Computation of stress resultants in plate bending problems using higher-order triangular elements

Engineering Structures

Volumn 30, Issue 10, 2008, Pages 2687-2706

  Ramesh, Sai Sudha ^a   Wang, C M ^a   Reddy, J N ^a   Ang, K K ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Boundary conditions; Corner supported plates; Higher order interpolation; L shaped plates; Plate bending; Skew plates; Stress resultants

Indexed keywords

BENDING (DEFORMATION); BOUNDARY VALUE PROBLEMS; FINITE ELEMENT METHOD; INTERPOLATION; PLATES (STRUCTURAL COMPONENTS);

ACCURATE PREDICTION; BENDING ANALYSIS; BOUNDARY CONDITIONING; CORNER SUPPORTED PLATES; FIELD VARIABLES; FINITE ELEMENTS; FINITE-ELEMENT INTERPOLATION; FIRST-ORDER SHEAR DEFORMATIONS; FREE EDGES; HIGHER-ORDER; HIGHER-ORDER INTERPOLATION; L-SHAPED PLATES; NATURAL BOUNDARY CONDITIONS; PLATE BENDING; PLATE BENDING ELEMENT; PLATE BENDING PROBLEMS; PLATE ELEMENTS; SKEW PLATES; STRESS RESULTANTS; SUPERIOR PERFORMANCE; TRANSVERSE SHEAR; TRIANGULAR ELEMENTS; TWISTING MOMENTS;

BOUNDARY CONDITIONS;

BENDING; BOUNDARY CONDITION; DEFORMATION; DISPLACEMENT; FINITE ELEMENT METHOD; INTERPOLATION; SHEAR;

EID: 53049096817     PISSN: 01410296     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.engstruct.2008.03.003     Document Type: Article

References (42)

1. Reddy J.N. An introduction to the finite element method. 3rd ed. (2006), McGraw-Hill, New York
2. Melosh R.J. A stiffness matrix for the analysis of thin plates in bending. Journal of Aeronautical Science 28 (1961) 34-42
3. Irons B.M., and Draper K. Inadequacy of nodal connections in a stiffness solution for plate bending. American Institute of Aeronautics and Astronautics 3 (1965) 965-966
4. Hinton E, Pugh EDL. Some quadrilateral isoparametric finite elements based on Mindlin plate theory. In: Proceedings of the symposium on applications of computer methods in engineering. 1977
5. Reddy J.N. A penalty plate-bending element for the analysis of laminated anisotropic composite plates. International Journal for Numerical Methods in Engineering 15 8 (1980) 1187-1206
6. 0 finite-element solutions of simply supported plates of polygonal shape. Journal of Applied Mechanics 44 2 (1977) 347-349
7. Mindlin R.D. Influence of rotary inertia and shear in flexural motion of isotropic, elastic plates. Journal of Applied Mechanics 18 (1951) 1031-1036
8. Croce L.D., and Scapolla T. High order finite elements for thin to moderately thick plates. Computational Mechanics 10 (1992) 262-279
9. Babuska I., Szabo B.A., and Katz I.N. The p-version of the finite element method. Society for Industrial and Applied Mathematics 18 3 (1981) 515-545
10. Peano A. Hierarchies of conforming finite elements for plane elasticity and plate bending. Computers & Mathematics with Applications 2 3-4 (1976) 211-224
11. Cheung Y.K., Wong P.M., and Chan H.C. Generation of higher-order subparametric bending elements. Engineering Structures 2 (1980) 2-8
12. 1 triangular element based on the p-version of the finite element method. Computers and Structures 19 3 (1984) 381-392
13. Chan H.C., and Chung W.C. Higher order sub parametric elements for large deflection analysis of plates. Computers and Structures 24 1 (1986) 119-126
14. Rank E., Krause R., and Preusch K. On the accuracy of p-version elements for the Reissner-Mindlin plate problem. International Journal for Numerical Methods in Engineering 43 (1988) 51-67
15. Sheikh A.H., Haldar S., and Sengupta D. A high precision shear deformable element for the analysis of laminated composite plates of different shapes. Composite Structures 55 (2002) 329-336
16. Xenophontos C., Kurtz J., and Fulton S. A p-version MITC finite element method for Reissner-Mindlin plates with curved boundaries. Journal of Computational and Applied Mathematics 192 2 (2003) 374-395
17. Pontaza J.P., and Reddy J.N. Mixed plate bending elements based on least-squares formulation. International Journal for Numerical Methods in Engineering 60 (2004) 891-922
18. Pontaza J.P., and Reddy J.N. Least-squares finite element formulation for shear-deformable shells. Computer Methods in Applied Mechanics and Engineering 194 21-24 (2005) 2464-2493
19. Houmat A. Free vibration analysis of membranes using the h-p version of the finite element method. Journal of Sound and Vibration 282 1-2 (2005) 401-410
20. Ribeiro P. Forced periodic vibrations of laminated composite plates by a p-version, first order shear deformation, finite element. Composites Science and Technology 66 11 (2006) 1844-1856
21. Reddy J.N., and Arciniega R.A. In: Shanmugam N.E., and Wang C.M. (Eds). Analysis and design of plated structures: Mechanical and thermal buckling of ceramic-metal plates (2006), Woodhead Publishing Limited, Cambridge (England) [Chapter 6]
22. Arciniega R.A., and Reddy J.N. Tensor-based finite element formulation for geometrically nonlinear analysis of shell structures. Computer Methods in Applied Mechanics and Engineering 196 4-6 (2007) 1048-1073
23. Arciniega R.A., and Reddy J.N. Large deformation analysis of functionally graded shells. International Journal of Solids and Structures 44 (2007) 2036-2052
24. Reddy J.N. Theory and analysis of elastic plates and shells. 2nd ed. (2007), CRC Press, Boca Raton (FL)
25. Solin P., Segeth K., and Dolezel I. Higher-order finite element methods. 1st ed. (2004), CRC Press
26. Huang H.C., and Hinton E. A nine-node Lagrangian Mindlin plate element with enhanced shear interpolation. Engineering Computations 1 (1984) 369-379
27. Kant T., and Hinton E. Mindlin plate analysis by segmentation method. Journal of Engineering Mechanics 109 (1983) 537-556
28. Wang C.M., Wang Y.C., and Reddy J.N. Improved computation of stress resultants in the p-Ritz Method. Journal of Structural Engineering 128 (2002) 249-257
29. Wang C.M., Wang Y.C., and Reddy J.N. Problems and remedy for the Ritz method in determining stress resultants of corner supported rectangular plates. Computers and Structures 80 (2002) 145-154
30. Shanmugam N.E., Huang R., Yu C.H., and Lee S.L. Corner supported isosceles triangular orthotropic plates. Computers and Structures 32 (1989) 963-972
31. Sengupta D. Performance study of a simple finite element in the analysis of skew rhombic plates. Computers and Structures 54 6 (1995) 1173-1182
32. Zienkiewicz O.C., and Lefebvre D. Three-field mixed approximation and the plate bending problem. Communications in Applied Numerical Methods 3 (1987) 301-309
33. Zienkiewicz O.C., and Lefebvre D. A robust triangular plate bending element of the Reissner-Mindlin type. International Journal for Numerical Methods in Engineering 26 (1988) 1169-1184
34. Butalia T.S., Kant T., and Dixit V.D. Performance of Heterosis element for bending of skew rhombic plates. Computers and Structures 34 1 (1990) 23-49
35. Lee N.S., and Bathe K.J. Effects of element distortions on the performance of isoparametric elements. International Journal for Numerical Methods in Engineering 36 20 (1993) 3553-3576
36. Bellman, Kashef B.G., and Casti J. Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations. Journal of Computational Physics 10 (1972) 40-52
37. Shu C., and Richards B.E. Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids 15 (1992) 791-798
38. Shu C., and Wang C.M. Treatment of mixed and non-uniform boundary conditions in GDQ vibration analysis of rectangular plates. Engineering Structures 21 2 (1999) 125-134
39. Liew K.M., and Han J.B. Bending analysis of simply supported shear deformable skew plates. Journal of Engineering Mechanics 123 3 (1997) 214-221
40. 0 finite element solution of simply supported plates of polygonal shape. ASME, Journal of Applied Mechanics 44 (1977) 347-349
41. Hughes T.J.R., Cohen M., and Haroun M.D. Reduced and selective integration techniques in finite element analysis of plates. Nuclear Engineering Design. 46 (1978) 203-222
42. Jirousek J. Hybrid-Treffitz plate bending elements with p-method capabilities. International Journal for Numerical Methods in Engineering 24 (1987) 1367-1393