Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/2191
標題: 軸向對稱無網格分析法收斂性之研究
The Convergence Study of Meshless Method for Axisymmetric Problems
作者: 張順國
Chang, Shuen-Kuo
關鍵字: meshless;無網格法;axisymmetric problem;moving least square method;軸向對稱;最小平方法
出版社: 機械工程學系所
引用: [1] 徐秉業, 劉信聲, 應用彈塑性力學, 1997 [2] Introduction to Finite Element Analysis. 6.3 Axisymmetric Solid Elem- ents http://www.me.mtu.edu/~bettig/MEEM4405/Lecture11.pdf [3] Mukherjee YX, Mukherjee S, “On boundary conditions in the Element- free Galerkin method,” Computational Mechanics. 1997; 22: 264-270. [4] Nayroles B, Touzot G, Villon P, “Generalizing the finite element method: diffuse approximation and diffuse elements,” Comput. Mech. 1992; 10 : 307-318. [5] Belytschko T, Lu YY, Gu L, “Element-free Galerkin methods,” Int. J. Numer. Meth. Eng. 1994; 37: 229–256. [6] Atluri SN, Zhu TL, “A new meshless local Petrov–Galerkin (MLPG) approach in computational mechanics,” Computational Mechanics. 1998; 22: 117–127. [7] Atluri SN, Zhu TL, “The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics,” Computational Mechanics. 2000; 25(2-3): 169–179. [8] Atluri SN, Cho JY, Kim HG, “Analysis of thin beams, using the meshless local Petrov-Galerkin method, with generalized moving least squares interpolations,” Computational Mechanics. 1999a; 24: 334–337. [9] Atluri SN, Zhu TL, “New concepts in meshless methods,” International Journal for Numerical Method in Engineering. 2000; 47(1-3): 537-556. [10] Atluri SN, Zhu T, “A New Meshless Local Petrov-Galerkin (MLPG) Approach to Nonlinear Problems in Computer Modeling & Simulation,” Computer Modeling & Simulation in Engineering. 1998; 3: 187-196. [11] Nayroles B, Touzot G, Villon P, “Generalizing the finite element method: diffuse approximation and diffuse elements,” Comput. Mech. 1992; 10 : 307-318. [12] Long SY, Atluri SN, “A meshless local Petrov-Galerkin method for solving the bending problem of a thin plate,” CMES-Computer Modeling in Engineering & Sciences. 2002; 3(1): 53-63. [13] Lancaster P, Salkauskas K, “Surfaces generated by moving least squares methods,” Math. Comput. 1981; 37(155): 141~158. [14] Gu YT, Liu GR, “A radial basis boundary point interpolation method for stress analysis of solids,” Struct. Eng. Mech. Int. J. 2003; 15(5): 535–550. [15] Gu YT, Liu GR, “A boundary point interpolation method for stress analysis of solids,” Comput. Mech. 2002; 28: 47–54. [16] Liu GR, “Mesh Free Methods: Moving Beyond the Finite Element Method,” CRC Press, USA. 2002. [17] Pan XF, Zhang X, Lu MW, “Meshless Galerkin least-squares method,” Comput. Mech. 2005; 35: 182–189. [18] Dolbow J, Belytschko T, “An Introduction to Programming the Meshless Element Free Galerkin Method,” Archives of Computational Methods in Engineering. 1998; 5(3): 207-241. [19] Dolbow J, Belytschko T, “Numerical integration of the Galerkin weak form in meshfree methods,” Comput. Mech. 1999; 23: 219-230. [20] Marc Duflot, Hung Nguyen-Dang, “A truly meshless Galerkin method based on a moving least squares quadrature,” Communications in Numerical Methods in Engineering 2002; 18: 441–449. [21] Giorgio Pini, Giuseppe Gambolati, “A comparison of numerical Integ- ration rules for the meshless local Petrov–Galerkin method,” Numerical Algorithms. 2007; 45(1-4): 61-74. [22] Massimiliano Ferronato, Annamaria Mazzia, Giorgio Pini,Giuseppe Gambolati, “Meshless Petrov-Galerkin Method Applied to Axisymmetric Problems” Int. J. Numer. Meth. Engng 2007; 70: 1346–1365. [23] HE Pei-xiang, LI Zi-ran, WU Chang-chun, “Element-Free Galerkin Method for Axi-symmetric Solids,” JOURNAL OF UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA. 2003; 33(3): 0253-22778 (2003) 03-20318206. [24] Liu GR, “Mesh Free Method: Moving Beyond the Finite Element Method,” CRC Press, New York. 2002. [25] Liu GR, Gu YT, “An introduction to meshfree methods and their programming, ” Springer, Netherlands. 2005. [26] Liu GR, Gu YT, “Meshless Local Petrov-Galerkin (MLPG) method in combination with finite element and boundary element approachs,” Comput. Mech, 2000; 26: 536-546.
摘要: 
軸向對稱無網格分析法收斂性之研究。推導及討論其一般性過程的方法並列舉例題與已知可用的公式解作比較。
在本研究中,我們給定分析目標一些有限節點,其中包括內部節點和邊界節點。然後,具體的定義出每一個節點的影響域和非線性的移動式最小平方法來建構影響域中每一個相關節點與鄰近的節點的內插函數。相對的導出節點內插函數也是經由數值近似計算。多點高斯面積分被使用在分析模型之影響域上來計算每一個節點的物理矩陣。得到節點的組合物理矩陣之後,並施加相關的邊界條件和載重來代入此問題中,並直接使用高斯消去法來獲得模型的位移,最後可以計算出每一個節點的應力。
由例題結果表示節點設定的數量在該目標必須是「合理的」,其數量既不是少也不是多。影響域的大小可能會嚴重地影響收斂性的問題。
對於CPU的計算時間大量的增加是涉及到該目標節點數的增加。

Convergence of meshless method for axisymmetric problems is studied. General procedures of the method are derived and discussed, and typical examples are derived comparing with available formula solutions.
In the study, we define the analyzing object into some finite nodes which include the inner nodes and the bounded nodes. Then, specific influence domain for each node is defined and the nonlinear moving least square algorithm is used to construct the interpolation function for each node associated with neighboring nodes in the influence domain. Relative derivatives of such nodal interpolation function are also calculated by numerical approximation. Multi-points Gaussian integration quadrature is applied withing the influence domain to derive the relative physical matrices for each node on the model. Having assembled nodal physical matrice and put related boundary condition and loads into the problem, direct Gaussian elimination algorithm is used to obtain the displacement of the model. Finally, stresses on each node are also calculated.
The results show that the number of nodes setup in the object must be “reasonable”, i.e., neither less nor larger. The size of the influential domain may affect the convergence of the problems seriously. CPU time used for calculation increases dramatically with respect to the increment of nodal numbers in the object.
URI: http://hdl.handle.net/11455/2191
其他識別: U0005-3107200818171500
Appears in Collections:機械工程學系所

Show full item record
 

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.