Generalized nodes and high-performance elements

International Journal for Numerical Methods in Engineering

Volumn 64, Issue 15, 2005, Pages 2039-2071

  Tian, Rong ^a   Yagawa, Genki ^b  

^a INSTITUTE OF INDUSTRIAL SCIENCE   (Japan)

^b TOYO UNIVERSITY   (Japan)

Author keywords

Free mesh method; Generalized finite element method; Generalized node; Partition of unity; Tetrahedron; Triangle

Indexed keywords

APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; ELASTICITY; MATRIX ALGEBRA; NUMERICAL METHODS; SHEAR DEFORMATION;

FREE MESH METHOD; GENERALIZED FINITE ELEMENT METHOD; GENERALIZED NODES; PARTITION OF UNITY; TETRAHEDRON;

FINITE ELEMENT METHOD;

FINITE ELEMENT METHOD;

EID: 28844465825     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1436     Document Type: Article

References (47)

1. Yagawa G. Node-by-node parallel finite elements: a virtually meshless method. International Journal for Numerical Methods in Engineering 2004; 60:69-102.
2. Fujisawa T, Inaba M, Yagawa G. Parallel computing of high-speed compressible flows using a node-based finite-element method. International Journal for Numerical Methods in Engineering 2003; 58:481-511.
3. Yagawa G, Yamada T. Free mesh method: a new meshless finite element method. Computational Mechanics 1996; 18:383-386.
4. Yagawa G, Furukawa T. Recent developments of free mesh methods. International Journal for Numerical Methods in Engineering 2000; 47:1419-1443.
5. Shirazaki M, Yagawa G. Large-scale parallel flow analysis based on free mesh method: a virtually meshless method. Computer Methods in Applied Mechanics and Engineering 1999; 174(3-4):419-431.
6. Furukawa T, Yang CQ, Yagawa G. Quadrilateral approaches for accurate free mesh method. International Journal for Numerical Methods in Engineering 2000; 47(8):1445-1462.
7. Matsubara H, Iraha S, Tomiyama J, Yagawa G. Free mesh method using a three-dimensional element with rotational dofs. Proceedings of the Annual Conference of Japan Concrete Institute (JCI), Kyoto, Japan, July 2003 (in Japanese).
8. Tian R, Matsubara H, Yagawa G, Iraha S, Tomiyama J. Accuracy improvement on free mesh method: a high performance quadratic tetrahedral/triangular element with only corners. Proceedings of the 2004 Sixth World Congress on Computational Mechanics (WCCM VI), Beijing, China, September 2004.
9. Tian R, Yagawa G, Matsubara H, Iraha S, Tomiyama J. Designs of high performance elements in free mesh method - Allman's rotational dofs, partition of unity, and generalized node. Proceedings of Computational Engineering Conference of the Japan Society for Computational Engineering and Science (JSCES), Tokyo, May 2004; 97-100.
10. Tian R, Yagawa G, Terasaka H. Linear dependence problems of partition-of-unity based generalized FEMs. Computer Methods in Applied Mechanics and Engineering 2005, in press.
11. Allman DJ. A compatible triangular element including vertex rotations for plane elasticity analyses. Computers and Structures 1984; 19(1-2):1-8.
12. Cook RD. On the Allman triangle and a related quadrilateral element. Computers and Structures 1986; 22(6):1065-1067.
13. Bergan PG, Felippa CA. A triangular membrane element with rotational degrees of freedom. Computer Methods in Applied Mechanics and Engineering 1985; 50:25-69.
14. Allman DJ. Evaluation of the constant strain triangle with drilling rotations. International Journal for Numerical Methods in Engineering 1988; 26:2645-2655.
15. Sekiguchi M, Kikuchi N. Re-examination of membrane elements with drilling freedom. Proceedings of the 2002 Fifth World Congress on Computational Mechanics (WCCMV), Vienna, Austria, July 2002.
16. Felippa CA. A study of optimal membrane triangles with drilling freedoms. Computer Methods in Applied Mechanics and Engineering 2003; 192:2125-2168.
17. Yunus SM, Pawlak TP, Cook RD. Solid elements with rotational degrees of freedom. Part I: hexahedron elements. International Journal for Numerical Methods in Engineering 1991; 31:573-592.
18. Ibrahimbegovic A, Wilson EL. Thick shell and solid finite elements with independent rotation fields. International Journal for Numerical Methods in Engineering 1991; 31:1393-1414.
19. Weissman SL. High-accuracy low-order three-dimensional brick elements. International Journal for Numerical Methods in Engineering 1996; 39(14):2337-2361.
20. Sze KY, Soh AK, Sim YS. An explicit hybrid-stabilized solid element with rotational degrees of freedom. International Journal for Numerical Methods in Engineering 1996; 39:2987-3005.
21. Cao YP, Hu N, Lu J, Fukunaga H, Yao ZH. A 3D brick element based on Hu-Washizu variational principle for mesh distortion. International Journal for Numerical Methods in Engineering 2002; 53(11):2529-2548.
22. Areias PMA, César de Sá JMA, Conceição António CA, Fernandes AA. Analysis of 3D problems using a new enhanced strain hexahedral element. International Journal for Numerical Methods in Engineering 2003; 58(11):1637-1682.
23. Pawlak TP, Yunus SM, Cook RD. Solid elements with rotational degrees of freedom. Part II: tetrahedron elements. International Journal for Numerical Methods in Engineering 1991; 31:593-610.
24. Sze KY, Pan YS. Hybrid stress tetrahedral elements with Allman's rotational D.O.F.s. International Journal for Numerical Methods in Engineering 2000; 48(7):1055-1070.
25. Babuska I, Melenk JM. Partition of unity method. International Journal for Numerical Methods in Engineering 1997; 40:727-758.
26. Melenk JM, Babuska I. The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering 1996; 139:289-314.
27. Duarte CA. The hp cloud method. Ph.D. Thesis, Faculty of the Graduate School of the University of Texas at Austin, 1996.
28. Oden JT, Duarte CA, Zienkiewicz OC. A new cloud-based hp finite element method. Computer Methods in Applied Mechanics and Engineering 1998; 153:113-126.
29. Strouboulis T, Babuska I, Copps K. The design and analysis of the generalized finite element method. Computer Methods in Applied Mechanics and Engineering 2000; 181(1-3):43-69.
30. Strouboulis T, Copps K, Babuska I. The generalized finite element method: an example of its implementation and illustration of its performance. International Journal for Numerical Methods in Engineering 2000; 47:1401-1417.
31. Strouboulis T, Copps K, Babuska I. The generalized finite element method. Computer Methods in Applied Mechanics and Engineering 2001; 190(32-33):4081-4193.
32. Duarte CA, Babuska I, Oden JT. Generalized finite element methods for three-dimensional structural mechanics problems. Computers and Structures 2000; 77(2):215-232.
33. Duarte CA, Babuska I. Mesh-independent p-orthotropic enrichment using the generalized finite element method. International Journal for Numerical Methods in Engineering 2002; 55:1477-1492.
34. Duarte CA, Hamzeh ON, Liszka TJ, Tworzydlo WW. A generalized finite element method for the simulation of three-dimensional dynamic crack propagation. Computer Methods in Applied Mechanics and Engineering 2001; 190:2227-2262.
35. Taylor RL, Zienkiewicz OC, Onate E. A hierarchical finite element method based on the partition of unity. Computer Methods in Applied Mechanics and Engineering 1998; 152:73-84.
36. Shi GH. Manifold method of material analysis. Transactions of the 9th Army Conference on Applied Mathematics and Computing, Report No. 92-1, U.S. Army Research Office, 1991.
37. Shi GH. Numerical manifold method. In Proceedings of the Second International Conference on Analysis of Discontinuous Deformation (ICADD-2), Yuzo O (ed.). Kyoto University, Japan, 1997; 1-34.
38. Chen GQ, Ohnishi Y, Ito T. Development of high-order manifold method. International Journal of Numerical Methods in Engineering 1998; 43:685-712.
39. Terada K, Asai M, Yamagishi M. Finite cover method for linear and non-linear analyses of heterogeneous solids. International Journal for Numerical Methods in Engineering 2003; 58:1321-1346.
40. Lin JS. A mesh-based partition of unity method for discontinuity modeling. Computer Methods in Applied Mechanics and Engineering 2003; 192:1515-1532.
41. Timoshenko SP, Goodier JN. Theory of Elasticity. McGraw-Hill: New York, 1970.
42. Wu JH, Ohnishi Y, Ohtsu H, Nishiyama S. Study on the rigid body rotation problem in Discontinuous Deformation Analysis (DDA). Journal of Applied Mechanics (JSCE) 2002; 5:191-198.
43. Zienkiewicz OC, Taylor RL. The Finite Element Method (5th edn). Butterworth-Heinemann: Stoneham, MA, 2000.
44. MSC. Marc User's Guide, Version 2001. MSC.Software Corporation.
45. MacNeal RH, Harder RL. A proposed standard set of problems to test finite element accuracy. Finite Elements in Analysis and Design 1985; 1:3-20.
46. Lo SH, Ling C. Improvement on the 10-node tetrahedral element for three-dimensional problems. Computer Methods in Applied Mechanics and Engineering 2000; 189:961-974.
47. Taylor RL, Beresford PJ, Wilson EL. A non-conforming element for stress analysis. International Journal for Numerical Methods in Engineering 1976; 10:1211-1219.