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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.
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Keywords:
- interpolating reproducing kernel particle method /
- elastic mechanics /
- principle of minimum potential energy /
- meshless method
[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 物理学报 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 物理学报 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 物理学报 54 4463]
[25] Cheng R J, Cheng Y M 2008 Acta Phys. Sin. 57 6037 (in Chinese) [程荣军, 程玉民 2008 物理学报 57 6037]
[26] Qin Y X, Cheng Y M 2006 Acta Phys. Sin. 55 3216 (in Chinese) [秦义校, 程玉民 2006 物理学报 55 3216]
[27] Chen L, Cheng Y M 2008 Acta Phys. Sin. 57 1 (in Chinese) [陈丽, 程玉民 2008 物理学报 57 1]
[28] Chen L, Cheng Y M 2008 Acta Phys. Sin. 57 6047 (in Chinese) [陈丽, 程玉民 2008 物理学报 57 6047]
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[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 物理学报 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 物理学报 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 物理学报 54 4463]
[25] Cheng R J, Cheng Y M 2008 Acta Phys. Sin. 57 6037 (in Chinese) [程荣军, 程玉民 2008 物理学报 57 6037]
[26] Qin Y X, Cheng Y M 2006 Acta Phys. Sin. 55 3216 (in Chinese) [秦义校, 程玉民 2006 物理学报 55 3216]
[27] Chen L, Cheng Y M 2008 Acta Phys. Sin. 57 1 (in Chinese) [陈丽, 程玉民 2008 物理学报 57 1]
[28] Chen L, Cheng Y M 2008 Acta Phys. Sin. 57 6047 (in Chinese) [陈丽, 程玉民 2008 物理学报 57 6047]
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