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Li, Dongming; Bai, Funong; Cheng, Yumin; Liew, Kim Moew

A novel complex variable element-free Galerkin method for two-dimensional large deformation problems. (English) Zbl 1253.74106

Comput. Methods Appl. Mech. Eng. 233-236, 1-10 (2012).
Summary: Based on complex variable theory and moving least-squares (MLS) approximation, the improved complex variable moving least-squares (ICVMLS) approximation is discussed in this paper. Compared with complex variable moving least-squares (CVMLS) approximation, the function in the ICVMLS approximation has an explicit physics meaning. By using a new basis function, the ICVMLS approximation can obtain greater precision and computational efficiency. Based on the ICVMLS approximation, an improved complex variable element-free Galerkin (ICVEFG) method, which belongs to a novel element free Galerkin (EFG) method, is presented for two-dimensional large deformation problems. The Galerkin weak form is employed to obtain the equations, while the penalty method is used to apply the essential boundary conditions. Then the corresponding formulae of the ICVEFG method for two-dimensional large deformation problems are obtained. Compared with the EFG method, the ICVEFG method has greater precision and efficiency.

Cited in 42 Documents

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

Keywords:

moving least-squares (MLS) approximation; improved complex variable moving least-squares (ICVMLS) approximation; element-free Galerkin (EFG) method; improved complex variable element-free Galerkin (ICVEFG) method; meshless method; large deformation
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\textit{D. Li} et al., Comput. Methods Appl. Mech. Eng. 233--236, 1--10 (2012; Zbl 1253.74106)
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References:

[1] Belytschko, T.; Krongauz, Y.; Organ, D.; Fleming, M.; Krysl, P., Meshless method: an overview and recent developments, Comput. Methods Appl. Mech. Engrg., 139, 3-47 (1996) · Zbl 0891.73075
[2] Ji, X.; Zang, Y.; Cheng, Y., Advances in Boundary Element Methods and the General Package (1997), Tongji University Press: Tongji University Press Shanghai
[3] Chen, J. S.; Pan, C.; Wu, C. T.; Liu, W. K., Reproducing Kernel Particle Methods for large deformation analysis of non-linear structures, Comput. Methods Appl. Mech. Engrg., 139, 195-227 (1996) · Zbl 0918.73330
[4] Jun, S.; Liu, W. K.; Belytschko, T., Explicit reproducing kernel particle methods for large deformation problems, Int. J. Numer. Methods Engrg., 41, 137-166 (1998) · Zbl 0909.73088
[5] Liu, W. K.; Jun, S., Multiple-scale reproducing kernel particle methods for large deformation problem, Int. J. Numer. Methods Engrg., 41, 1339-1362 (1998) · Zbl 0916.73060
[6] Li, S.; Hao, W.; Liu, W. K., Mesh-free simulations of shear banding in large deformation, Int. J. Solids Struct., 37, 7185-7206 (2000) · Zbl 0995.74082
[7] Liew, K. M.; Ng, T. Y.; Wu, Y. C., Meshfree method for large deformation analysis - A reproducing kernel particle approach, Engrg. Struct., 24, 543-551 (2002)
[8] Sladek, J.; Sladek, V. A., A meshless method for large deflection of plates, Comput. Mech., 30, 2, 155-163 (2003) · Zbl 1128.74345
[9] Han, Z. D.; Rajendran, A. M.; Atluri, S. N., Meshless local Petrov-Galerkin (MLPG) approaches for solving nonlinear problems with large deformations and rotations, Comput. Model. Engrg. Sci., 10, 1-12 (2005) · Zbl 1232.74117
[10] Lu, H.; Cheng, H. S.; Cao, J.; Liu, W. K., Adaptive enrichment meshfree simulation and experiment on buckling and post-buckling analysis in sheet metal forming, Comput. Methods Appl. Mech. Engrg., 194, 2569-2590 (2005) · Zbl 1082.74017
[11] Naffa, M.; Al-Gahtani, H. J., Rbf-based meshless method for large deflection of thin plates, Engrg. Anal. Bound. Elem., 31, 311-317 (2007) · Zbl 1195.74250
[12] Rossi, R.; Alves, M. K., On the analysis of an Efg method under large deformations and volumetric locking, Comput. Mech., 39, 381-399 (2007) · Zbl 1178.74185
[13] Liew, K. M.; Peng, L. X.; Kitipornchai, S., Nonlinear analysis of corrugated plates using a Fsdt and a meshfree method, Comput. Methods Appl. Mech. Engrg., 196, 2358-2376 (2007) · Zbl 1173.74353
[14] Tiago, C.; Pimenta, P. M., An Efg method for the nonlinear analysis of plates undergoing arbitrarily large deformations, Engrg. Anal. Bound. Elem., 32, 494-511 (2008) · Zbl 1244.74233
[15] Doweidar, M. H.; Calvo, B.; Alfaro, I.; Groenenboomd, P.; Doblaré, M., A comparison of implicit and explicit natural element methods in large strains problems: application to soft biological tissues modeling, Comput. Methods Appl. Mech. Engrg., 199, 1691-1700 (2010) · Zbl 1231.74477
[16] Lancaster, P.; Salkauskas, K., Surface generated by moving least squares methods, Math. Comput., 37, 141-158 (1981) · Zbl 0469.41005
[17] Liew, K. M.; Cheng, Y.; Kitipornchai, S., Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems, Int. J. Numer. Methods Engrg., 65, 8, 1310-1332 (2006) · Zbl 1147.74047
[18] Cheng, Y.; Peng, M., Boundary element-free method for elastodynamics, Sci. China Ser. G Phys. Mech. Astron., 48, 6, 641-657 (2005)
[19] Liew, K. M.; Cheng, Y.; Kitipornchai, S., Boundary element-free method (BEFM) for two-dimensional elastodynamic analysis using Laplace transform, Int. J. Numer. Methods Engrg., 64, 12, 1610-1627 (2005) · Zbl 1122.74533
[20] Kitipornchai, S.; Liew, K. M.; Cheng, Y., A boundary element-free method (BEFM) for three-dimensional elasticity problems, Comput. Mech., 36, 13-20 (2005) · Zbl 1109.74372
[21] Sun, Y.; Zhang, Z.; Kitipornchai, S.; Liew, K. M., Analyzing the interaction between collinear interfacial cracks by an efficient boundary element-free method, Int. J. Engrg. Sci., 44, 37-48 (2006) · Zbl 1213.74270
[22] Liew, K. M.; Cheng, Y.; Kitipornchai, S., Analyzing the 2D fracture problems via the enriched boundary element-free method, Int. J. Solids Struct., 44, 4220-4233 (2007) · Zbl 1346.74162
[23] Liew, K. M.; Sun, Y.; Kitipornchai, S., Boundary element-free method for fracture analysis of 2-D anisotropic piezoelectric solids, Int. J. Numer. Methods Engrg., 69, 729-749 (2007) · Zbl 1194.74531
[24] Sun, Y.; Hu, Y. G.; Liew, K. M., A mesh-free simulation of cracking and failure using the cohesive segments method, Int. J. Engrg. Sci., 45, 541-553 (2007) · Zbl 1213.74312
[25] Miers, L. S.; Telles, J. C.F., The boundary element-free method for elastoplastic implicit analysis, Int. J. Numer. Methods Engrg., 76, 1090-1107 (2008) · Zbl 1195.74246
[26] Zhang, Z.; Liew, K. M.; Cheng, Y., Coupling of improved element-free Galerkin and boundary element methods for the 2D elasticity problems, Engrg. Anal. Bound. Elem., 32, 100-107 (2008) · Zbl 1244.74204
[27] Zhang, Z.; Liew, K. M.; Cheng, Y.; Lee, Y. Y., Analyzing 2D fracture problems with the improved element-free Galerkin method, Engrg. Anal. Bound. Elem., 32, 241-250 (2008) · Zbl 1244.74240
[30] Cheng, Y.; Li, J., A complex variable meshless method for fracture problems, Sci. China Ser. G Phys. Mech. Astron., 49, 1, 46-59 (2006) · Zbl 1147.74410
[31] Liew, K. M.; Feng, C.; Cheng, Y.; Kitipornchai, S., Complex variable moving least-squares method: a meshless approximation technique, Int. J. Numer. Methods Engrg., 70, 46-70 (2007) · Zbl 1194.74554
[32] Cheng, Y.; Peng, M.; Li, J., The complex variable moving least-square approximation and its application, Chin. J. Theoret. Appl. Mech., 37, 6, 719-723 (2005)
[33] Liew, K. M.; Cheng, Y., Complex variable boundary element-free method for two-dimensional elastodynamic problems, Comput. Methods Appl. Mech. Engrg., 198, 3925-3933 (2009) · Zbl 1231.74502
[34] Peng, M.; Liu, P.; Cheng, Y., The complex variable element-free Galerkin (CVEFG) method for two-dimensional elasticity problems, Int. J. Appl. Mech., 1, 2, 367-385 (2009)
[35] Peng, M.; Li, D.; Cheng, Y., The complex variable element-free Galerkin (CVEFG) method for elasto-plasticity problems, Engrg. Struct., 33, 127-135 (2011)
[36] Li, D.; Peng, M.; Cheng, Y., The complex variable element-free Galerkin (CVEFG) method for elastic large deformation problems, Sci. Sin. Phys. Mech. Astron., 41, 8, 1003-1014 (2011)
[37] Zhou, W.; Kou, X., Element-free method and its application in engineering, Acta Mech. Sin., 30, 2, 193-202 (1998)
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