弹性力学的插值型重构核粒子法

李中华; 秦义校; 崔小朝

doi:10.7498/aps.61.080205

摘要

采用具有离散点插值特性的重构核粒子法形函数, 较精确地重构弹性体变形的位移试函数, 再与弹性力学的最小势能原理相结合, 形成新的分析弹性力学平面问题的插值型重构核粒子法. 由于插值型重构核粒子法形函数具有点插值特性和不低于核函数的高阶光滑性, 因而既克服了多数无网格方法处理本质边界条件的困难, 也保证了较高的数值精度. 与早期的无网格方法相比, 本方法具有精度高、解题规模较小、可直接施加边界条件等优点. 通过对典型弹性力学问题数值模拟, 验证了所提方法的有效性和正确性.

关键词:

Abstract

The displacement trial function is reconstructed by reproducing kernel particle shape function method with interpolation property on discrete points, then combining the principle of minimum potential energy of elasticity, the new interpolating reproducing kernel particle method to analyze the plane problem of elasticity is obtained. Because interpolation reproducing kernel particle shape function has a point interpolation property and no less than the high-order smoothness of kernel function, the difficulty for most of meshless methods to be used to deal with the essential boundary conditions is already overcome, and the high numerical accuracy is assured as well. Compared with the early meshless methods, this method has a high accuracy and a small scale of solving problem and it can be directly applied to boundary conditions. Numerical results for some typical examples of elasticity prove the proposed method to be valid.

Keywords:

interpolating reproducing kernel particle method /
elastic mechanics /
principle of minimum potential energy /
meshless method

作者及机构信息

1.
太原科技大学应用科学学院, 太原 030024;

2.
太原科技大学机械工程学院, 太原 030024

基金项目: 国家自然科学基金(批准号: 10871124)和山西省自然科学基金(批准号: 20051061)资助的课题.

Authors and contacts

1.
College of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China;

2.
College of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10871124) and the Natural Science Foundation of Shanxi Province, China (Grant No. 20051061).

参考文献

[1]	Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P 1996 Comput. Meth. Appl. Mech. Eng. 139 3
[2]	Li S F, Liu W K 2002 Appl. Mech. Rev. 55 134
[3]	Zhang X, Song K Z, Lu M W 2003 Chin. J. Comput. Mech. 20 731 (in Chinese) [张雄, 宋康祖, 陆明万 2003 计算力学学报 20 731]
[4]	Gao H F, Cheng Y M 2010 Int. J. Comput. Meth. 7 55
[5]	Wang J F, Cheng Y M 2011 Chin. Phys. B 20 030206
[6]	Cheng Y M, Ji X, He P F 2004 Acta Mech. Sin. 36 43 (in Chinese) [程玉民、嵇醒、贺鹏飞 2004 力学学报 36 43]
[7]	Cheng R J, Cheng Y M 2011 Acta Phys. Sin. 60 070206 (in Chinese) [程荣军、程玉民2011 60 070206]
[8]	Gao H F, Cheng Y M 2009 Acta Mech. Sin. 41 480 (in Chinese) [高洪芬, 程玉民 2009 力学学报 41 480]
[9]	Liu W K, Jun S, Zhang Y F 1995 Int. J. Numer. Meth. Eng. 20 1081
[10]	Liu W K, Chen Y, Uras R A, Chang C T 1996 Comput. Meth. Appl. Mech. Eng. 139 91
[11]	Chen J S, Pan C, Wu C T, Liu W K 1996 Comput. Meth. Appl. Mech. Eng. 139 195
[12]	Li S, Liu W K 1997 Comput. Meth. Appl. Mech. Eng. 143 113
[13]	Li S, Liu W K 1999 Int. J. Numer. Meth. Eng. 45 251
[14]	Chen J S, Yoon S, Wang H P, Liu W K 2000 Comput. Meth. Appl. Mech. Eng. 181 117
[15]	Han W M, Meng X P 2001 Comput. Meth. Appl. Mech. Eng. 190 6157
[16]	Chen J S, Han W, You Y, Meng X 2003 Int. J. Numer. Meth. Eng. 56 935
[17]	Cheng Y M, Peng M J 2005 Sci. China G 48 641
[18]	Cheng Y M, Li J H 2006 Sci. China G 49 46
[19]	Dai B D, Cheng Y M 2007 Acta Phys. Sin. 56 597 (in Chinese) [戴保东, 程玉民 2007 56 597]
[20]	Cheng Y M, Liew K M, Kitipornchai S 2009 Int. J. Numer. Meth. Eng. 78 1258
[21]	Cheng R J, Cheng Y M 2008 Appl. Numer. Math. 58 884
[22]	Cheng Y M, Chen M J 2003 Acta Mech. Sin. 35 181 (in Chinese) [程玉民, 陈美娟 2003 力学学报 35 181]
[23]	Li S C, Cheng Y M 2004 Acta Mech. Sin. 36 496 (in Chinese) [李树忱, 程玉民 2004 力学学报 36 496]
[24]	Cheng Y M, Li J H 2005 Acta Phys. Sin. 54 4463 (in Chinese) [程玉民, 李九红 2005 54 4463]
[25]	Cheng R J, Cheng Y M 2008 Acta Phys. Sin. 57 6037 (in Chinese) [程荣军, 程玉民 2008 57 6037]
[26]	Qin Y X, Cheng Y M 2006 Acta Phys. Sin. 55 3216 (in Chinese) [秦义校, 程玉民 2006 55 3216]
[27]	Chen L, Cheng Y M 2008 Acta Phys. Sin. 57 1 (in Chinese) [陈丽, 程玉民 2008 57 1]
[28]	Chen L, Cheng Y M 2008 Acta Phys. Sin. 57 6047 (in Chinese) [陈丽, 程玉民 2008 57 6047]

施引文献

[1]	Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P 1996 Comput. Meth. Appl. Mech. Eng. 139 3
[2]	Li S F, Liu W K 2002 Appl. Mech. Rev. 55 134
[3]	Zhang X, Song K Z, Lu M W 2003 Chin. J. Comput. Mech. 20 731 (in Chinese) [张雄, 宋康祖, 陆明万 2003 计算力学学报 20 731]
[4]	Gao H F, Cheng Y M 2010 Int. J. Comput. Meth. 7 55
[5]	Wang J F, Cheng Y M 2011 Chin. Phys. B 20 030206
[6]	Cheng Y M, Ji X, He P F 2004 Acta Mech. Sin. 36 43 (in Chinese) [程玉民、嵇醒、贺鹏飞 2004 力学学报 36 43]
[7]	Cheng R J, Cheng Y M 2011 Acta Phys. Sin. 60 070206 (in Chinese) [程荣军、程玉民2011 60 070206]
[8]	Gao H F, Cheng Y M 2009 Acta Mech. Sin. 41 480 (in Chinese) [高洪芬, 程玉民 2009 力学学报 41 480]
[9]	Liu W K, Jun S, Zhang Y F 1995 Int. J. Numer. Meth. Eng. 20 1081
[10]	Liu W K, Chen Y, Uras R A, Chang C T 1996 Comput. Meth. Appl. Mech. Eng. 139 91
[11]	Chen J S, Pan C, Wu C T, Liu W K 1996 Comput. Meth. Appl. Mech. Eng. 139 195
[12]	Li S, Liu W K 1997 Comput. Meth. Appl. Mech. Eng. 143 113
[13]	Li S, Liu W K 1999 Int. J. Numer. Meth. Eng. 45 251
[14]	Chen J S, Yoon S, Wang H P, Liu W K 2000 Comput. Meth. Appl. Mech. Eng. 181 117
[15]	Han W M, Meng X P 2001 Comput. Meth. Appl. Mech. Eng. 190 6157
[16]	Chen J S, Han W, You Y, Meng X 2003 Int. J. Numer. Meth. Eng. 56 935
[17]	Cheng Y M, Peng M J 2005 Sci. China G 48 641
[18]	Cheng Y M, Li J H 2006 Sci. China G 49 46
[19]	Dai B D, Cheng Y M 2007 Acta Phys. Sin. 56 597 (in Chinese) [戴保东, 程玉民 2007 56 597]
[20]	Cheng Y M, Liew K M, Kitipornchai S 2009 Int. J. Numer. Meth. Eng. 78 1258
[21]	Cheng R J, Cheng Y M 2008 Appl. Numer. Math. 58 884
[22]	Cheng Y M, Chen M J 2003 Acta Mech. Sin. 35 181 (in Chinese) [程玉民, 陈美娟 2003 力学学报 35 181]
[23]	Li S C, Cheng Y M 2004 Acta Mech. Sin. 36 496 (in Chinese) [李树忱, 程玉民 2004 力学学报 36 496]
[24]	Cheng Y M, Li J H 2005 Acta Phys. Sin. 54 4463 (in Chinese) [程玉民, 李九红 2005 54 4463]
[25]	Cheng R J, Cheng Y M 2008 Acta Phys. Sin. 57 6037 (in Chinese) [程荣军, 程玉民 2008 57 6037]
[26]	Qin Y X, Cheng Y M 2006 Acta Phys. Sin. 55 3216 (in Chinese) [秦义校, 程玉民 2006 55 3216]
[27]	Chen L, Cheng Y M 2008 Acta Phys. Sin. 57 1 (in Chinese) [陈丽, 程玉民 2008 57 1]
[28]	Chen L, Cheng Y M 2008 Acta Phys. Sin. 57 6047 (in Chinese) [陈丽, 程玉民 2008 57 6047]

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