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Static and dynamic analysis of elastic shell structures with smoothed particle method

Ming Fu-Ren Zhang A-Man Yao Xiong-Liang

Static and dynamic analysis of elastic shell structures with smoothed particle method

Ming Fu-Ren, Zhang A-Man, Yao Xiong-Liang
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  • Meshfree smoothed particle method has great advantages in dealing with nonlinear problems of solid structures However, due to the instability and poor accuracy, it has been limited to the application in solid mechanics for a long time; especially the study on shell structure with smoothed particle method is even rarely reported on account of expensive three-dimensional continuum modeling and the phenomenon of numerical fracture in the traditional method The moving least square function and total Lagrangian equations are introduced as an approximation function and approximation equations respectively to improve the stability and numerical accuracy of smoothed particle method; on this basis, the method of static analysis is proposed, and meanwhile the dynamic analysis method is also refined. Finally, the internationally recognized standard test models on static and dynamic problems are adopted to verify the above shell theory, and the results are in good agreement with the existing data, which proves the validity and reliability of the present numerical model. This paper aims to provide a reference for the further research of smoothed particle method on nonlinear shell structures, such as crack, crushing, etc.
    • Funds: Project supported by the Excellent Young Scientists Fund (Grant No. 51222904), the Key Program of the National Natural Science Foundation of China (Grant No. 50939002), and the Llyod's Register Educational Trust (The LRET).
    [1]

    Au F T K, Cheung Y K 1996 Thin wall Struct. 24 53

    [2]

    Morino L, Leech J W, Witmer E A 1971 J. Appl. Mech. 38 429

    [3]

    Rossing T D, Fletcher N H 1983 J. Acoust. Soc. Am. 73 345

    [4]

    Timoshenko S, Woinowsky-Krieger S 1959 Theory of plates and shells (2nd Edn.) (New York: Mcgraw-Hill) p201

    [5]

    Parisch H 1995 Int. J. Numer. Meth. Engng. 38 1855

    [6]

    Reddy J N 2007 Theory and analysis of elastic plates and shells (2nd Edn.) (Florida: CRC) p21

    [7]

    Krysl P, Belytschko T 1996 Int. J. Solids Struct. 33 3057

    [8]

    Noguchi H, Kawashima T, Miyamura T 2000 Int. J. Numer. Meth Engng. 47 1215

    [9]

    Rabczuk T, Areias P M A, BelytschkoT 2007 Int. J. Numer. Meth Engng. 72 524

    [10]

    Wang D, Chen J S 2003 Comput. Methods Appl. Mech. Engrg. 193 1065

    [11]

    Miao Y, WangY 2005 Eng. Anal. Bound. Elem. 29 703

    [12]

    Li S, Hao W, Liu W K 2000 Comput. Mech. 25 102

    [13]

    Garcia O, Fancello E A, de Barcellos C S, Duarte C A 2000 Int. J. Numer. Meth Engng. 47 1381

    [14]

    Sladek J, SladekV, Wen P H, Aliabadi M H 2006 CMES-Comp. Model Eng. 13 103

    [15]

    Oh H S, Davis C, Jeong J W 2012 Comput. Methods Appl. Mech. Engrg. 209 156

    [16]

    Liu G R 2002 Int. J. Solids Struct. 39 261

    [17]

    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]

    [18]

    Yang X L, Dai B D, Li Z F 2012 Acta Phys. Sin. 61 050204 (in Chinese) [杨秀丽, 戴保东, 栗振锋 2012 物理学报 61 050204]

    [19]

    Qin Y X, Cheng Y M 2006 Acta Phys. Sin. 55 3215 (in Chinese) [秦义校, 程玉民 2006 物理学报 55 3215]

    [20]

    Belytschko T, Black T 1999 Int. J. Numer. Meth Engng. 45 601

    [21]

    Unossona M, Olovssona L, Simonssonb K 2006 Finite Elem. Anal. Des. 42 283

    [22]

    Moes N, Dolbow J, Belytschko T 1999 Int. J. Numer. Meth. Engng. 46 133

    [23]

    Chang J Z, Liu M B, Liu H T 2008 Acta Phys. Sin. 57 3954 (in Chinese) [常建忠, 刘谋斌, 刘汉涛 2008 物理学报 57 3954]

    [24]

    Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌, 常建忠 2010 物理学报 59 3654]

    [25]

    Shao J R, Li H Q, Liu G R, Liu M B 2012 Comput. Struct. 100-101 18

    [26]

    Randles P W, Libersky L D 2000 Int. J. Numer. Meth Engng. 48 1445

    [27]

    Dilts G A 1999 Int. J. Numer. Meth Engng. 44 1115

    [28]

    Dilts G A 2000 Int. J. Numer. Meth Engng. 48 1503

    [29]

    Vidal Y, Bonet J, Huerta A 2007 Int. J. Numer. Meth Engng. 69 2687

    [30]

    Belytschko T, Rabczuk T, Xiao S P 2004 Comput. Methods Appl. Mech. 193 1035

    [31]

    Maurel B, Combescure A 2008 Int. J. Numer. Meth Engng. 76 949

    [32]

    Maurel B, Combescure A, Potapov S 2006 Eur. J. Comput. Mech. 15 495

    [33]

    Shepard D 1968 Proceedings of the 23rd ACM national conference New York, August 27-29, 1968 p517

    [34]

    Bonet J, Lok T S L 1999 Comput. Methods Appl. Mech. Engrg. 180 97

    [35]

    Liu W K, Li S, Belytschko T 1997 Comput. Methods Appl. Mech. Engrg. 143 113

    [36]

    Johnson G R, Stryk R A, Beissel S R 1996 Comput. Methods Appl. Mech. Engrg. 139 347

    [37]

    Belytschko T, Krongauz Y, Dolbow J, Gerlach C 1998 Int. J. Numer. Meth Engng. 43 785

    [38]

    KrongauzY, BelytschkoT 1997 Comput. Methods Appl. Mech. Engrg. 146 371

    [39]

    Randles P W, Libersky L D 1996 Comput. Methods Appl. Mech. Engrg. 139 375

    [40]

    Kanok-Nukulchai W, Bary W, Saran-Yasoontorn K, Bouillard P H 2001 Int. J. Numer. Meth Engng. 52 705

    [41]

    Belytschko T, Liu W K, Moran B 2000 Nonlinear Finite Elements for Continua and Structures ( New York: John Wiley and Sons Ltd) p1

    [42]

    Liu G R, Liu M B 2003 Smoothed particle hydrodynamics: a meshfree particle method. (Singapore: World Scientific) p1

    [43]

    Caleyron F, Combescure A, Faucher V Potapov S 2012 Int. J. Numer. Meth Engng. 90 707

    [44]

    Dyka C T, Randles P W, Ingel R P 1997 Int. J. Numer. Meth Engng. 40 2325

    [45]

    Belytschko T, Guo Y, Liu W K, Xiao S P 2000 Int. J. Numer. Meth Engng. 40 1359

    [46]

    Hughes T J R, Liu W K 1978 J. Appl. Mech. 45 371

    [47]

    Monaghan J J, Gingold R 1983 J. Comput. Phys. 52 374

    [48]

    Betsch P, Menzel A, Stein E 1998 Comput. Methods Appl. Mech. 155 273

    [49]

    Macneal R H, Harder R L 1985 Finite Elem. Anal. Des. 1 3

    [50]

    Simo J C, Fox D D, Rifai M S 1989 Comput. Methods Appl. Mech. 73 53

    [51]

    Swaddiwudhipong S, Liu Z S 1996 Thin Wall Struct. 26 223

    [52]

    Owen D R J, Hinton E 1980 Finite Elements in Plasticity: Theory and Practice (Swansea: Pineridge press) p254

  • [1]

    Au F T K, Cheung Y K 1996 Thin wall Struct. 24 53

    [2]

    Morino L, Leech J W, Witmer E A 1971 J. Appl. Mech. 38 429

    [3]

    Rossing T D, Fletcher N H 1983 J. Acoust. Soc. Am. 73 345

    [4]

    Timoshenko S, Woinowsky-Krieger S 1959 Theory of plates and shells (2nd Edn.) (New York: Mcgraw-Hill) p201

    [5]

    Parisch H 1995 Int. J. Numer. Meth. Engng. 38 1855

    [6]

    Reddy J N 2007 Theory and analysis of elastic plates and shells (2nd Edn.) (Florida: CRC) p21

    [7]

    Krysl P, Belytschko T 1996 Int. J. Solids Struct. 33 3057

    [8]

    Noguchi H, Kawashima T, Miyamura T 2000 Int. J. Numer. Meth Engng. 47 1215

    [9]

    Rabczuk T, Areias P M A, BelytschkoT 2007 Int. J. Numer. Meth Engng. 72 524

    [10]

    Wang D, Chen J S 2003 Comput. Methods Appl. Mech. Engrg. 193 1065

    [11]

    Miao Y, WangY 2005 Eng. Anal. Bound. Elem. 29 703

    [12]

    Li S, Hao W, Liu W K 2000 Comput. Mech. 25 102

    [13]

    Garcia O, Fancello E A, de Barcellos C S, Duarte C A 2000 Int. J. Numer. Meth Engng. 47 1381

    [14]

    Sladek J, SladekV, Wen P H, Aliabadi M H 2006 CMES-Comp. Model Eng. 13 103

    [15]

    Oh H S, Davis C, Jeong J W 2012 Comput. Methods Appl. Mech. Engrg. 209 156

    [16]

    Liu G R 2002 Int. J. Solids Struct. 39 261

    [17]

    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]

    [18]

    Yang X L, Dai B D, Li Z F 2012 Acta Phys. Sin. 61 050204 (in Chinese) [杨秀丽, 戴保东, 栗振锋 2012 物理学报 61 050204]

    [19]

    Qin Y X, Cheng Y M 2006 Acta Phys. Sin. 55 3215 (in Chinese) [秦义校, 程玉民 2006 物理学报 55 3215]

    [20]

    Belytschko T, Black T 1999 Int. J. Numer. Meth Engng. 45 601

    [21]

    Unossona M, Olovssona L, Simonssonb K 2006 Finite Elem. Anal. Des. 42 283

    [22]

    Moes N, Dolbow J, Belytschko T 1999 Int. J. Numer. Meth. Engng. 46 133

    [23]

    Chang J Z, Liu M B, Liu H T 2008 Acta Phys. Sin. 57 3954 (in Chinese) [常建忠, 刘谋斌, 刘汉涛 2008 物理学报 57 3954]

    [24]

    Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌, 常建忠 2010 物理学报 59 3654]

    [25]

    Shao J R, Li H Q, Liu G R, Liu M B 2012 Comput. Struct. 100-101 18

    [26]

    Randles P W, Libersky L D 2000 Int. J. Numer. Meth Engng. 48 1445

    [27]

    Dilts G A 1999 Int. J. Numer. Meth Engng. 44 1115

    [28]

    Dilts G A 2000 Int. J. Numer. Meth Engng. 48 1503

    [29]

    Vidal Y, Bonet J, Huerta A 2007 Int. J. Numer. Meth Engng. 69 2687

    [30]

    Belytschko T, Rabczuk T, Xiao S P 2004 Comput. Methods Appl. Mech. 193 1035

    [31]

    Maurel B, Combescure A 2008 Int. J. Numer. Meth Engng. 76 949

    [32]

    Maurel B, Combescure A, Potapov S 2006 Eur. J. Comput. Mech. 15 495

    [33]

    Shepard D 1968 Proceedings of the 23rd ACM national conference New York, August 27-29, 1968 p517

    [34]

    Bonet J, Lok T S L 1999 Comput. Methods Appl. Mech. Engrg. 180 97

    [35]

    Liu W K, Li S, Belytschko T 1997 Comput. Methods Appl. Mech. Engrg. 143 113

    [36]

    Johnson G R, Stryk R A, Beissel S R 1996 Comput. Methods Appl. Mech. Engrg. 139 347

    [37]

    Belytschko T, Krongauz Y, Dolbow J, Gerlach C 1998 Int. J. Numer. Meth Engng. 43 785

    [38]

    KrongauzY, BelytschkoT 1997 Comput. Methods Appl. Mech. Engrg. 146 371

    [39]

    Randles P W, Libersky L D 1996 Comput. Methods Appl. Mech. Engrg. 139 375

    [40]

    Kanok-Nukulchai W, Bary W, Saran-Yasoontorn K, Bouillard P H 2001 Int. J. Numer. Meth Engng. 52 705

    [41]

    Belytschko T, Liu W K, Moran B 2000 Nonlinear Finite Elements for Continua and Structures ( New York: John Wiley and Sons Ltd) p1

    [42]

    Liu G R, Liu M B 2003 Smoothed particle hydrodynamics: a meshfree particle method. (Singapore: World Scientific) p1

    [43]

    Caleyron F, Combescure A, Faucher V Potapov S 2012 Int. J. Numer. Meth Engng. 90 707

    [44]

    Dyka C T, Randles P W, Ingel R P 1997 Int. J. Numer. Meth Engng. 40 2325

    [45]

    Belytschko T, Guo Y, Liu W K, Xiao S P 2000 Int. J. Numer. Meth Engng. 40 1359

    [46]

    Hughes T J R, Liu W K 1978 J. Appl. Mech. 45 371

    [47]

    Monaghan J J, Gingold R 1983 J. Comput. Phys. 52 374

    [48]

    Betsch P, Menzel A, Stein E 1998 Comput. Methods Appl. Mech. 155 273

    [49]

    Macneal R H, Harder R L 1985 Finite Elem. Anal. Des. 1 3

    [50]

    Simo J C, Fox D D, Rifai M S 1989 Comput. Methods Appl. Mech. 73 53

    [51]

    Swaddiwudhipong S, Liu Z S 1996 Thin Wall Struct. 26 223

    [52]

    Owen D R J, Hinton E 1980 Finite Elements in Plasticity: Theory and Practice (Swansea: Pineridge press) p254

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  • Received Date:  25 December 2012
  • Accepted Date:  17 January 2013
  • Published Online:  05 June 2013

Static and dynamic analysis of elastic shell structures with smoothed particle method

  • 1. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
Fund Project:  Project supported by the Excellent Young Scientists Fund (Grant No. 51222904), the Key Program of the National Natural Science Foundation of China (Grant No. 50939002), and the Llyod's Register Educational Trust (The LRET).

Abstract: Meshfree smoothed particle method has great advantages in dealing with nonlinear problems of solid structures However, due to the instability and poor accuracy, it has been limited to the application in solid mechanics for a long time; especially the study on shell structure with smoothed particle method is even rarely reported on account of expensive three-dimensional continuum modeling and the phenomenon of numerical fracture in the traditional method The moving least square function and total Lagrangian equations are introduced as an approximation function and approximation equations respectively to improve the stability and numerical accuracy of smoothed particle method; on this basis, the method of static analysis is proposed, and meanwhile the dynamic analysis method is also refined. Finally, the internationally recognized standard test models on static and dynamic problems are adopted to verify the above shell theory, and the results are in good agreement with the existing data, which proves the validity and reliability of the present numerical model. This paper aims to provide a reference for the further research of smoothed particle method on nonlinear shell structures, such as crack, crushing, etc.

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