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研究生:孟令軒
研究生(外文):Ling-Xuan Meng
論文名稱:顆粒體微觀熱傳與力學理論的基準測試
論文名稱(外文):nono
指導教授:鍾雲吉
指導教授(外文):Yun-Chi Chung
學位類別:碩士
校院名稱:國立中央大學
系所名稱:機械工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2020
畢業學年度:108
語文別:中文
論文頁數:66
中文關鍵詞:離散元素電腦模擬顆粒體熱傳理論顆粒體力學理論電腦模擬驗證研究顆粒結晶結構
外文關鍵詞:Discrete element simulationGranule heat transferGranular mechanicssimulation verificationPacking structure
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本研究提出離散元素法( Discrete Element Method, DEM )顆粒體微觀熱傳與力學理論,為了驗證顆粒體微觀熱傳與力學理論,本研究建立八個基準測試,確認離散元素模型的合理性與正確性,並作為開發3D列印離散元素模型的基礎。八個基準測試分別為:(1)兩端固定桿件的受熱應力分析;(2)無邊界束制彈性立方體受熱分析;(3)具邊界束制彈性立方體受熱應力分析;(4)半無限垂直圓柱試體的受熱分析;(5)矩形柱體承受兩端溫差的受熱分析;(6)含半圓形孔平板試體的受熱穩態應力分析;(7)含半圓形孔平板試體的受熱暫態應力分析;(8)顆粒排列方式對熱傳效應的影響。經由八個基準測試得知離散元素模擬結果與現有連續體理論解析解及有限元素法數值解相當吻合,證明了顆粒體熱傳理論、接觸鍵接理論及顆粒應力張量理論的合理性與正確性,並連接了微觀與巨觀理論的一致性。研究顯示配位數越大與粒子體積佔有率越高,其熱傳導性越佳,不同的結晶結構熱傳導性排序為:六方緊密堆積(HCP) ≒ 面心立方(FCC) 體心立方(BCC) ≒ 隨機排列(Random) 簡單立方(SC)。本研究提出的顆粒體熱傳理論尚未考量顆粒接觸面積的影響,在未來應納入顆粒接觸面積的因素。
This study investigates mechanical and thermal behaviours of granular assemblies by using discrete element modelling (DEM). To verify the proposed model of granule heat transfer, eight benchmark tests were established as follows:(1) a rectangular prism with fixed ends subjected to sudden temperature increases;(2) an isotropic and elastic cube with free boundary subject to sudden temperature changes;(3) an isotropic and elastic cube with boundary constraints subject to sudden temperature changes;(4) Semi-infinite vertical isotropic cylinder given the initial lower temperature and subjected to a fixed higher temperature at the top;(5) a rectangular body with simple cubic (SC) structure with free boundary, given the initial lower temperature and subjected to a fixed higher temperature at the left side;(6) Steady-state analysis of a plate with a semi-circular hole with boundary constraints, subjected to sudden temperature increases;(7) Transient analysis of a plate with a semi-circular hole with boundary constraints, subjected to sudden temperature increases;(8) a rectangular body formed of different crystal structures, given the initial lower temperature and subjected to a fixed higher temperature at the left side. The study shows that the DEM results match very well with the FEM and analytical solutions of continuum theory, which proves the rationality of the granule heat transfer, the bonding theory and the particle stress formula. The results also show that the heat conductivity of the face-centered cubic (FCC) structure is very close to that of the hexagonal closest packed (HCP) structure, and the heat conductivities of the body-centered cubic (BCC) structure and the random packing (RP) structure are very close. The heat conductivity follows the sequence : FCC ≒ HCP > BCC ≒ RP > SC.
摘要 i
英文摘要 ii
目錄 iii
第一章 緒論 1
1-1 緒論 1
1-2 研究動機 5
第二章 數值架構 6
2-1 離散元素法之架構 6
2-2 三維剛體運動方程式 8
2-3 接觸力模型 9
2-4 接觸鍵接模式 11
2-5 顆粒體熱傳理論 12
2-6 熱應變的計算 15
2-7 顆粒體應力張量 16
2-8 臨界時間步 18
第三章 結果與討論 19
3-1 兩端固定桿件的受熱應力分析 19
3-2 無邊界束制彈性立方體受熱分析 22
3-3 具邊界束制彈性立方體受熱應力分析 25
3-4 半無限垂直圓柱試體的受熱分析 31
3-5 矩形柱體承受兩端溫差的受熱分析 34
3-6 含半圓形孔平板試體的受熱穩態應力分析 37
3-7 含半圓形孔平板試體的受熱暫態應力分析 43
3-8 顆粒排列方式對熱傳效應的影響 50
第四章 結論 55
參考文獻 56
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