An alternative alpha finite element method with discrete shear gap technique for analysis of isotropic Mindlin-Reissner plates

Finite Elements in Analysis and Design

Volumn 47, Issue 5, 2011, Pages 519-535

  Nguyen Thanh, N ^a   Rabczuk, Timon ^a   Nguyen Xuan, H ^b,c   Bordas, S ^d  

^a Institute of Structural Mechanics   (Germany)

^b UNIVERSITY OF NATURAL SCIENCES   (Viet Nam)

^c TON DUC THANG UNIVERSITY   (Viet Nam)

^d CARDIFF UNIVERSITY   (United Kingdom)

Author keywords

Discrete shear gap (DSG); Finite element method; Plate bending; Smooth finite element method (SFEM); Transverse shear locking

Indexed keywords

ADJUSTABLE PARAMETERS; BUCKLING ANALYSIS; DISCRETE SHEAR GAP (DSG); FINITE ELEMENT; FREE VIBRATION; HIGH RELIABILITY; MINDLIN-REISSNER PLATE; NUMERICAL EXAMPLE; OVER-ESTIMATION; PIECEWISE CONSTANT; PLATE BENDING; SMOOTH FINITE ELEMENT METHOD (SFEM); STRAIN FIELDS; TRANSVERSE SHEAR; TRANSVERSE SHEAR LOCKING; TRIANGULAR ELEMENTS;

COMPUTATIONAL MECHANICS; COUPLED CIRCUITS; MINDLIN PLATES; VIBRATION ANALYSIS;

FINITE ELEMENT METHOD;

EID: 79551601213     PISSN: 0168874X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.finel.2011.01.004     Document Type: Article

References (57)

1. O.C. Zienkiewicz, and D. Lefebvre A robust triangular plate bending element of the ReissnerMindlin type International Journal for Numerical Methods in Engineering 26 1988 1169 1184 (Pubitemid 18617261)
2. G.D. Ayad, and J.L. Batoz A new hybrid-mixed variational approach for ReissnerMindlin plate International Journal for Numerical Methods in Engineering 42 1998 1149 1179 (Pubitemid 128500010)
3. C. Lovadina Analysis of a mixed finite element method for the ReissnerMindlin plate problems Computer Methods in Applied Mechanics and Engineering 163 1998 71 85
4. R.L. Taylor, and F. Auricchio Linked interpolation for ReissnerMindlin plate element: part II-A simple triangle International Journal for Numerical Methods in Engineering 36 1993 3043 3056
5. J.C. Simo, and M.S. Rifai A class of mixed assumed strain methods and the method of incompatible modes International Journal for Numerical Methods in Engineering 29 1990 1595 1638 (Pubitemid 20718675)
6. J.M.A. Csar de S, and R.M. Natal Jorge New enhanced strain elements for incompatible problems International Journal for Numerical Methods in Engineering 44 1999 229 248
7. J.M.A. Csar de S, R.M. Natal Jorge, R.A. Fontes Valente, and P.M.A. Areias Development of shear locking-free shell elements using an enhanced assumed strain formulation International Journal for Numerical Methods in Engineering 53 2002 1721 1750 (Pubitemid 34119965)
8. R.P.R. Cardoso, J.W. Yoon, M. Mahardika, S. Choudhry, R.J. Alves de Sousa, and R.A. Fontes Valente Enhanced assumed strain (EAS) and assumed natural strain (ANS) methods for one-point quadrature solid-shell elements International Journal for Numerical Methods in Engineering 75 2008 156 187
9. K.U. Bletzinger, M. Bischoff, and E. Ramm A unified approach for shear-locking free triangular and rectangular shell finite elements International Journal for Numerical Methods in Engineering 75 2000 321 334 (Pubitemid 32133067)
10. G.R. Liu, K.Y. Dai, and T.T. Nguyen A smoothed finite element method for mechanics problems Computational Mechanics 39 2007 859 877 (Pubitemid 46327302)
11. K.Y. Dai, G.R. Liu, and T.T. Nguyen An n-sided polygonal smoothed finite element method (nSFEM) for solid mechanics Finite Elements in Analysis and Design 43 2007 847 860 (Pubitemid 47336989)
12. K.Y. Dai, and G.R. Liu Free and forced vibration analysis using the smoothed finite element method (SFEM) Journal of Sound and Vibration 301 2007 803 820 (Pubitemid 46157249)
13. H. Nguyen-Xuan, T. Nguyen-Thoi, A stabilized smoothed finite element method for free vibration analysis of MindlinReissner plates, Communications in Numerical Methods in Engineering, doi: 10.1002/cnm.1137, in press.
14. T. Rabczuk, S. Bordas, and G. Zi A three dimensional meshfree method for static and dynamic multiple crack nucleation/propagation with crack path continuity Computational Mechanics 40 3 2007 473 495
15. H. Nguyen-Xuan, T. Rabczuk, S. Bordas, and J.F. Debongnie A smoothed finite element method for plate analysis Computer Methods in Applied Mechanics and Engineering 197 2008 1184 1203
16. N. Nguyen-Thanh, T. Rabczuk, H. Nguyen-Xuan, and S. Bordas A smoothed finite element method for shell analysis Computer Methods in Applied Mechanics and Engineering 198 2008 165 177
17. T. Rabczuk, P.M.A. Areias, and T. Belytschko A meshfree thin shell method for non-linear dynamic fracture International Journal for Numerical Methods in Engineering 72 5 2007 524 548 (Pubitemid 47617038)
18. T. Rabczuk, and P. Areias A meshfree thin shell for arbitrary evolving cracks based on an external enrichment Computer Modeling in Engineering and Sciences 16 2 2006 115 130 (Pubitemid 46142894)
19. S. Bordas, T. Rabczuk, and G. Zi Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment Engineering Fracture Mechanics 75 5 2008 943 960 (Pubitemid 350225350)
20. S. Bordas, T. Rabczuk, H. Nguyen-Xuan, P. Nguyen Vinh, S. Natarajan, T. Bog, Q. Do Minh, and H. Nguyen Vinh Strain smoothing in FEM and XFEM Computers and Structures 88 2324 2010 1419 1443
21. T. Rabczuk, and T. Belytschko Adaptivity for structured meshfree particle methods in 2D and 3D International Journal for Numerical Methods in Engineering 63 11 2005 1559 1582 (Pubitemid 40990230)
22. T. Rabczuk, and T. Belytschko Application of meshfree particle methods to static fracture of reinforced concrete structures International Journal of Fracture 137 14 2006 19 49 (Pubitemid 43362072)
23. T. Rabczuk, P.M.A. Areias, and T. Belytschko A simplified meshfree method for shear bands with cohesive surfaces International Journal for Numerical Methods in Engineering 69 5 2007 993 1021 (Pubitemid 46189069)
24. T. Rabczuk, T. Belytschko, and S.P. Xiao Stable particle methods based on Lagrangian kernels Computer Methods in Applied Mechanics and Engineering 193 2004 1035 1063 (Pubitemid 38439205)
25. T. Rabczuk, J.H. Song, and T. Belytschko Simulations of instability in dynamic fracture by the cracking particles method Engineering Fracture Mechanics 76 2009 730 741
26. G.R. Liu A generalized gradient smoothing technique and the smoothed bilinear form for Galerkin formulation of a wide class of computational methods International Journal Computation Methods 2 2008 199 236
27. G.R. Liu, T. Nguyen-Thoi, H. Nguyen-Xuan, and K.Y. Lam A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems Computational Structural 87 2009 14 26
28. G.R. Liu, H. Nguyen-Xuan, T. Nguyen-Thoi, and X. Xu A novel Galerkin-like weakform and a superconvergent alpha finite element method (SαFEM) for mechanics problems using triangular meshes Journal of Computational Physics 228 2009 4055 4087
29. G.R. Liu, T. Nguyen-Thoi, and K.Y. Lam A novel alpha finite element method (α FEM) for exact solution to mechanics problems using triangular and tetrahedral elements Computer Methods in Applied Mechanics and Engineering 197 2008 3883 3897
30. N. Nguyen-Thanh, T. Rabczuk, H. Nguyen-Xuan, and S. Bordas An alternative alpha finite element method (Aαfem ) free and forced vibration analysis of solids using triangular meshes Journal of Computational and Applied Mathematics 223 9 2010 2112 2135
31. K.M. Liew, J. Wang, T.Y. Ng, and M.J. Tan Free vibration and buckling analyses of shear-deformable plates based on FSDT meshfree method Journal of Sound and Vibration 276 2004 997 1017
32. G.R. Liu, X. Xu, G.Y. Zhang, and T. Nguyen-Thoi A superconvergent point interpolation method (SC-PIM) with piecewise linear strain field using triangular mesh International Journal for Numerical Methods in Engineering 77 2008 1439 1467
33. O.C. Zienkiewicz, and R.L. Taylor The Finite Element Method fifth ed. 2000 Butterworth Heinemann Oxford
34. T. Belytschko, and W.E. Bachrach Efficient implementation of quadrilaterals with high coarse-mesh accuracy Computer Methods in Applied Mechanics and Engineering 54 1986 279 301 (Pubitemid 16532310)
35. T. Belytschko, and L.P. Bindeman Assumed strain stabilization of the 4-node quadrilateral with 1-point quadrature for nonlinear problems Computer Methods in Applied Mechanics and Engineering 88 1983 311 340
36. M. Fredriksson, and N.S. Ottosen Fast and accurate 4-node quadrilateral International Journal for Numerical Methods in Engineering 61 2004 1809 1834 (Pubitemid 39558468)
37. R. Piltner, and R.L. Taylor Triangular finite elements with rotational degrees of freedom and enhanced strain modes Computers and Structures 75 2000 361 368 (Pubitemid 30566125)
38. T.H.H. Pian, and C.C. Wu Hybrid and Incompatible Finite Element Methods 2006 CRC Press Boca Raton
39. K.J. Bathe, and E.N. Dvorkin A four-node plate bending element based on MindlinReissner plate theory and a mixed interpolation International Journal for Numerical Methods in Engineering 21 1985 367 383
40. A. Tessler, and T.J.R. Hughes A three-node Mindlin plate element with improved transverse shear Computer Methods in Applied Mechanics and Engineering 50 1985 71 101 (Pubitemid 15588702)
41. H. Nguyen-Xuan, G.R. Liu, C. Thai-Hoang, and T. Nguyen-Thoi An edge-based smoothed finite element method with stabilized discrete shear gap technique for analysis of ReissnerMindlin plates Computer Methods in Applied Mechanics and Engineering 199 912 2010 471 489
42. O.C. Zienkiewicz, Z. Xu, L.X. Zeng, A. Samuelsson, and N.E. Wiberg Linked interpolation for ReissnerMindlin plate elements: part I-a simple quadrilateral International Journal for Numerical Methods in Engineering 36 1993 3043 3056
43. I. Katili A new discrete KirchhoffMindlin element based on MindlinReissner plate theory and assumed shear strain fieldspart II: an extended DKQ element for thick-plate bending analysis International Journal for Numerical Methods in Engineering 36 1993 1885 1908
44. S.J. Lee Free vibration analysis of plates by using a four-node finite element formulated with assumed natural transverse shear strain Journal of Sound and Vibration 278 2004 657 684
45. S.J. Lee, and S.E. Han Free-vibration analysis of plates and shells with a nine-node assumed natural degenerated shell element Journal of Sound and Vibration 241 2001 605 633 (Pubitemid 32425139)
46. K.M. Liew, and X.L. Chen Buckling of rectangular Mindlin plates subjected to partial in-plane edge loads using the radial point interpolation method International Journal of Solids and Structures 41 2004 1677 1695 (Pubitemid 38149671)
47. W. Karunasena, S. Kitipornchai, and F.G.A. Al-bermani Free vibration of cantilevered arbitrary triangular Mindlin plates Mechanical Sciences 38 1996 431 442 (Pubitemid 126349569)
48. T. Nagashima Node-by-node meshless approach and its applications to structural analyses International Journal for Numerical Methods in Engineering 46 1999 341 385
49. L.S.D. Morley Skew Plates and Structures 1963 Pergamon Press
50. S. Cen, Y.Q. Long, Z.H. Yao, and S.P. Chiew Application of the quadrilateral area co-ordinate method: a new element for MindlinReissner plate International Journal for Numerical Methods in Engineering 66 2006 1 45
51. F. Abbassian, D.J. Dawswell, and N.C. Knowles Free Vibration Benchmarks 1987 Atkins Engineering Sciences
52. A.W. Leissa, Vibration of plates, NASA, SP-160, Washington DC, 1969.
53. O.G. McGee, A.W. Leissa, and C.S. Huang Vibrations of cantilevered skewed trapezodial and triangular plates with corner stress singularities Mechanical Sciences 34 1992 63 84
54. S.P. Timoshenko, and J.M. Gere Theory of Elastic Stability third ed. 1970 McGraw-Hill New York
55. L.G. Tham, and H.Y. Szeto Buckling analysis of arbitrary shaped plates by spline finite strip method Computers and Structures 36 1990 729 735
56. S. Kitipornchai, Y. Xiang, C.M. Wang, and K.M. Liew Buckling of thick skew plates International Journal for Numerical Methods in Engineering 36 1993 1299 1310
57. M. Azhari, S. Hoshdar, and M.A. Bradford On the use of bubble functions in the local buckling analysis of plate structures by the spline finite strip method International Journal for Numerical Methods in Engineering 48 2000 583 593