Robust C 0 high-order plate finite element for thin to very thick structures: Mechanical and thermo-mechanical analysis

International Journal for Numerical Methods in Engineering

Volumn 90, Issue 4, 2012, Pages 429-451

  Polit, O ^a   Vidal, P ^a   D'Ottavio, M ^a  

^a UNIV PARIS NANTERRE   (France)

Author keywords

C 0 finite element; Mechanical load; Normal stresses; Numerical locking; Sinus model; Thermo mechanical load; Thick plates

Indexed keywords

FINITE ELEMENT; MECHANICAL LOADS; NORMAL STRESS; NUMERICAL LOCKING; THERMO MECHANICAL LOADS; THICK PLATE;

DEGREES OF FREEDOM (MECHANICS); MINDLIN PLATES; STRESSES;

C (PROGRAMMING LANGUAGE);

EID: 84858703955     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.3328     Document Type: Article

References (46)

1. Mackerle J. Finite element linear and nonlinear, static and dynamic analysis of structural elements: a bibliography (1992-1995). Engineering Computations 1997; 14(4):347-440.
2. Mackerle J. Finite- and boundary-element linear and nonlinear analysis of shells and shell-like structures a bibliography (1999-2001). Finite Elements in Analysis and Design 2002; 38:765-782.
3. Hughes T, Tezduyar T. Finite elements based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element. ASME - Journal of Applied Mechanics 1981; 48:587-596.
4. Bathe K, Dvorkin E. A four node plate bending element based on Mindlin-Reissner plate theory and a mixed interpolation. International Journal for Numerical Methods in Engineering 1985; 35:503-519.
5. Somashekar B, Prathap G, Ramesh B. A field consistent four-node laminated anisotropic plate/shell element. Computers & Structures 1987; 25:345-353.
6. Park K, Pramono E, Stanley G, Cabiness H. The ANS shell elements earlier and recent improvements. In Analytical and Computational Models of Shells, Vol. 3, Noor AK, et al. (eds), 1989; 359-382.
7. Batoz J, Lardeur P. A discrete shear triangular nine DOF element for the analysis of thick to very thin plates. International Journal for Numerical Methods in Engineering 1989; 28:533-560.
8. Simo JC, Rifai S, Fox DD. On stress resultant geometrically exact shell model. Part IV variable thickness shells with through the thickness stretching. Computer Methods in Applied Mechanics and Engineering 1990; 81:53-91.
9. Bletzinger KU, Bischoff M, Ramm E. A unified approach for shear-locking-free triangular and rectangular shell finite elements. Computers & Structures 2000; 75:321-334.
10. Reddy JN. Mechanics of laminated composite plates and shells. Theory and analysis, Second ed. CRC Press, 2004.
11. Kapania K. A review on the analysis of laminated shells. ASME - Journal of Pressure Vessel Technology 1989; 111(2):88-96.
12. Noor AK, Burton WS. Assessment of computational models for multilayered composite shells. Applied Mechanics Reviews 1989; 43(4):67-97.
13. Reddy JN, Robbins DH. Theories and computational models for composite laminates. Applied Mechanics Reviews 1994; 47(6):147-165.
14. Kant T, Swaminathan K. Estimation of transverse/interlaminar stresses in laminated composites-a selective review and survey of current developments. Composite Structures 2000; 49:65-75.
15. Carrera E. Theories and finite elements for multilayered, anisotropic, composite plates and shells. Archives of Computational Methods in Engineering 2002; 9(2):87-140.
16. Carrera E. Historical review of ZIGZAG theories for multilayered plates and shells. Applied Mechanics Reviews 2003; 56:287-308.
17. Zhang Y, Yang C. Recent developments in finite elements analysis for laminated composite plates. Composite Structures 2009; 88:147-157.
18. Yu W, Hodges DH, Volovoi VV. Asympotically accurate 3D recovery from Reissner-like composite plate finite elements. Computers & Structures 2003; 81:439-454.
19. Yu W, Hodges DH, Volovoi VV. Mathematical construction of a Reissner-Mindlin plate theory for composite laminates. International Journal of Solids and Structures 2005; 42:6680-6699.
20. Polit O, Touratier M. A multilayered/sandwich triangular finite element applied to linear and nonlinear analysis. Composite Structures 2002; 58(1):121-128.
21. 1 plate and shell finite elements for geometrically non linear analysis of multilayered structures. Computers & Structures 2006; 84:1264-1274.
22. Vidal P, Polit O. A thermomechanical finite element for the analysis of rectangular sandwich beams. Finite Elements in Analysis and Design 2006; 42:868-883.
23. Vidal P, Polit O. A family of sinus finite elements for the analysis of rectangular laminated beams. Composite Structures 2008; 84:56-72.
24. Touratier M. An efficient standard plate theory. International Journal of Engineering Science 1991; 29:901-916.
25. Touratier M. A refined theory of laminated shallow shells. International Journal of Solids and Structures 1992; 29(11):1401-1415.
26. 1 finite element including transverse shear and torsion warping for rectangular sandwich beams. International Journal for Numerical Methods in Engineering 1999; 45(1):47-75.
27. Polit O, Touratier M. High order triangular sandwich plate finite element for linear and nonlinear analyses. Computer Methods in Applied Mechanics and Engineering 2000; 185:305-324.
28. D'Ottavio M, Polit O. Sensitivity analysis of thickness assumptions for piezoelectric plate models. Journal of Intelligent Material Systems and Structures 2009; 20:1815-1834.
29. Vidal P, Polit O. A refined sine-based finite element with transverse normal deformation for the analysis of laminated under thermomechanical loads. Journal of Mechanics of Materials and Structures 2009; 4:1127-1155.
30. Polit O, Touratier M, Lory P. A new eight-node quadrilateral shear-bending plate finite element. International Journal for Numerical Methods in Engineering 1994; 37:387-411.
31. Touratier M. A generalization of shear deformation theories for axisymmetric multilayered shells. International Journal of Solids and Structures 1992; 29:1379-1399.
32. Büchter N, Ramm E, Roehl D. Three-dimensional extension of non-linear shell formulation based on the enhanced assumed strain concept. International Journal for Numerical Methods in Engineering 1994; 37:2551-2568.
33. Parisch H. A continuum-based shell theory for non-linear applications. International Journal for Numerical Methods in Engineering 1995; 38:1855-1883.
34. Tessler A. An improved plate theory of 1, 2-order for thick composite laminates. International Journal of Solids and Structures 1993; 30:981-1000.
35. Barut A, Madenci E, Heinrich J, Tessler A. Analysis of thick sandwich construction by a 3, 2-order theory. International Journal of Solids and Structures 2001; 38:6063-6077.
36. Carrera E, Brischetto S. Analysis of thickness locking in classical, refined and mixed plate theories. Composite Structures 2008; 82(4):549-562.
37. Cheng S. Elasticity theory of plates and a refined theory. ASME - Journal of Applied Mechanics 1979; 46:644-650.
38. 0 eight-node membrane-shear-bending element for geometrically non-linear (static and dynamic) analysis of laminates. International Journal for Numerical Methods in Engineering 1996; 39:3453-3474.
39. Pagano NJ. Exact solutions for rectangular bidirectional composites and sandwich plates. Journal of Composite Materials 1970; 4:20-34.
40. Bhaskar K, Varadan TK, Ali JSM. Thermoelastic solutions for orthotropic and anisotropic composite laminates. Composites Part B: Engineering 1996; 27B:415-420.
41. Carrera E. Developments, ideas, and evaluations based upon Reissner's mixed variational theorem in the modelling of multilayered plates and shells. Applied Mechanics Reviews 2001; 54:301-329.
42. Carrera E. Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Archives of Computational Methods in Engineering 2003; 10(3):216-296.
43. Babuska I, Suri M. On locking and robustness in the finite element method. SIAM Journal Numerical Analysis 1992; 51:221-258.
44. Bischoff M, Ramm E. On the physical significance of higher order kinematic and static variables in a three-dimensional shell formulation. International Journal of Solids and Structures 2000; 37:6933-6960.
45. Klinkel S, Gruttmann F, Wagner W. A continuum based three-dimensional shell element for laminated structures. Computers & Structures 1999; 71:43-62.
46. 3 plate theories for thick and thin plates: the generalized unified formulation. Composite Structures 2008; 84:256-270.