求。本研究的目的是尋找測力計的最佳拓樸結構使其能有高基頻和低剛性。在材料性質固定的前提下，以矩形為設計範圍，利用多目標基因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。多目標基因演算法則參考NSGA-Ⅱ的非受控排序法和群聚比較法，避免在演算過程中錯失較好的結果，並且維持族群的多樣性。
測力計的邊界條件和外力都對稱於中心線，因此本研究在計算過程中強制測力計結構有同樣的對稱性。另外也計算沒有強制對稱的測力計並比較其和對稱測力計的異同。為了節省計算時間，先以粗網格作全域設計範圍的初步拓樸最佳化，接著以初步最佳化的結果進行局部優化以減少需要計算的元素數量。最後以3D列印製造數個不同的最佳化設計的原型，量測這些原型的特性並和數值模擬的結果相比對。

關鍵字

多目標基因演算法 ； NSGA-Ⅱ ； 拓樸最佳化 ； 有限元素法 ； 古典平板理論

並列摘要

A load cell for measuring the lift force generated by flapping wings of an insect must have a high fundamental frequency and low stiffness to meet the stringent precision requirements. This thesis aims to design a load cell that can record the waveform of the lift of an insect accurately. Starting from a rectangular shape with specified material properties, a multi-objective genetic algorithm, called NSGA-II, is employed to find the optimal shape of the load cell. A finite element analysis program is developed to determine the values of the objective functions. In NSGA-II, the non-dominated sorting method and crowded-comparison approach are used to increase the genetic diversity as well as keep the elite genes.
Because the boundary conditions and applied force are symmetric with respect to the central line of the load cell, we restrict the outcomes of the optimization program to symmetrical structures. The restriction is then removed. The performance of the asymmetrical optimal results thus generated is compared with that of the performance of the symmetrical ones. In order to reduce the computation time, the optimization is first performed on a coarse mesh for the generation of primitive structures. Then the meshes of some specified areas of a primitive optimal structure are refined. Optimization is performed on the refined meshes to determine the final topology of the load cell. In this way, the computational burden can be largely reduced. Prototypes of several optimal designs are manufactured by 3D printing. Experimental test results for the fundamental frequency and flexibility of these prototypes are compared with those of the numerical simulation.

並列關鍵字

multi-objective genetic algorithm ； NSGA-Ⅱ ； topology optimization ； finite element analysis ； Classical Plate Theory

參考文獻

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