Improved complex variable element-free Galerkin method for viscoelasticity problems

Peng Miao-Juan; Liu Qian

doi:10.7498/aps.63.180203

Abstract

In this paper, based on the improved complex variable least-square (ICVMLS) approximation, the improved complex variable element-free Galerkin (ICVEFG) method for two-dimensional viscoelasticity problems is proposed. The ICVMLS approximation is used to form the shape function, the Galerkin weak form is used to obtain the system equations, and the penalty method is used to impose the essential boundary conditions, then the corresponding formulae of the ICVEFG method for two-dimensional viscoelasticity problems are obtained. Finally, some numerical examples are given, and the numerical results from the ICVEFG method are compared with those from the CVEFG method and finite element method, and the results show that the ICVEFG method in this paper has the high computational precision and efficiency.

Keywords:

Authors and contacts

1.
Department of Civil Engineering, Shanghai University, Shanghai 200072, China
Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11171208).

References

[1]	Belytschko T, Krongauz Y, Organ D 1996 Comput. Methods Appl. Mech. Engineer. 139 3
[2]	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]
[3]	Belytschko T, Lu Y Y, Gu L 1994 Int. J. Numeri. Methods Engineer. 37 229
[4]	Zhang Z, Li D M, Cheng Y M, Liew K M 2012 Acta Mech. Sin. 28 808
[5]	Zhang Z, Wang J F, Cheng Y M, Liew K M 2013 Sci. China G: Phys. Mech. Astron. 56 1568
[6]	Zhang Z, Hao S Y, Liew K M, Cheng Y M 2013 Engineering Analysis with Boundary Elements 37 1576
[7]	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]
[8]	Monaghan J J 1998 Comput. Phys. Commun. 48 89
[9]	Cheng R J, Cheng Y M 2008 Appl. Numer. Math. 58 884
[10]	Cheng R J, Cheng Y M 2007 Acta Phys. Sin. 56 5569(in Chinese)[程荣军, 程玉民 2007 物理学报 56 5569]
[11]	Cheng R J, Cheng Y M 2007 Acta Mech. Sin. 39 843(in Chinese)[程荣军, 程玉民 2007 力学学报 39 843]
[12]	Dai B D, Cheng J, Zheng B J 2013 Int. J. Appl. Mech. 5 1350011
[13]	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]
[14]	Li S C, Li S C, Cheng Y M 2005 Theoret. Appl. Fract. Mech. 44 234
[15]	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]
[16]	Chen L, Cheng Y M 2010 Sci. China G: Phys. Mech. Astron. 40 242(in Chinese)[陈丽, 程玉民 2010 中国科学 G辑物理学力学天文学 40 242]
[17]	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]
[18]	Cheng Y M, Peng M J 2005 Sci. China G: Phys. Mech. Astron. 35 435(in Chinese)[程玉民, 彭妙娟 2005 中国科学 G辑物理学力学天文学 35 435]
[19]	Cheng Y M, Peng M J 2005 Sci. China G: Phys. Mech. Astron. 48 641
[20]	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]
[21]	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]
[22]	Peng M J, Cheng Y M 2009 Engineering Analysis with Boundary Elements 33 77
[23]	Cheng Y M, Liew K M, Kitipornchai S 2009 Int. J. Numer. Methods Engineer. 78 1258
[24]	Yang H T, Liu Y 2003 Int. J. Solids Struct. 40 701
[25]	Sladek J, Sladek V, Zhang C H 2005 Engineering Analysis with Boundary Elements 29 597
[26]	Sladek J, Sladek V, Zhang C H, Schanz M 2006 Computat. Mech. 37 279
[27]	Cheng Y M, Li R X, Peng M J 2012 Chin. Phys. B 21 090205
[28]	Cheng Y M, Peng M J, Li J H 2005 Acta Mech. Sin. 37 719(in Chinese)[程玉民, 彭妙娟, 李九红 2005 力学学报 37 719]
[29]	Cheng Y M, Li J H 2005 Sci. China G: Phys. Mech. Astron. 35 548(in Chinese)[程玉民, 李九红 2005 中国科学 G辑物理学力学天文学 35 548]
[30]	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]
[31]	Cheng Y M, Li J H 2006 Sci. China G: Phys. Mech. Astron. 49 46
[32]	Liew K M, Feng C, Cheng Y M, Kitipornchai S 2007 Int. J. Numer. Methods Engineer 70 46
[33]	Cheng Y M, Wang J F, Li R X 2012 Int. J. Appl. Mech. 4 1250042
[34]	Liew K M, Cheng Y 2009 Comput. Methods Appl. Mech. Engineer. 198 3925
[35]	Gao H, Cheng Y 2010 Int. J. Computat. Methods 7 55
[36]	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]
[37]	Bai F N, Li D M, Wang J F, Cheng Y M 2012 Chin. Phys. B 21 020204
[38]	Cheng Y M, Wang J F, Bai F N 2012 Chin. Phys. B 21 090203
[39]	Wang J F, Cheng Y M 2012 Chin. Phys. B 21 120206
[40]	Wang J F, Cheng Y M 2013 Chin. Phys. B 22 030208
[41]	Li D M, Bai F N, Cheng Y M, Liew K M 2012 Comput. Methods Appl. Mech. Engineer. 233–236 1
[42]	Li D M, Liew K M, Cheng Y M 2014 Comput. Methods Appl. Mech. Engineer. 269 72
[43]	Peng M, Liu P, Cheng Y 2009 Int. J. Appl. Mech. 1 367
[44]	Liu P, Peng M J, Cheng Y M 2009 Comput. Aided Engineer. 18 10(in Chinese)[刘沛, 彭妙娟, 程玉民 2009 计算机辅助工程 18 10]
[45]	Peng M J, Li D M, Cheng Y M 2011 Engineer. Struct. 33 127
[46]	Li D M, Peng M J, Cheng Y M 2011 Sci. China G: Phys. Mech. Astron. 41 1003(in Chinese)[李冬明, 彭妙娟, 程玉民 2011 中国科学 G辑物理学力学天文学 41 1003]
[47]	Peng M J, Li R X, Cheng Y M 2014 Engineering Analysis with Boundary Elements 40 104
[48]	Li D M, Liew K M, Cheng Y M 2014 Computat. Mech. 53 1149
[49]	Chen L, Cheng Y 2010 Sci. China G: Phys. Mech. Astron. 53 954
[50]	Chen L, Cheng Y M 2010 Chin. Phys. B 19 090204
[51]	Chen L, Ma H P, Cheng Y M 2013 Chin. Phys. B 22 050202
[52]	Weng Y J, Cheng Y M 2013 Chin. Phys. B 22 090204
[53]	Weng Y J, Zhang Z, Cheng Y M 2014 Engineering Analysis with Boundary Elements 44 36
[54]	Ren H, Cheng J, Huang A 2012 Appl. Math. Computat. 219 1724
[55]	Flgge W 1975 Viscoelasticity (2nd Ed) (New York: Springer-Verlag)

Cited By

[1]	Belytschko T, Krongauz Y, Organ D 1996 Comput. Methods Appl. Mech. Engineer. 139 3
[2]	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]
[3]	Belytschko T, Lu Y Y, Gu L 1994 Int. J. Numeri. Methods Engineer. 37 229
[4]	Zhang Z, Li D M, Cheng Y M, Liew K M 2012 Acta Mech. Sin. 28 808
[5]	Zhang Z, Wang J F, Cheng Y M, Liew K M 2013 Sci. China G: Phys. Mech. Astron. 56 1568
[6]	Zhang Z, Hao S Y, Liew K M, Cheng Y M 2013 Engineering Analysis with Boundary Elements 37 1576
[7]	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]
[8]	Monaghan J J 1998 Comput. Phys. Commun. 48 89
[9]	Cheng R J, Cheng Y M 2008 Appl. Numer. Math. 58 884
[10]	Cheng R J, Cheng Y M 2007 Acta Phys. Sin. 56 5569(in Chinese)[程荣军, 程玉民 2007 物理学报 56 5569]
[11]	Cheng R J, Cheng Y M 2007 Acta Mech. Sin. 39 843(in Chinese)[程荣军, 程玉民 2007 力学学报 39 843]
[12]	Dai B D, Cheng J, Zheng B J 2013 Int. J. Appl. Mech. 5 1350011
[13]	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]
[14]	Li S C, Li S C, Cheng Y M 2005 Theoret. Appl. Fract. Mech. 44 234
[15]	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]
[16]	Chen L, Cheng Y M 2010 Sci. China G: Phys. Mech. Astron. 40 242(in Chinese)[陈丽, 程玉民 2010 中国科学 G辑物理学力学天文学 40 242]
[17]	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]
[18]	Cheng Y M, Peng M J 2005 Sci. China G: Phys. Mech. Astron. 35 435(in Chinese)[程玉民, 彭妙娟 2005 中国科学 G辑物理学力学天文学 35 435]
[19]	Cheng Y M, Peng M J 2005 Sci. China G: Phys. Mech. Astron. 48 641
[20]	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]
[21]	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]
[22]	Peng M J, Cheng Y M 2009 Engineering Analysis with Boundary Elements 33 77
[23]	Cheng Y M, Liew K M, Kitipornchai S 2009 Int. J. Numer. Methods Engineer. 78 1258
[24]	Yang H T, Liu Y 2003 Int. J. Solids Struct. 40 701
[25]	Sladek J, Sladek V, Zhang C H 2005 Engineering Analysis with Boundary Elements 29 597
[26]	Sladek J, Sladek V, Zhang C H, Schanz M 2006 Computat. Mech. 37 279
[27]	Cheng Y M, Li R X, Peng M J 2012 Chin. Phys. B 21 090205
[28]	Cheng Y M, Peng M J, Li J H 2005 Acta Mech. Sin. 37 719(in Chinese)[程玉民, 彭妙娟, 李九红 2005 力学学报 37 719]
[29]	Cheng Y M, Li J H 2005 Sci. China G: Phys. Mech. Astron. 35 548(in Chinese)[程玉民, 李九红 2005 中国科学 G辑物理学力学天文学 35 548]
[30]	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]
[31]	Cheng Y M, Li J H 2006 Sci. China G: Phys. Mech. Astron. 49 46
[32]	Liew K M, Feng C, Cheng Y M, Kitipornchai S 2007 Int. J. Numer. Methods Engineer 70 46
[33]	Cheng Y M, Wang J F, Li R X 2012 Int. J. Appl. Mech. 4 1250042
[34]	Liew K M, Cheng Y 2009 Comput. Methods Appl. Mech. Engineer. 198 3925
[35]	Gao H, Cheng Y 2010 Int. J. Computat. Methods 7 55
[36]	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]
[37]	Bai F N, Li D M, Wang J F, Cheng Y M 2012 Chin. Phys. B 21 020204
[38]	Cheng Y M, Wang J F, Bai F N 2012 Chin. Phys. B 21 090203
[39]	Wang J F, Cheng Y M 2012 Chin. Phys. B 21 120206
[40]	Wang J F, Cheng Y M 2013 Chin. Phys. B 22 030208
[41]	Li D M, Bai F N, Cheng Y M, Liew K M 2012 Comput. Methods Appl. Mech. Engineer. 233–236 1
[42]	Li D M, Liew K M, Cheng Y M 2014 Comput. Methods Appl. Mech. Engineer. 269 72
[43]	Peng M, Liu P, Cheng Y 2009 Int. J. Appl. Mech. 1 367
[44]	Liu P, Peng M J, Cheng Y M 2009 Comput. Aided Engineer. 18 10(in Chinese)[刘沛, 彭妙娟, 程玉民 2009 计算机辅助工程 18 10]
[45]	Peng M J, Li D M, Cheng Y M 2011 Engineer. Struct. 33 127
[46]	Li D M, Peng M J, Cheng Y M 2011 Sci. China G: Phys. Mech. Astron. 41 1003(in Chinese)[李冬明, 彭妙娟, 程玉民 2011 中国科学 G辑物理学力学天文学 41 1003]
[47]	Peng M J, Li R X, Cheng Y M 2014 Engineering Analysis with Boundary Elements 40 104
[48]	Li D M, Liew K M, Cheng Y M 2014 Computat. Mech. 53 1149
[49]	Chen L, Cheng Y 2010 Sci. China G: Phys. Mech. Astron. 53 954
[50]	Chen L, Cheng Y M 2010 Chin. Phys. B 19 090204
[51]	Chen L, Ma H P, Cheng Y M 2013 Chin. Phys. B 22 050202
[52]	Weng Y J, Cheng Y M 2013 Chin. Phys. B 22 090204
[53]	Weng Y J, Zhang Z, Cheng Y M 2014 Engineering Analysis with Boundary Elements 44 36
[54]	Ren H, Cheng J, Huang A 2012 Appl. Math. Computat. 219 1724
[55]	Flgge W 1975 Viscoelasticity (2nd Ed) (New York: Springer-Verlag)

[1]	Zhou Hao, Li Yi, Liu Hai, Chen Hong, Ren Lei-Sheng. Optimized transportation meshfree method and its apllication in simulating droplet surface tension effect. Acta Physica Sinica, 2021, 70(24): 240203. doi: 10.7498/aps.70.20211078
[2]	Zhang Peng-Xuan, Peng Miao-Juan. Interpolating element-free Galerkin method for viscoelasticity problems. Acta Physica Sinica, 2019, 68(17): 170203. doi: 10.7498/aps.68.20191047
[3]	Zou Shi-Ying, Xi Wei-Cheng, Peng Miao-Juan, Cheng Yu-Min. Analysis of fracture problems of airport pavement by improved element-free Galerkin method. Acta Physica Sinica, 2017, 66(12): 120204. doi: 10.7498/aps.66.120204
[4]	Du Hong-Xiu, Wei Hong, Qin Yi-Xiao, Li Zhong-Hua, Wang Tong-Zun. Interpolating particle method for mechanical analysis of space axisymmetric components. Acta Physica Sinica, 2015, 64(10): 100204. doi: 10.7498/aps.64.100204
[5]	Feng Zhao, Wang Xiao-Dong, Ouyang Jie. The element-free Galerkin method based on the shifted basis for solving the Kuramoto- Sivashinsky equation. Acta Physica Sinica, 2012, 61(23): 230204. doi: 10.7498/aps.61.230204
[6]	Li Zhong-Hua, Qin Yi-Xiao, Cui Xiao-Chao. Interpolating reproducing kernel particle method for elastic mechanics. Acta Physica Sinica, 2012, 61(8): 080205. doi: 10.7498/aps.61.080205
[7]	Yang Xiu-Li, Dai Bao-Dong, Li Zhen-Feng. Meshless local Petrov-Galerkin method with complex variables for elasticity. Acta Physica Sinica, 2012, 61(5): 050204. doi: 10.7498/aps.61.050204
[8]	Cheng Yu-Min, Cheng Rong-Jun. Error estimate of element-free Galerkin method for elasticity. Acta Physica Sinica, 2011, 60(7): 070206. doi: 10.7498/aps.60.070206
[9]	Zheng Bao-Jing, Dai Bao-Dong. Improved meshless local Petrov-Galerkin method for two-dimensional potential problems. Acta Physica Sinica, 2010, 59(8): 5182-5189. doi: 10.7498/aps.59.5182
[10]	Li Jun, Dong Hai-Ying. Modelling of chaotic systems using wavelet kernel partial least squares regression method. Acta Physica Sinica, 2008, 57(8): 4756-4765. doi: 10.7498/aps.57.4756
[11]	Tang Bo, Li Jun-Feng, Wang Tian-Shu. Numerical simulation of liquid drop phenomenon by least square particle finite element method. Acta Physica Sinica, 2008, 57(11): 6722-6729. doi: 10.7498/aps.57.6722
[12]	Chen Li, Cheng Yu-Min. Complex variable reproducing kernel particle method for transient heat conduction problems. Acta Physica Sinica, 2008, 57(10): 6047-6055. doi: 10.7498/aps.57.6047
[13]	Chen Li, Cheng Yu-Min. Reproducing kernel particle method with complex variables for elasticity. Acta Physica Sinica, 2008, 57(1): 1-10. doi: 10.7498/aps.57.1
[14]	Cheng Rong-Jun, Cheng Yu-Min. Error estimates of element-free Galerkin method for potential problems. Acta Physica Sinica, 2008, 57(10): 6037-6046. doi: 10.7498/aps.57.6037
[15]	Dai Bao-Dong, Cheng Yu-Min. Local boundary integral equation method based on radial basis functions for potential problems. Acta Physica Sinica, 2007, 56(2): 597-603. doi: 10.7498/aps.56.597
[16]	Cheng Rong-Jun, Cheng Yu-Min. The meshless method for solving the inverse heat conduction problem with a source parameter. Acta Physica Sinica, 2007, 56(10): 5569-5574. doi: 10.7498/aps.56.5569
[17]	Li Shu-Chen, Cheng Yu-Min, Li Shu-Cai. Meshless manifold method for dynamic fracture mechanics. Acta Physica Sinica, 2006, 55(9): 4760-4766. doi: 10.7498/aps.55.4760
[18]	Cheng Yu-Min, Li Jiu-Hong. A meshless method with complex variables for elasticity. Acta Physica Sinica, 2005, 54(10): 4463-4471. doi: 10.7498/aps.54.4463
[19]	GUO CHANG-LIN, HUANG YUE-HONG. STABLE SOLUTIONS OF THE LEAST SQUARE SIMULTANEOUS EQUATIONS IN QUANTITATIVE X-RAY PHASE ANALYSIS WITHOUT STANDARDS. Acta Physica Sinica, 1993, 42(7): 1106-1111. doi: 10.7498/aps.42.1106
[20]	ZHANG HUNG-TU. PLASTICAL PROBLEMS OF A CRYSTAL THAT HAS A TWO-HOLD SYMMETRICAL AXIS. Acta Physica Sinica, 1959, 15(1): 1-12. doi: 10.7498/aps.15.1

Catalog

Vol. 63, Issue 18 - 2014-09-20

Metrics

Abstract views: 5759
PDF Downloads: 410
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板