A superconvergent point interpolation method (SC-PIM) with piecewise linear strain field using triangular mesh

International Journal for Numerical Methods in Engineering

Volumn 77, Issue 10, 2009, Pages 1439-1467

  Liu, G R ^a,c   Xu, X ^b,c,d   Zhang, G Y ^c   Nguyen Thoi, T ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b BEIJING INSTITUTE OF TECHNOLOGY   (China)

^c SINGAPORE MIT ALLIANCE   (Singapore)

^d JILIN UNIVERSITY   (China)

Author keywords

Finite element method; Hellinger Reissner's variational principle; Meshfree methods; Point interpolation method; Solution bound; Superconvergence

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; CONTROL THEORY; EDDY CURRENTS; FUNCTION EVALUATION; INTERMODULATION; INTERMODULATION MEASUREMENT; INTERPOLATION; PIECEWISE LINEAR TECHNIQUES; STRAIN; VARIATIONAL TECHNIQUES;

HELLINGER-REISSNER'S VARIATIONAL PRINCIPLE; MESHFREE METHODS; POINT INTERPOLATION METHOD; SOLUTION BOUND; SUPERCONVERGENCE;

FINITE ELEMENT METHOD;

EID: 60949093096     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2464     Document Type: Article

References (32)

1. Lucy LB. A numerical approach to testing the fission hypothesis. The Astronomical Journal 1977; 8(12): 1013-1024.
2. Liu GR, Liu MB. Smoothed Particle Hydrodynamics - A Meshfree Practical Method. World Scientific: Singapore, 2003.
3. Zhou CE, Liu GR, Lam KY. Three-dimensional penetration simulation using smoothed particle hydrodynamics. International Journal of Computational Methods 2008; 4(1):671-691.
4. Liu MB, Liu GR, Zong Z. An overview on smoothed particle hydrodynamics. International Journal of Computational Methods 2008; 5(1):135-188.
5. Nayroles B, Touzot G, Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics 1992; 10:307-318.
6. Belytschko Y, Lu YY, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 1994; 37:229-256.
7. Liu WK, Jun S, Zhang YF. Reproducing kernel particle methods. International Journal for Numerical Methods in Engineering 1995; 20:1081-1106.
8. Atluri SN, Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Computational Mechanics 1998; 22:117-127.
9. Liu GR, Gu YT. A point interpolation method for two-dimensional solids. International Journal for Numerical Methods in Engineering 2001; 50:937-951.
10. Wang JG, Liu GR. A point interpolation meshless method based on radial basis functions. International Journal for Numerical Methods in Engineering 2002; 54:1623-1648.
11. Gu L. Moving kriging interpolation and element-free Galerkin method. International Journal for Numerical Methods in Engineering 2003; 56:1-11.
12. Dai KY, Liu GR, Lim KM, Gu YT. Comparison between the radial point interpolation and the kriging based interpolation using in meshfree methods. Computational Mechanics 2003; 32:60-70.
13. Tongsuk P, Kanok-Nukulchai W. Further investigation of element-free Galerkin method using moving kriging interpolation. International Journal of Computational Methods 2004; 1:345-365.
14. Liu GR. Meshfree Methods: Moving beyond the Finite Element Method. CRC Press: Boca Raton, U.S.A., 2002.
15. Liu GR, Gu YT. An Introduction to Meshfree Methods and their Programming. Springer: Dordrecht, The Netherlands, 2005.
16. Liu GR, Zhang GY, Dai KY, Wang YY, Zhong ZH, Li GY, Han X. A linearly conforming point interpolation method (LC-PIM) for 2D solid mechanics problems. International Journal of Computational Methods 2005; 2(4):645-665.
17. Zhang GY, Liu GR, Wang YY, Huang HT, Zhong ZH, Li GY, Han X. A linearly conforming point interpolation method (LC-PIM) for three-dimensional elasticity problems. International Journal for Numerical Methods in Engineering 2007; 72:1524-1543.
18. Chen JS, Wu CT, Yoon S, You Y. A stabilized conforming nodal integration for Galerkin mesh-free methods. International Journal for Numerical Methods in Engineering 2001; 50:435-466.
19. Li Y, Liu GR, Luan MT, Dai KY, Zhong ZH, Li G, Han X. Contact analysis for solids based on linearly conforming radial point interpolation method. Computational Mechanics 2007; 39:859-877.
20. Liu GR, Li Y, Dai KY, Luan MY, Xue W. A linearly conforming RPIM for 2D solid mechanics. International Journal of Computational Methods 2006; 3(4):401-428.
21. Liu GR, Zhang GY. Upper bound solution to elasticity problems: a unique property of the linearly conforming point interpolation method (LC-PIM). International Journal for Numerical Methods in Engineering 2008; 74:1128-1161.
22. Zhang GY, Liu GR, Nguyen TT, Song CX, Han X, Hong ZH, Li GY. The upper bound property for solid mechanics of the linearly conforming radial point interpolation method (LC-RPIM). International Journal of Computational Methods 2007; 4(3):521-541.
23. Zienkiewicz OC, Taylor RL. The Finite Element Method (5th edn). Butterworth Heinemann: Oxford, U.K., 2000.
24. Hughes TJR. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice-Hall: Englewood Cliffs, NJ, 1987.
25. Liu GR, Quek SS. The Finite Element Method: A Practical Course. Butterworth Heinemann: Oxford, 2003.
26. Zhang GY, Liu GR, Li Y. An efficient adaptive analysis procedure for certified solutions with exact bounds of strain energy for elasticity problems. Finite Elements in Analysis and Design 2008; DOI: 10.1016/j.finel.2008.06.010.
27. Wu HC. Variational Principle in Elasticity and Applications. Scientific Press: Beijing, 1982.
28. Pian THH, Wu CC. Hybrid and Incompatible Finite Element Methods. CRC Press: Boca Raton, FL, 2006.
29. Rong TY, Lee AQ. Generalized mixed variational principles and solutions of ill-conditioned problem in computational mechanics. Part 1: volumetric locking. Computer Methods in Applied Mechanics and Engineering 2001; 191:407-412.
30. Liu GR. A generalized gradient smoothing technique and the smoothed bilinear form for Galerkin formulation of a wide class of computational methods. International Journal of Computational Methods 2008; 5(2):199-236.
31. Li RH, Chen ZY. Generalized Difference Methods for Differential Equations. Jilin University Press: Changchun, China, 1994.
32. Timoshenko SP, Goodier JN. Theory of Elasticity (3rd edn). McGraw-Hill: New York, 1970.