橡膠材料有限大圓孔非對稱變形近似解的誤差分析

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姓名

馮詩維(Shi-Wei Feng) 查詢紙本館藏

畢業系所

土木工程學系

論文名稱

橡膠材料有限大圓孔非對稱變形近似解的誤差分析
(The rubber Materials of finite voids of asymmetric deformation of the approximate solution of the error analysis)

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摘要(中)

摘　　　要
本文在探討不同橡膠材料模型中(包含Ogden、Beda、Mooney-Rivlin、neo-Hookean材料模型)有限大孔洞的非對稱變形。而橡膠材料在不少地方都有使用到，如土木工程的橋樑支承、機械工程的輪胎或皮帶等等都有使用到橡膠材料。本文將探討在Hou和Abeyaratne[21]的文章裡所提到的圓孔非圓對稱變形的近似解，此解使用橢圓變形公式來逼近圓孔的非對稱變形，本文則探討此近似解在各種橡膠材料模型下的誤差。
關鍵字: 橡膠材料、Hou-Abeyaratne filed (HAF)、誤差

摘要(英)

Abstract
This thesis investigates the asymmetrical deformation of finite voids in rubber materials described by different models includes Ogden,Beda, Mooney-Rivlin and neo-Hookean materials model. The use of rubber materials is extensive, such as bridge supports in civil engineering,tires and belts in mechanical engineering .This thesis analyzes the approximate solution proposed in [21] for asymmetrical deformation of a circular voide. This approximate solution was proposed by assuming that the circular void will be deformed into an elliptical one. This thesis compute the error of this approximate solution for materials modelled by those models mentioned above.
Keywords: Rubber, Hou-Abeyaratne filed (HAF),error

關鍵字(中)

★ Hou-Abeyaratne filed (HAF)
★ 橡膠材料
★ 誤差

關鍵字(英)

★ error
★ Hou-Abeyaratne filed (HAF)
★ Rubber

論文目次

目　　　錄
摘　　　要 I
Abstract II
誌　　　謝 III
目　　　錄 IV
圖目錄 V
符號表 X
第一章緒論 1
第二章基礎理論 6
2-1橡膠材料變形控制方程式的推導 6
2-2計算出壓力場的梯度 8
2-3誤差原理 9
第三章 Hou-Abeyaratne變形場 12
3-1 Hou-Abeyaratne變形場公式推導 12
3-2圓對稱與非圓對稱圓孔變形 16
3-3球體兩種會產生exact solution的變形形態: 21
第四章誤差之比較 29
4-1 HAF yi=Aiψi(R)Xi的誤差 29
4-1-1四種真實材料之誤差比較 29
4-1-2主伸展應變λ1、λ2、λ3的比值大小不同之誤差比較 34
4-2 改良HAF yi=Aiψi(ρ)Xi的誤差 43
4-2-1四種真實材料之誤差比較 44
4-2-2主伸展應變λ1、λ2、λ3的比值大小不同之誤差比較 47
4-3小結 55
第五章 HAF之實用性 56
5-1 HAF yi=Aiψi(R)Xi的誤差 56
5-2 改良HAF yi=Aiψi(ρ)Xi的誤差 73
5-3 小結 89
第六章結論與建議 91
6-1結論 91
6-2建議 92
參考文獻 93

參考文獻

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指導教授

李顯智(Xian-Zhi Lei)

審核日期

2012-7-24

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