Guidelines and recommendations on the use of higher order finite elements for bending analysis of plates

International Journal for Computational Methods in Engineering Science and Mechanics

Volumn 12, Issue 6, 2011, Pages 303-324

  Carrera, E ^a   Miglioretti, F ^a,b   Petrolo, M ^a  

^a POLITECNICO DI TORINO   (Italy)

^b UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

Author keywords

Finite element; Plate model; Refined theories; Unified formulation

Indexed keywords

BOUNDARY CONDITIONS; PLATES (STRUCTURAL COMPONENTS);

DISPLACEMENT AND STRESS; DISPLACEMENT DISTRIBUTION; FINITE ELEMENT MATRICES; HIGHER-ORDER DISPLACEMENT FIELDS; PLATE FINITE ELEMENTS; PLATE MODEL; REFINED THEORY; UNIFIED FORMULATIONS;

FINITE ELEMENT METHOD;

EID: 84855186586     PISSN: 15502287     EISSN: 15502295     Source Type: Journal    
DOI: 10.1080/15502287.2011.615792     Document Type: Article

References (56)

1. L. Euler, De Curvis Elasticis, Bousquet, Lausanne, 1744.
2. D. Bernoulli, De Vibrationibus et Sono Laminarum Elasticarum, Commentarii Academiae Scientiarum Imperialis Petropolitanae, vol. 13, pp. 105-120, 1751.
3. A. Cauchy, Sur l'Equilibre et le Mouvement d'une Plaque Solide, Exercises de Matematique, Vol. 3, pp. 328-355, 1828.
4. S. Poisson, Memoire Sur l'Equilibre et le Mouvement des Corps Elastique, Mem. Acad. Sci., Vol. 8, p. 357, 1829.
5. G. Kirchhoff, Uber das Gleichgewicht und die Bewegung Einer Elastishen Scheibe, J. Angew. Math., Vol. 40, pp. 51-88, 1850.
6. A.D. Saint-Venant, De la Torsion des Prismes, avec des Considérations sur leur Flexion, Ainsi que sur l' Equilibre des Solideś Elastiques en Général, et des Formules Pratiques pour le Calcul de leur Résistance à Divers Efforts s'exerçant Simultanément, V. Dalmont, 1855.
7. A. E. H. Love, The Mathematical Theory of Elasticity, 4th ed., Cambridge University Press, Cambridge, 1927.
8. E. Reissner, The Effect of Transverse Shear Deformation on the Bending of Elastic Plates, Journal of Applied Mechanics, Vol. 12, pp. 69-76, 1945.
9. R. D. Mindlin, Influence of Rotatory Inertia and Shear in Flexural Motions of Isotropic Elastic Plates, Journal of Applied Mechanics, Vol. 18, pp. 1031-1036, 1951.
10. B. Vlasov, On the Equations of Bending of Plates, Dokla Ak Nauk Azerbeijanskoi-SSR, Vol. 3, pp. 955-979, 1975.
11. S. Ambartsumian Contributions to the theory of anisotropic layered shells, Appl. Mech. Rev., Vol. 15, pp. 245-249, 1962.
12. L. Librescu, and J. Reddy, A Critical Review and Generalization of Transverse Shear Deformable Anisotropic Plates, Euromech Colloquium 219, Kassel, Refined Dynamical Theories of Beams, Plates and Shells and Their Applications, pp. 32-43, Springer Verlag, Berlin, 1986.
13. E. Grigolyuk, and G. Kulikov, General Directions of the Development of Theory of Shells, Mekhanica Kompozitnykh Materialov, Vol. 24, pp. 287-298, 1988.
14. K. Kapania, and S. Raciti, Recent Advances in Analysis of Laminated Beams and Plates, Part I: Sheare Effects and Buckling, AIAA Journal, Vol. 27, No. 7, pp. 923-935, 1989.
15. K. Kapania, and S. Raciti, Recent Advances in Analysis of Laminated Beams and Plates, Part II: Vibrations andWave Propagation, AIAA Journal, Vol. 27, No. 7, pp. 935-946, 1989. (Pubitemid 20683723)
16. K. Kapania, A Review on the Analysis of Laminated Shells, ASME J. Pressure Vessel Technol., Vol. 111, No. 2, pp. 88-96, 1989.
17. A. Noor, and W. Burton, Assessment of Shear Deformation Theories for Multilayered Composite Plates, Appl.Mech. Rev., Vol. 42, No. 1, pp. 1-18, 1989.
18. A. Noor, and W. Burton, Assessment of Computational Models for Multilayered Composite Shells, Appl. Mech. Rev., Vol. 43, No. 4, pp. 67-97, 1989.
19. A. Noor,W.Burton, andC.Bert, ComputationalModel for Sandwich Panels and Shells, Appl. Mech. Rev., Vol. 49, No. 3, pp. 155-199, 1986.
20. J. Reddy, and D. Robbins, Theories and Computational Models for Composite Laminates, Appl. Mech. Rev., Vol. 47, No. 6, pp. 147-165, 1994.
21. E. Carrera,Developments, Ideas and Evaluations BasedUpon theReissner's Mixed Variational Theorem in the Modeling of Multilayered Plates and Shells, Applied Mechanics Reviews, Vol. 54, pp. 301-329, 2001.
22. E. Carrera, Theories and Finite Elements forMultilayered Plates and Shells, Archives of Computational Methods in Engineering, Vol. 9, No. 2, pp. 87-140, 2002.
23. M. Qatu, Recent Research Advances in the Dynamic Behavior of Shells. Part 1: Laminated Composite Shells, Applied Mechanics Reviews, Vol. 55, No. 4, pp. 325-350, 2002.
24. M. Qatu, Recent Research Advances in the Dynamic Behavior of Shells. Part 2: Homogenous Shells, Applied Mechanics Reviews, Vol. 55, No. 5, pp. 415-434, 2002. (Pubitemid 40205887)
25. L. Librescu, Elasto-statics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures. Noordhoff Int, Leyden, Netherland, 1976.
26. J. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton, FL, 2004.
27. M. Qatu, Vibration of Laminated Shells and Plates. Elsevier, Oxford, UK, 2004.
28. P. Cicala, Sulla Teoria Elastica della Parete Sottile, Giornale del Genio Civile, 4,6 and 9, 1959.
29. O. Fettahlioglu, and C. Steele, Asymptotic Solutions for Orthotropic Non-Homogeneous Shells of Revolution, ASME J. Appl. Mech., Vol. 44, pp. 753-758, 1974.
30. V. Berdichevsky,VariationalAsymptotic Method of Shell Theory Construction. PMM, Vol. 43, pp. 664-667, 1979.
31. V. Berdichevsky, and V.Misyura, Effect of Accuracy Loss in Classical Shell Theory, Journal of Applied Mechanics, Vol. 59, pp. s217-s223, 1992.
32. D. Widera, and L. Logan, Refined Theories for Nonhomogeneous Anisotropic Cylindrical Shells: Part I-Derivation, Journal of the Engineering Mechanics Division, Vol. 106, No. 6, pp. 1053-1074, 1980.
33. D. Widera, and H. Fan, On the Derivation of a Refined Theory for Nonhomogeneous Anisotropic Shells of Revolution, ASME J. Appl. Mech., Vol. 110, pp. 102-105, 1988. (Pubitemid 18566593)
34. A.J.M. Spencer, P. Watson, and T.G. Rogers, Stress Analysis of Laminated Circular Cylindrical Shells 1990.
35. Recent Developments in Composite Materials Structures, 1990. Presented at theWinter Annual meeting of ASME, Dallas, Nov., AD 19, AMD 113, ASME, New York, 1990.
36. P. Cicala, Systematic Approximation Approach to Linear Shell Theory. Levrotto e Bella, Torino, 1965.
37. A.L. Goldenweizer, Theory of Thin Elastic Shells, International Series of Monograph in Aeronautics and Astronautics, Pergamon Press, New York, 1961.
38. E. Carrera, and M. Petrolo, Guidelines and Recommendations to Construct Refinements of Classical Theories forMetallic andComposite Plates,AIAA Journal in Press.
39. M. Ganapathi, O. Polit, and M. Touratier, A c0 Eight-Node Membrane-Shear-Bending Element for Geometrically Non-Linear (Static and Dynamic) Analysis of Laminates, International journal for Numerical Methods in Engineering Vol. 39, pp. 3453-3474, 1996. (Pubitemid 126546982)
40. O. Polit, and M. Touratier, High-order Triangular Sandwich Plate Finite Element for Linear and Non-Linear Analyses, Comput. Methods Appl. Mech. Engrg. Vol. 185, pp. 305-324, 2000.
41. M. Touratiert, and J. Faye, On a Refined Model in Structural Mechanics: Finite Element Approximation and Edge Effect Analysis for Axisymmetric Shells. Computers and Structures, Vol. 54, No. 5, pp. 897-920, 1995.
42. E. Carrera, and L. Demasi, Classical and Advanced Multilayerd Plate Elements Based Upon PVD and RMVT. Part 1: Derivation of finite element matrices, Int. J. Numer. Meth. Engng., Vol. 55, pp. 191-231, 2002.
43. E. Carrera, and L. Demasi, Classical and Advanced Multilayerd Plate Elements Based upon PVD and RMVT. part 2: Numerical implementation, Int. J. Numer. Meth. Engng., Vol. 55, pp. 253-291, 2002. (Pubitemid 34955892)
44. T. Kant, and K. Swaminathan, Estimation of Transverse/Interlaminar Stresses in Laminated Composites-a Selective Review and Survey of Current Developments. Composite Structures, Vol. 49, pp. 65-75, 2000. (Pubitemid 30559994)
45. E. Carrera, Historical review of Zig-Zag Theories for Multilayered Plates and Shells, Applied Mechanics Reviews, Vol. 56, pp. 287-308, 2003. (Pubitemid 40205918)
46. E. Carrera, Theories and Finite Elements forMultilayered Plates and Shells: A Unified Compact Formulation with Numerical Assessment and Benchmarking. Archives of Computational Methods in Engineering, Vol. 10, No. 3, pp. 216-296, 2003.
47. E. Carrera, and G. Giunta, Refined Beam Theories Based on Carrera's Unified formulation, International Journal of Applied Mechanics, Vol. 2, No. 1, pp. 117-143, 2010.
48. E. Carrera, and M. Petrolo, On the Effectiveness of Higher Order Terms in Refined Beam Theories, Journal of Applied Mechanics, vol. 78, No. 2, 2011.
49. E. Carrera, M. Cinefra, and P. Nali, Mitc Technique Extended to Variable Kinematic Multilayered Plate Elements Composite Structures, Composite Structures, vol. 92, No. 8, pp. 1888-1895, 2010.
50. E. Carrera, and S. Brischetto, Analysis of Thickness Locking in Classical, Refined and Mixed Theories for Layered Shells, Composite Structures, Vol. 85, pp. 83-90, 2008.
51. E. Carrera, and S. Brischetto, Analysis of Thickness Locking in Classical, Refined andMixed Multilayered Plate Theories, Composite Structures,Vol. 82, pp. 549-562, 2008. (Pubitemid 47543566)
52. B. Pandya, and T. Kant, Finite Element Analysis of Laminated Compiste Plates Using High-Order Displacement Model, Composites Science and Technology, Vol. 32, pp. 137-155, 1988. (Pubitemid 18650850)
53. T. Kant, and B. Manjunatha, An Unsymmetric Frc Laminate c° Finite Element Model With 12 degrees of Freedom Per Node, Eng Comput, Vol. (5), No. 3, pp. 292-308, 1988.
54. T. Kant, Numerical Analysis of Thick Plates, Comput Meth Appl Mech Eng., Vol. 31, pp. 1-18, 1982.
55. E. Dvorkin, and K. Bathe, A Continuum Mechanics Based Four-Node Shell Element for General Nonlinear Analysis, Eng. Computations, Vol. 1, pp. 77-88, 1984. (Pubitemid 16521754)
56. E. Carrera, M. Cinefra, and P. Nali, Mitc Technique Extended to Variable Kinematic Multilayered Plate Elements, Composite Structures, Vol. 92, pp. 1888-1895, 2010.