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題 名 | 共轉座標在撓曲梁大變形動力分析上之應用 |
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作 者 | 凌烽生; | 書刊名 | 四海學報 |
卷 期 | 9 1994.12[民83.12] |
頁 次 | 頁17-31 |
分類號 | 441.1 |
關鍵詞 | 共轉座標; 非線性有限元素; 顯性時間積分法; 結構動力分析; Corotational cordinate; Nonlinear finite element; Structural dynamic analysis; Explicit time integration; |
語 文 | 中文(Chinese) |
中文摘要 | 本文主要介紹二種非線性有限元素共轉座標系統演算法,稱之為TOTAL COROTATION(TC)FORMULATION與UP-DATE COROTATION(UC)FORMULLATION,並採用元素堆積質量分佈 (LUMPED MAASS)計算 ,配合中心差分法 (CENTRAL DIFFERENCEMETHOD)做顯性時間積分,進行結構動力分析。TC與UC的特點,在於可分離結構之大旋轉運動為剛體旋轉與變形旋轉,分離後之變形反應即可使用線性小變形理論求解,以解決幾何非線性之大變形反應。文中以懸臂梁梁端承受集中動力載荷或初始速度為例,除了使用TC及UC法外,亦採用傳統有限元(FEM)解小、位移之動力分析法,計算梁端之變形動力反應,並比較UC、TC及FEM所算得之結果。顯示小位移及擬靜態之動力分析,三者結果相似,皆具有相當之正確性;大變形之動力分析結果,TC法首先遭遇不穩定反應,若克服不穩定現象,其解與UC較接近:FEM解雖然穩定,依循小位移之基本解,顯得太過保守而失去精確性:UC解則似乎較為合理,在穩定的狀況下,全梁產生大變形之正常動力反應,並進行觀察結構之彎矩變化,由於慣性力效應,使得彎矩分佈亦隨時間變化,尤其在變形越大時,懸臂梁固定端彎矩增加量,較全梁其餘部位彎矩增加量呈次方級數的變化,而非靜態梁之線性彎矩分佈。關於初始速度引起之自由振動問題,其穩定解的順利獲得,在於臨界時間步程的正確選擇。 |
英文摘要 | This paper mainly introduce three different geometrically nonlinear computation procedure for dynamic large deflection analysis of2-D cantilever beam. Small deformation assumption still can be used to calculate structure deform dtress because the convicted coordinate system is used here in each element in order that deformed structure element can be separated into rigid body and deformed motion. The time integration techniques used in the research is the central-difference explicit method. And the types of mass matrix used in conjunction with explicit time integration is the lumped nodal mass matrix. We make use of conventional finite element method (FEM), total corotational formulation (TL) and up-date corotation formulation (UC) in the examples which are pseudo static, dynamic large deflection and initial velocity problems. And we compare the effects of solving the same problems using these different method. The results of three ways to solve pseudo static problem are not different. But in the dynamic large deflection problem, unstable response first appear in the TC method, if it can overcome the unstable condition, its result is near the answer of the UC method. Although conventional FEM can obtain the stable response. It's too conservative and accuracy lost. The result ofUC method seems more reasonable, in the stable condition showing the normal dynamic response. In the meantime, we observe the dynamic moment distribution in the whole beam. Clearly, it's different from the static moment distribution and the more large deflection, the more internal moment in the fix end of the beam. About the initial velocity problem, free vibration response is obtained, and the critical time step must be choosed carefully. |
本系統中英文摘要資訊取自各篇刊載內容。