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研究生:陳柏維
研究生(外文):Pou-Wei Chen
論文名稱:微分再生核方法於板、樑結構行為分析
論文名稱(外文):A Differential Reproducing Kernel Particle Method for the Structural Behaviors of Beams and Plates
指導教授:吳致平
指導教授(外文):Chih-Pin Wu
學位類別:碩士
校院名稱:國立成功大學
系所名稱:土木工程學系碩博士班
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:中文
論文頁數:54
中文關鍵詞:變形層板再生核無網格法撓曲適點法
外文關鍵詞:BendingLaminatesPlatesDeformationsPoint collocationMeshless methodsReproducing kernels
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  • 下載下載:15
  • 收藏至我的研究室書目清單書目收藏:0
為了解決在物理問題中面臨偏微分控制方程式之求解,各式計算方法於焉產生。本文引用王永明研究群提出之微分再生核節點法,進行樑、板結構力學行為之應用研究。該法提出新穎的概念來推衍再生核節點法中導函數相應之形狀函數。有別於傳統再生核節點法中對於形狀函數需直接由微分程序求得,本方法建立一組微分再生條件去計算再生核節點法中導函數相應之形狀函數。
文中將根據微分再生核適點法,應用在樑與板的動、靜態分析中,對於該相關一維度及二維度之物理問題,將本法逐點代入其物理域內部之無因次化控制方程與邊界之邊界條件中,進行聯立代數方程式之求解。本分析法所得之數值結果,除與文獻中之解析解進行綜合比較外,對本法應用時適當之影響半徑(a)及基底函數最高階次(n)亦將進一步探討。
A differential reproducing kernel particle (DRKP) method is developed for solving partial differential equations governing a certain physical problem. A novel idea is proposed for determining the shape functions for derivatives of the reproducing kernel (RK) approximants. Contrary to the manipulation in the reproducing kernel particle (RKP) method where the differential operation toward the shape functions of the RK approximants is directly taken, we construct a set of differential reproducing conditions to determine the shape functions for the derivatives of RK approximants. A point collocation approach based on the present DRKP approximations for multi-dimensional problems is formulated. It is shown from the illustrative examples that the present method indeed is a fully meshless approach with excellent accuracy and fast rate of convergence.
中文摘要 Ⅰ
英文摘要 Ⅱ
致謝 Ⅲ
目錄 Ⅳ
表目錄 Ⅵ
圖目錄 Ⅶ
第一章 緒論 1
1.1 研究動機 1
1.2 研究內容 2
第二章 微分再生核(DRKP)方法 4
2.1 DRK法在一維問題之探討 4
2.1.1 再生核形狀函數 4
2.1.2 再生核形狀函數之導函數 6
2.1.3 加權函數及相對誤差的定義 8
2.2 DRK法在多維問題之探討 10
2.2.1 再生核形狀函數 10
2.2.1.1 二維問題 2.2.1.2 三維問題
2.2.2 再生核形狀函數之導函數 12
2.2.2.1 二維問題 2.2.2.2 三維問題
第三章 應用問題解析 16
3.1 樑之撓曲靜態分析 16
3.2 板之撓曲靜態分析 17
3.3 圓形板之動態基頻分析 19
第四章 數值範例 23
4.1 樑之撓曲靜態分析 23
4.2 板之撓曲靜態分析 24
4.3 圓形板之動態基頻分析 26
第五章 結論 27
參考文獻 28
表 32
圖 38
[1] Chen JS, Pan C, Wu CT, Liu WK. : Reproducing kernel particle methods for large deformation analysis of non-linear structures. Comput Methods Appl Mech Engrg, vol. 139, pp.195_227, 1996.
[2] Liu WK, Jun S, Li S, Adee J, Belytschko T. : Reproducing kernel particle methods for structural dynamics. Int J Numer Methods Engrg, vol. 38, pp.1655_1679, 1995.
[3] Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P. : Meshless methods: An overview and recent developments. Comput Methods Appl Mech Engrg, vol. 139, pp.3_47, 1996.
[4] Liu WK, Jun S, Zhang YF. : Reproducing kernel particle methods. Int J Numer Methods Engrg, vol.20, pp.1081_1106, 1995.
[5] Lucy L. : A numerical approach to testing the fission hypothesis. Astrophys J, vol.82, pp.1013_1024, 1977.
[6] Monaghan JJ. : An introduction to SPH. Comput Physics Commun, vol.48, pp.89_96, 1988.
[7] Libersky LD, Petschek AG, Carney TC, Hipp JR, Allahdadi FA. : High strain Lagrangian hydrodynamics_a three-dimensional SPH code for dynamic material response. J Comput Phys, vol.109, pp.67_75, 1993.
[8] Chen JS, Pan C, Wu CT. : Large deformation analysis of rubber based on a reproducing kernel particle method. Comput Mech, vol.19, pp.211-227, 1997.
[9] Chen JS, Yoon S, Wang HP, Liu WK. : Improved reproducing kernel particle method for nearly incompressible finite elasticity. Comput Methods Appl Mech Engrg, vol.181, pp.117-145, 2000.
[10] Liew KM, Ng TY, Wu YC. : Meshfree method for large deformation analysis-a reproducing kernel particle approach. Eng Struct, vol.24, pp. 543-551, 2002.
[11] Zhou JX, Zhang HY, Zhang L. : Reproducing kernel particle method for free and forced vibration analysis. J Sound Vib, vol.279, pp.389-402, 2005.
[12] Zhao X, Liew KM, Ng TY. : Vibration analysis of laminated composite cylindrical panels via a meshfree approach. Int J Solids Struct., vol.40, pp.161-180, 2003.
[13] Liew KM, Wang J, Ng TY, Tan MJ. : Free vibration and buckling analyses of shear-deformable plates based on FSDT meshfree method. J Sound Vib, vol.276, pp.997-1017, 2004.
[14] Zhao X, Ng TY, Liew KM. : Free vibration of two-side simply-supported laminated cylindrical panels via the mesh-free kp-Ritz method. Int J Mech Sci, vol.46, pp. 123-142, 2004.
[15] Aluru NR. : A point collocation method based on reproducing kernel approximations. Int J Numer Methods Engrg, vol.47, pp.1083_1021, 2000.
[16] Lancaster P, Salkauakas K. : Surfaces generated by moving least squares methods. Math Comput, vol.37, pp.141_158, 1981.
[17] Belytschko T, Lu YY, Gu L. : Element-Free Galerkin Methods. Int J Numer Methods Engrg, vol.37, pp.229_256, 1994.
[18] Lu YY, Belytschko T, Gu L. : A new implementation of the element free Galerkin method. Comput Methods Appl Mech Engrg, vol.113, pp. 397_414, 1994.
[19] Atluri SN, Cho JY, Kim HG. : Analysis of thin beams, using the meshless local Petrov-Galerkin method, with generalized moving least squares interpolations. Comput Mech, vol.24, pp. 334_347, 1999.
[20] Atluri SN, Zhu T. : A new meshless local Petro-Galerkin (MLPG) approach in computational mechanics. Comput Mech, vol.22, pp.117_2127, 1998.
[21] Onate E, Idelsohn S, Zienkiewicz OC, Taylor RL. : A finite point method in computational mechanics_Applications to convective transport and fluid flow. Int J Numer Methods Engrg, vol.39, pp.3839_3866, 1996.
[22] Du H, Lim MK, Lin RM.: Application of generalized differential quadrature method to structural problems. Int J Numer Methods Engrg, vol.37, pp. 1881_1896, 1994.
[23] 王永明;黃子倫,微分再生核近似法於三維彈性力學上之應用,國立成功大學土木系碩士論文,2002。
[24] 王永明;汪神義,複合層板之無網格法分析,國立成功大學土木系碩士論文,2003。
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