Hybrid natural element method for viscoelasticity problems

doi:10.1088/1674-1056/24/1/010204

›› 2015, Vol. 24 ›› Issue (1): 10204-010204.doi: 10.1088/1674-1056/24/1/010204

Hybrid natural element method for viscoelasticity problems

周延凯^a, 马永其^{a b}, 董轶^c, 冯伟^a

a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
b Department of Mechanics, Shanghai University, Shanghai 200444, China;
c Shanghai Industrial Urban Development Group Limited, Shanghai 200030, China

收稿日期:2014-08-24 修回日期:2014-09-12 出版日期:2015-01-05 发布日期:2015-01-05
基金资助:
Project supported by the Natural Science Foundation of Shanghai, China (Grant No. 13ZR1415900).

Hybrid natural element method for viscoelasticity problems

Zhou Yan-Kai (周延凯)^a, Ma Yong-Qi (马永其)^{a b}, Dong Yi (董轶)^c, Feng Wei (冯伟)^a

a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
b Department of Mechanics, Shanghai University, Shanghai 200444, China;
c Shanghai Industrial Urban Development Group Limited, Shanghai 200030, China

Received:2014-08-24 Revised:2014-09-12 Online:2015-01-05 Published:2015-01-05
Contact: Ma Yong-Qi E-mail:mayq@staff.shu.edu.cn
Supported by:
Project supported by the Natural Science Foundation of Shanghai, China (Grant No. 13ZR1415900).

摘要/Abstract

摘要： A hybrid natural element method (HNEM) for two-dimensional viscoelasticity problems under the creep condition is proposed. The natural neighbor interpolation is used as the test function, and the discrete equation system of the HNEM for viscoelasticity problems is obtained using the Hellinger-Reissner variational principle. In contrast to the natural element method (NEM), the HNEM can directly obtain the nodal stresses, which have higher precisions than those obtained using the moving least-square (MLS) approximation. Some numerical examples are given to demonstrate the validity and superiority of this HNEM.

关键词: hybrid natural element method, viscoelasticity, Hellinger-Reissner variational principle, meshless method

Abstract: A hybrid natural element method (HNEM) for two-dimensional viscoelasticity problems under the creep condition is proposed. The natural neighbor interpolation is used as the test function, and the discrete equation system of the HNEM for viscoelasticity problems is obtained using the Hellinger-Reissner variational principle. In contrast to the natural element method (NEM), the HNEM can directly obtain the nodal stresses, which have higher precisions than those obtained using the moving least-square (MLS) approximation. Some numerical examples are given to demonstrate the validity and superiority of this HNEM.

Key words: hybrid natural element method, viscoelasticity, Hellinger-Reissner variational principle, meshless method

中图分类号: (Numerical simulation; solution of equations)

02.60.Cb

02.60.Lj (Ordinary and partial differential equations; boundary value problems) 46.35.+z (Viscoelasticity, plasticity, viscoplasticity)

周延凯, 马永其, 董轶, 冯伟. Hybrid natural element method for viscoelasticity problems[J]. , 2015, 24(1): 10204-010204.

Zhou Yan-Kai (周延凯), Ma Yong-Qi (马永其), Dong Yi (董轶), Feng Wei (冯伟). Hybrid natural element method for viscoelasticity problems[J]. Chin. Phys. B, 2015, 24(1): 10204-010204.

参考文献 74

[1]	Belytschko T, Lu Y Y and Gu L 1994 Int. J. Numer. Methods Eng. 37 229
[2]	Wang J F, Sun F X and Cheng R J 2010 Chin. Phys. B 19 060201
[3]	Cheng R J and Cheng Y M 2011 Chin. Phys. B 20 070206
[4]	Zhang Z, Liew K M and Cheng Y M 2008 Engin. Anal. Bound. Elem. 32 100
[5]	Zhang Z, Liew K M, Cheng Y M and Lee Y Y 2008 Engin. Anal. Bound. Elem. 32 241
[6]	Zhang Z, Hao S Y, Liew K M and Cheng Y M 2013 Engin. Anal. Bound. Elem. 37 1576
[7]	Zhang Z, Wang J F, Cheng Y M and Liew K M 2013 Sci. China-Phys. Mech. Astron. 56 1568
[8]	Cheng Y M and Li J H 2005 Acta Phys. Sin. 54 4463 (in Chinese)
[9]	Wang J F and Cheng Y M 2012 Chin. Phys. B 21 120206
[10]	Wang J F and Cheng Y M 2013 Chin. Phys. B 22 030208
[11]	Peng M J, Liu P and Cheng Y M 2009 Int. J. Appl. Mech. 1 367
[12]	Peng M J, Li D M and Cheng Y M 2011 Eng. Struct. 33 127
[13]	Bai F N, Li D M, Wang J F and Cheng Y M 2012 Chin. Phys. B 21 020204
[14]	Cheng Y M, Wang J F and Bai F N 2012 Chin. Phys. B 21 090203
[15]	Li D M, Bai F N, Cheng Y M and Liew K M 2012 Comput. Meth. Appl. Mech. Eng. 233-236 1
[16]	Cheng Y M, Wang J F and Li R X 2012 Int. J. Appl. Mech. 4 1250042
[17]	Li D M, Liew K M and Cheng Y M 2014 Comput. Meth. Appl. Mech. Eng. 269 72
[18]	Ren H P and Cheng Y M 2011 Int. J. Appl. Mech. 3 735
[19]	Ren H P and Cheng Y M 2012 Eng. Anal. Bound. Elem. 36 873
[20]	Dai B D and Cheng Y M 2007 Acta Phys. Sin. 56 597 (in Chinese)
[21]	Cheng R J and Cheng Y M 2007 Acta Phys. Sin. 56 5569 (in Chinese)
[22]	Wang J F, Bai F N and Cheng Y M 2011 Chin. Phys. B 20 030206
[23]	Atluri S N and Zhu T 1998 Comput. Mech. 22 117
[24]	Chen L and Cheng Y M 2008 Acta Phys. Sin. 57 1 (in Chinese)
[25]	Chen L and Cheng Y M 2008 Acta Phys. Sin. 57 6047 (in Chinese)
[26]	Chen L and Cheng Y M 2010 Chin. Phys. B 19 090204
[27]	Chen L, Ma H P and Cheng Y M 2013 Chin. Phys. B 22 050202
[28]	Weng Y J and Cheng Y M 2013 Chin. Phys. B 22 090204
[29]	Li S C, Cheng Y M and Li S C 2006 Acta Phys. Sin. 55 4760 (in Chinese)
[30]	Gao H F and Cheng Y M 2010 Int. J. Comput. Methods 7 55
[31]	Cheng Y M and Chen M J 2003 Acta Mech. Sin. 35 181 (in Chinese)
[32]	Cheng Y M and Peng M J 2005 Sci. Chin. Ser. G: Phys. Mech. Astron 48 641
[33]	Kitipornchai S, Liew K M and Cheng Y M 2005 Comput. Mech. 36 13
[34]	Liew K M, Cheng Y M and Kitipornchai S 2005 Int. J. Numer. Methods Eng. 64 1610
[35]	Liew K M, Cheng Y M and Kitipornchai S 2006 Int. J. Numer. Methods Eng. 65 1310
[36]	Qin Y X and Cheng Y M 2006 Acta Phys. Sin. 55 3215 (in Chinese)
[37]	Liew K M, Cheng Y M and Kitipornchai S 2007 Int. J. Solids Struct. 44 4220
[38]	Cheng Y M, Liew K M and Kitipornchai S 2009 Int. J. Numer. Methods Eng. 78 1258
[39]	Liew K M and Cheng Y M 2009 Comput. Meth. Appl. Mech. Eng. 198 3925
[40]	Peng M J and Cheng Y M 2009 Eng. Anal. Bound. Elem. 33 77
[41]	Ren H P, Cheng Y M and Zhang W 2009 Chin. Phys. B 18 4065
[42]	Ren H P, Cheng Y M and Zhang W 2010 Sci. China-Phys. Mech. Astron. 53 758
[43]	Wang J F, Sun F X and Cheng Y M 2012 Chin. Phys. B 21 090204
[44]	Wang J F, Wang J F, Sun F X and Cheng Y M 2013 Int. J. Comput. Methods 10 1350043
[45]	Braun J and Sambridge M 1995 Nature 376 655
[46]	Sukumar N, Moran B and Belytschko T 1998 Int. J. Numer. Methods Eng. 43 839
[47]	Bueche D, Sukumar N and Moran B 2000 Comput. Mech. 25 207
[48]	Cueto E, Calvo B and Doblare M 2002 Int. J. Numer. Methods Eng. 54 871
[49]	Martínez M, Cueto E, Doblaré M and Chinesta F 2003 J. Non-Newton. Fluid Mech. 115 51
[50]	Calvo B, Martinez M A and Doblaré M 2005 Int. J. Numer. Methods Eng. 62 159
[51]	Daneshmand F and Niroomandi S 2007 Eng. Comput. 24 269
[52]	Daneshmand F, Javanmard S S, Liaghat T, Moshksar M M and Adamowski J F 2010 Can. J. Civ. Eng. 37 1550
[53]	Shahrokhabadi S, Toufigh M M and Gholizadeh R 2010 GeoShanghai International Conference-Geoenvironmental Engineering and Geotechnics, June 3-5, 2010 Shanghai, China, p. 245
[54]	Cho J R, Lee H W and Yoo W S 2013 Comput. Meth. Appl. Mech. Eng. 256 17
[55]	Sibson R 1980 Mathematical Proceedings of the Cambridge Philosophical Society, January, 1980 Cambridge, England, p. 151
[56]	Farin G 1990 Comput. Aided Geom. Des. 7 281
[57]	Brown J L 1994 An international conference on curves and surfaces on Wavelets, images, and surface fitting, 1994 Chamonix-Mont-Blanc, France, p. 67
[58]	Tabbara M, Blacker T and Belytschko T 1994 Comput. Methods Appl. Mech. Engin. 117 211
[59]	Dong Y, Ma Y Q and Feng W 2012 Acta Mech. Sin. 44 568 (in Chinese)
[60]	Ma Y Q, Dong Y, Zhou Y K and Feng W 2014 Math. Probl. Eng. 2014 9
[61]	Belikov V, Ivanov V, Kontorovich V, Korytnik S and Semenov A Y 1997 Comput. Math. Math. Phys. 37 9
[62]	Sukumar N 2001 Proceedings of the first MIT Conference on Fluid and Solid Mechanics, June 12-14, 2001 Cambridge, USA, p. 1665
[63]	Tian Z S and Pian T H 2011 Multivariable Variation Principle and Multivariable Finite Element Method (Vol. 1) (Beijing: Science Press) p. 1 (in Chinese)
[64]	Pian T H and Chen D P 1982 Int. J. Numer. Methods Eng. 18 1679
[65]	Peng M J and Xu Z H 2006 Sci. Chin. Ser.G: Phys. Mech. Astron. 49 671
[66]	Flügge W 1975 Viscoelasticity (2nd edn.) (New York: Springer-Verlag) p. 1
[67]	Yang H T and Liu Y 2003 Int. J. Solids Struct. 40 701
[68]	Sladek J, Sladek V and Zhang C 2005 Engin. Anal. Bound. Elem. 29 597
[69]	Sladek J, Sladek V, Zhang C and Schanz M 2006 Comput. Mech. 37 279
[70]	Guan Y J, Zhao G Q, Wu X and Lu P 2007 J. Mater. Process. Technol. 187-188 412
[71]	Canelas A and Sensale B 2010 Eng. Anal. Bound. Elem. 34 845
[72]	Cheng Y M, Li R X and Peng M J 2012 Chin. Phys. B 21 090205
[73]	Peng M J, Li R X and Cheng Y M 2014 Engin.Anal. Bound. Elem. 40 104
[74]	Lawson C L 1977 Mathematical Software Ⅲ (3nd edn.) (New York: Academic Press) pp. 161-194

Hybrid natural element method for viscoelasticity problems

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