The interpolating element-free Galerkin (IEFG) method for two-dimensional elasticity problems

International Journal of Applied Mechanics

Volumn 3, Issue 4, 2011, Pages 735-738

  Ren, Hongping ^a   Cheng, Yumin ^b  

^a TAIYUAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b SHANGHAI UNIVERSITY   (China)

Author keywords

elasticity; interpolating element free Galerkin (IEFG) method; interpolating moving least squares (IMLS) method; Meshless method; moving least squares (MLS) approximation

Indexed keywords

COMPUTING EFFICIENCY; EFG METHOD; ELASTICITY PROBLEMS; ELEMENT-FREE; GALERKIN; MESH-LESS METHODS; MOVING LEAST SQUARES; MOVING LEAST SQUARES APPROXIMATION; NUMERICAL EXAMPLE; SHAPE FUNCTIONS; TWO-DIMENSIONAL ELASTICITY; WEAK FORM;

COMPUTATIONAL MECHANICS; ELASTICITY; GALERKIN METHODS; INTERPOLATION; NUMERICAL METHODS; TWO DIMENSIONAL;

LEAST SQUARES APPROXIMATIONS;

EID: 84855952330     PISSN: 17588251     EISSN: 1758826X     Source Type: Journal    
DOI: 10.1142/S1758825111001214     Document Type: Article

References (39)

1. Aluru, N. R. [2000] "A point collocation method based on reproducing kernel approximations," International Journal for Numerical Methods in Engineering 47(6), 1083-1121. (Pubitemid 30542455)
2. Atluri, S. N. and Zhu, T. [1998] "A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics," Computational Mechanics 22(2), 117-127. (Pubitemid 128620889)
3. Belytschko, T., Lu, Y. Y. and Gu, L. [1994] "Element-free Galerkin Methods," International Journal for Numerical Methods in Engineering 37(2), 229-256.
4. Chen, L. and Liew, K. M. [2011] "A local Petrov-Galerkin approach with moving Kriging interpolation for solving transient heat conduction problems," Computational Mechanics 47(4), 455-467.
5. Cheng, Y. and Li, J. [2006] "A complex variable meshless method for fracture problems," Science in China Series G Physics, Mechanics & Astronomy 49(1), 46-59. (Pubitemid 43322908)
6. Cheng, Y. and Peng, M. [2005a] "Boundary element-free method for elastodynamics," Science in China Series G Physics, Mechanics & Astronomy 48(6), 641-657. (Pubitemid 43322615)
7. Cheng, Y., Peng, M. and Li, J. [2005b] "The complex variable moving least-square approximation and its application," Chinese Journal of Theoretical and Applied Mechanics 37(6), 719-723.
8. Cui, X. Y., Liu, G. R. and Li, G. Y. [2010] "Analysis of Mindlin-Reissner plates using cellbased smoothed radial point interpolation method," International Journal of Applied Mechanics 2(3), 653-680.
9. Dai, B. and Cheng, Y. [2010] "An improved local boundary integral equation method for two-dimensional potential problems," International Journal of Applied Mechanics 2(2), 421-436.
10. Elhassan, B., Lahbib, B., Gery de, S. and Ali, C. [2009] "A meshless method analysis of elasto-plastic contact problems with friction," International Journal of Applied Mechanics 1(4), 631-645.
11. Gu, Y. T. and Liu, G. R. [2003] "A boundary radial point interpolation method (BRPIM) for 2-D structural analyses," Structural Engineering and Mechanics 15(5), 535-550.
12. Idelsohn, S. R., Onate, E. and Calvo, N. [2003] "The meshless finite element method," International Journal for Numerical Methods in Engineering 58(6), 893-912. (Pubitemid 37262049)
13. Kitipornchai, S., Liew, K. M. and Cheng, Y. [2005] "A boundary element-free method (BEFM) for three-dimensional elasticity problems," Computational Mechanics 36(2), 13-20. (Pubitemid 40666684)
14. Krongauz, Y. and Belytschko, T. [1996a] "Enforcement of essential boundary conditions in meshless approximation using finite elements," Computer Methods in Applied Mechanics and Engineering 139(1-2), 133-145. (Pubitemid 126393899)
15. Krongauz, Y., Belytschko, T., Organ, D., Fleming, M. and Krysl, P. [1996b] "Meshless methods: An overview and recent developments," Computer Methods in Applied Mechanics and Engineering 139(1-4), 3-47. (Pubitemid 126382692)
16. Lancaster, P. and Salkauskas, K. [1981] "Surfaces generated by moving least square methods," Mathematics of Computation 37(155), 141-158.
17. Liew, K. M., Cheng, Y. and Kitipornchai, S. [2005] "Boundary element-free method (BEFM) for two-dimensional elastodynamic analysis using Laplace transform," International Journal of Numerical Methods in Engineering 64(12), 1610-1627. (Pubitemid 41716058)
18. Liew, K. M., Cheng, Y. and Kitipornchai, S. [2006] "Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems," International Journal of Numerical Methods in Engineering 65(8), 1310-1332. (Pubitemid 43224818)
19. Liew, K. M., Cheng, Y. and Kitipornchai, S. [2007a] "Analyzing the 2D fracture problems via the enriched boundary element-free method," International Journal of Solids and Structures 44(11-12), 4220-4233. (Pubitemid 46483437)
20. Liew, K. M., Feng, C., Cheng, Y. and Kitipornchai, S. [2007b] "Complex variable moving least-squares method: A meshless approximation technique," International Journal of Numerical Methods in Engineering 70(1), 46-70. (Pubitemid 46502359)
21. Liew, K. M., Sun, Y. and Kitipornchai, S. [2007c] "Boundary element-free method for fracture analysis of 2-D anisotropic piezoelectric solids," International Journal for Numerical Methods in Engineering 69(4), 729-749. (Pubitemid 46117464)
22. Liew, K. M. and Cheng, Y. [2009] "Complex variable boundary element-free method for two-dimensional elastodynamic problems," Computer Methods in Applied Mechanics and Engineering 198(49-52), 3925-3933.
23. Liu, G. R. and Zhang, G. Y. [2009] "A novel scheme of strain-constructed point interpolation method for static and dynamic mechanics problems," International Journal of Applied Mechanics 1(1), 233-258.
24. Liu, W. K., Jun, S. and Zhang, Y. F. [1995] "Reproducing kernel partical methods," International Journal for Numerical Methods in Fluid 20(8-9), 1081-1106.
25. Miers, L. S. and Telles, J. C. F. [2008] "The boundary element-free method for elastoplastic implicit analysis," International Journal of Numerical Methods in Engineering 76(7), 1090-1107.
26. Nayroles, B., Touzot, G. and Villon, P. [1992] "Generalizing the finite element method: Diffuse approximation and diffuse elements," Computational Mechanics 10(5), 307-318. (Pubitemid 23570159)
27. Onate, E., Idelsohn, S. and Zienkiewicz, O. C. [1996] "A finite point method in computational mechanics. Applications to convective transport and fluid flow," International Journal for Numerical Methods in Engineering 39(22), 3839-3866.
28. Peng, M., Cheng, Y. [2009a] "A boundary element-free method (BEFM) for twodimensional potential problems," Engineering Analysis with Boundary Elements 33(1), 77-82.
29. Peng, M., Liu, P. and Cheng, Y. [2009b] "The complex variable element-free Galerkin (CVEFG) method for two-dimensional elasticity problems," International Journal of Applied Mechanics 1(2), 367-385.
30. Peng, M., Li, D. and Cheng, Y. [2011] "The complex variable element-free Galerkin (CVEFG) method for elasto-plasticity problems," Engineering Structures 33(1), 127-135.
31. Sun, Y., Hu, Y. G. and Liew, K. M. [2007] "A mesh-free simulation of cracking and failure using the cohesive segments method," International Journal of Engineering Science 45(2-8), 541-553. (Pubitemid 47094785)
32. Sun, Y., Zhang, Z., Kitipornchai, S. and Liew, K. M. [2006] "Analyzing the interaction between collinear interfacial cracks by an efficient boundary element-free method," International Journal of Engineering Science 44(1-2), 37-48. (Pubitemid 43177732)
33. Timoshenko, S. P. and Goodier, J. N. [1970] Theory of Elasticity (Third Edition) (New York: McGraw-Hill Inc.).
34. Tinh, Q. B. and Minh, N. N. [2011] "Eigenvalue analysis of thin plate with complicated shapes by a novel mesh-free method," International Journal of Applied Mechanics 3(1), 21-46.
35. Wendland, H. [1999] "Meshless Galerkin method using radial basic functions," Mathematics of Computation 68(228), 1521-1531.
36. Zhang, Z., Liew, K. M. and Cheng, Y. [2008a] "Coupling of improved element-free Galerkin and boundary element methods for the 2D elasticity problems," Engineering Analysis with Boundary Elements 32(2), 100-107. (Pubitemid 350198871)
37. Zhang, Z., Liew, K. M., Cheng, Y. and Lee, Y. Y. [2008b] "Analyzing 2D fracture problems with the improved element-free Galerkin method," Engineering Analysis with Boundary Elements 32(3), 241-250.
38. Zhu, T. and Atluri, S. N. [1998a] "A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method," Computational Mechanics 21(3), 211-222. (Pubitemid 128566411)
39. Zhu, T., Zhang, J. and Atluri, S. N. [1998b] "A local boundary integral equation (LBIE) method in computational mechanics and a meshless discretization approach," Computational Mechanics 21(3), 223-235. (Pubitemid 128566412)