The complex variable reproducing kernel particle method for two-dimensional elastodynamics

doi:10.1088/1674-1056/19/9/090204

中国物理B ›› 2010, Vol. 19 ›› Issue (9): 90204-090204.doi: 10.1088/1674-1056/19/9/090204

The complex variable reproducing kernel particle method for two-dimensional elastodynamics

陈丽¹, 程玉民²

(1)Department of Engineering Mechanics, Chang'an University, Xi'an 710064, China; (2)Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

收稿日期:2010-01-28 修回日期:2010-02-24 出版日期:2010-09-15 发布日期:2010-09-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10871124), and the Innovation Program of Shanghai Municipal Education Commission, China (Grant No. 09ZZ99).

The complex variable reproducing kernel particle method for two-dimensional elastodynamics

Chen Li(陈丽)^a) and Cheng Yu-Min(程玉民)^b)†

^a Department of Engineering Mechanics, Chang'an University, Xi'an 710064, China; ^b Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

Received:2010-01-28 Revised:2010-02-24 Online:2010-09-15 Published:2010-09-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10871124), and the Innovation Program of Shanghai Municipal Education Commission, China (Grant No. 09ZZ99).

摘要/Abstract

摘要： On the basis of the reproducing kernel particle method (RKPM), a new meshless method, which is called the complex variable reproducing kernel particle method (CVRKPM), for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM.

Abstract: On the basis of the reproducing kernel particle method (RKPM), a new meshless method, which is called the complex variable reproducing kernel particle method (CVRKPM), for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM.

Key words: meshless method, reproducing kernel particle method, complex variable reproducing kernel particle method, elastodynamics

中图分类号:

0260

陈丽, 程玉民. The complex variable reproducing kernel particle method for two-dimensional elastodynamics[J]. 中国物理B, 2010, 19(9): 90204-090204.

Chen Li(陈丽) and Cheng Yu-Min(程玉民). The complex variable reproducing kernel particle method for two-dimensional elastodynamics[J]. Chin. Phys. B, 2010, 19(9): 90204-090204.

参考文献 52

[1]	Yang Z J and Deeks A J 2007 Comput. Mech. 40 725
[2]	Belytschko T, Krongauz Y, Organ D, Fleming M and Krysl P 1996 Comput. Meth. Appl. Mech. Eng. 139 3
[3]	Li S F and Liu W K 2002 Appl. Mech. Rev. 55 1
[4]	Gingold R A and Monaghan J J 1977 Mon. Not. R. Astron. Soc. 18 375
[5]	Nayroles B, Touzot G and Villon P G 1992 Comput. Mech. 10 307
[6]	Belytschko T, Lu Y Y and Gu L 1994 Int. J. Numer. Meth. Eng. 37 229
[7]	Liu W K, Jun S and Zhang Y F 1995 Int. J. Numer. Meth. Eng. 20 1081
[8]	Onate E 1996 Int. J. Numer. Meth. Eng. 39 3839
[9]	Atluri S N and Zhu T L 1998 Comput. Mech. 22 117
[10]	Aluru N R 2000 Int. J. Numer. Meth. Eng. 47 1083
[11]	Liu W K and Chen Y J 1995 Int. J. Numer. Meth. Fluids 21 901
[12]	Wendland H 1999 Math. Comput. 68 1521
[13]	Idelsohn S R, Onate E and Calvo N 2003 Int. J. Numer. Meth. Eng. 58 893
[14]	Cheng Y M and Li J H 2005 Acta Phys. Sin. 54 4463 (in Chinese)
[15]	Cheng Y M and Li J H 2006 Sci. China Ser. G Phys. Mech. Astron. 49 46
[16]	Liew K M, Feng C, Cheng Y M and Kitipornchai S 2007 Int. J. Numer. Meth. Eng. 70 46
[17]	Chati M K, Mukherjee S and Mukherjee Y X 1999 Int. J. Numer. Meth. Eng. 46 1163
[18]	Zhu T, Zhang J and Atluri S N 1999 Eng. Anal. Bound. Elem. 23 375
[19]	Gu Y T and Liu G R 2003 Struct. Eng. Mech. 15 535
[20]	Liew K M, Cheng Y M and Kitipornchai S 2006 Int. J. Numer. Meth. Eng. 65 1310
[21]	Kitipornchai S, Liew K M and Cheng Y M 2005 Comput. Mech. 36 13
[22]	Cheng Y M and Peng M J 2005 Sci. China Ser. G Phys. Mech. Astron. 48 641
[23]	Liew K M, Cheng Y M and Kitipornchai S 2005 Int. J. Numer. Meth. Eng. 64 1610
[24]	Liew K M, Cheng Y M and Kitipornchai S 2007 Int. J. Solids Struct. 44 4220
[25]	Peng M J and Cheng Y M 2009 Eng. Anal. Bound. Elem. 33 77
[26]	Cheng Y M, Liew K M and Kitipornchai S 2009 Int. J. Numer. Meth. Eng. 78 1258
[27]	Ren H P and Zhang W 2009 Chin. Phys. B 18 4065
[28]	Lu Y Y, Belytschko T and Tabbara M 1995 Comput. Meth. Appl. Mech. Eng. 126 131
[29]	Liu W K, Jun S, Li S, Adee J and Belytschko T 1995 Int. J. Numer. Meth. Eng. 38 1655
[30]	Han Z D and Atluri S N 2004 Comput. Mater. Continua 1 129
[31]	Liu K Y, Long S Y and Li G Y 2006 Eng. Anal. Bound. Elem. 30 72
[32]	Gu Y T and Liu G R 2001 Comput. Mech. 27 188
[33]	Bueche D, Sukumar N and Moran B 2000 Comput. Mech. 25 207
[34]	Li S C, Li S C and Zhu W S 2006 Chinese J. R. Mech. Eng. 25 141 (in Chinese)
[35]	Li S C, Cheng Y M and Li S C 2006 Acta Phys. Sin. 55 4760 (in Chinese)
[36]	Sladek J, Sladek V and Keer R V 2003 Int. J. Numer. Meth. Eng. 57 235
[37]	Sellountos E J and Polyzos D 2005 Comput. Mech. 35 265
[38]	Li H, Wang Q X and Lam K Y 2004 Comput. Meth. Appl. Mech. Eng. 193 2599
[39]	Liew K M and Cheng Y M 2009 Comput. Meth. Appl. Mech. Eng. 198 3925
[40]	Monaghan J J 1988 Comput. Phys. Commun. 48 89
[41]	Liu W K, Chen Y, Jun S, Chen J S and Belytschko T 1996 Arch. Comput. Meth. Eng. 3 3
[42]	Zhou J X, Zhang H Y and Zhang L 2005 J. Sound Vib. 279 389
[43]	Zhang J P, Gong S G and Huang Y Q 2008 Struct. Multidiscip. Optim. 36 307
[44]	Kiani K, Nikkhoo A and Mehri B 2009 J. Sound Vib. 320 632
[45]	Gan N F, Li G Y and Long S Y 2009 Eng. Anal. Bound. Elem. 33 1211
[46]	Chen J S, Chen C, Wu C T and Liu W K 1996 Comput. Meth. Appl. Mech. Eng. 139 195
[47]	Liu W K and Jun S 1998 Int. J. Numer. Meth. Eng. 41 1339
[48]	Liu W K, Jun S, Thomas S D, Chen Y and Hao W 1997 Int. J. Numer. Meth. Fluids 24 1391
[49]	Chen L and Cheng Y M 2008 Acta Phys. Sin. 57 1 (in Chinese)
[50]	Chen L and Cheng Y M 2008 Acta Phys. Sin. 57 6047 (in Chinese)
[51]	Danielson K T, Hao S, Liu W K, Uras R A and Li S F 2000 Int. J. Numer. Meth. Eng. 47 1323
[52]	Ching H K 2002 Solution of Linear Elastostatic and Elastodynamic Plane Problems by the Meshless Local Petrov--Galerkin Method (Ph.D. Thesis) (Blacksburg: Virginia Polytechnic Institute and State University) endfootnotesize

The complex variable reproducing kernel particle method for two-dimensional elastodynamics

The complex variable reproducing kernel particle method for two-dimensional elastodynamics

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 52

相关文章 2

Metrics

本文评价

推荐阅读 0

[1]	李兴国, 戴保东, 王灵卉. A moving Kriging interpolation-based boundary node method for two-dimensional potential problems[J]. 中国物理B, 2010, 19(12): 120202-120202.
[2]	程荣军, 葛红霞. Meshless analysis of three-dimensional steady-state heat conduction problems[J]. 中国物理B, 2010, 19(9): 90201-090201.