應用有限元素法分析生物薄殼材料的力學性能

Finite Element Analysis of the Mechanics of Biological Shells

顏安(An Yen)

指導教授 ： 莊嘉揚

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/NTU201802125

摘要

鳥類被認為是存活至現代的恐龍，具有很高的物種多樣性，是一群在生物演化上極為成功的動物。鳥類除了擁有飛行能力，還具備非常有效的生殖模式：以硬殼的卵孕育幼鳥。鳥類的蛋殼必須足夠堅固而能在親鳥接觸孵化的過程中承受重量，孵化完成之後幼鳥又能順利破殼而出。這兩個相互矛盾的條件暗示了一個最佳化的設計準則。本研究結合薄殼理論、壓縮試驗及有限元素法，建構一個用以分析蛋殼力學的模型。對收集到的鳥蛋進行壓縮試驗，以此為基礎建立有限元素模擬的方法。利用有限元素模擬，除了可以與實驗做比較，還能夠分析無法實際取得的蛋殼，拓展了研究對象的種類和數量。本研究將挫曲失效模式視為蛋殼的承重極限，定義了一個無因次的標準化參數作為蛋殼本質剛性的指標。研究結果得到一個接觸孵化體重上限的理論值，同時顯示鳥類蛋殼具有一定的不變量。這個不變量除了可視為鳥類蛋殼本身的設計準則，也對鳥類的演化和生殖模式提供線索。

關鍵字

薄殼理論 ； 有限元素法 ； 鳥類蛋殼 ； 接觸孵化 ； 異率測定

並列摘要

Birds are a group of successfully evolved animals. They are widely recognized as the descendants of dinosaurs and exhibit exceptional diversity. In addition to the capability of flight, birds are characterized by their efficient reproduction method through the laying of hard-shelled eggs. An avian eggshell has to be robust enough to withstand the body weight of its parent bird during contact incubation, but remain breakable for the chick to hatch. These contradicting demands require an optimization. This research combines shell theory, compression test, and finite element method (FEM) to construct a model for analyzing the mechanics of eggshells. Compression tests are conducted for the collected egg samples and a simulation method, using FEM, is developed based on the experiment. The result of the finite element simulation not only offers a comparison to those of the experiments but also provides a way of analyzing eggshells that cannot be collected. This greatly expands both the variety and the number of studied objects. A dimensionless normalized parameter is defined to indicate the shell stiffness, and the failure mode of buckling is considered as an indication of the load-bearing limit. The results show a theoretical upper limit of body mass for contact incubation and reveal certain degrees of invariance in avian eggshells throughout evolution. The invariance can be viewed as a design guideline for eggshells and provide implications for the evolution and reproductive mode of birds.

並列關鍵字

shell theory ； finite element method ； avian eggshell ； contact incubation ； allometry

參考文獻

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