The RMVT- and PVD-based finite layer methods for the three-dimensional analysis of multilayered composite and FGM plates

Composite Structures

Volumn 92, Issue 10, 2010, Pages 2476-2496

  Wu, Chih Ping ^a   Li, Hao Yuan ^a  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

Author keywords

FGM; Finite layer methods; Mixed theories; Plates; Reissner; Virtual displacements

Indexed keywords

3D SOLUTIONS; CONVERGENCE RATES; CONVERGENT SOLUTIONS; FIELD VARIABLES; FINITE LAYER METHODS; H-REFINEMENT; LAGRANGE POLYNOMIALS; LAYER-WISE; MATERIAL PROPERTY; MECHANICAL LOADS; MIXED VARIATIONAL THEOREM; MULTILAYERED COMPOSITES; OUT-OF-PLANE; PARABOLIC FUNCTION DISTRIBUTION; POWER LAW DISTRIBUTION; PRINCIPLE OF VIRTUAL DISPLACEMENTS; REFINEMENT PROCESS; THREE-DIMENSIONAL (3D) ANALYSIS; THREE-DIMENSIONAL ANALYSIS; TRIGONOMETRIC FUNCTIONS; VIRTUAL DISPLACEMENTS;

BEAMS AND GIRDERS; FUNCTION EVALUATION; FUNCTIONALLY GRADED MATERIALS; THREE DIMENSIONAL;

PILE FOUNDATIONS;

COMPOSITE; MATHEMATICAL ANALYSIS; SIMULATION; STRUCTURAL ANALYSIS; THEORETICAL ANALYSIS;

EID: 77952429361     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2010.03.001     Document Type: Article

References (53)

1. Noor A.K., Burton W.S. Assessment of computational models for multilayered anisotropic plates. Compos Struct 1990, 14:233-265.
2. Noor A.K., Burton W.S. Computational models for high-temperature multilayered composite plates and shells. Appl Mech Rev 1992, 45:419-446.
3. Noor A.K., Burton W.S., Bert C.W. Computational model for sandwich panels and shells. Appl Mech Rev 1996, 49:155-199.
4. Reddy J.N. An evaluation of equivalent single layer and layerwise theories of composite laminates. Compos Struct 1993, 25:21-35.
5. Carrera E. Historical review of zig-zag theories for multilayered plates and shells. Appl Mech Rev 2003, 56:287-308.
6. Carrera E., Ciuffreda A. Bending of composites and sandwich plates subjected to localized lateral loadings: a comparison of various theories. Compos Struct 2005, 68:185-202.
7. Carrera E. A priori vs. a posteriori evaluation of transverse stresses in multilayered orthotropic plates. Compos Struct 2000, 48:245-260.
8. Ramirez F., Heyliger P.R., Pan E. Static analysis of functionally graded elastic anisotropic plates using a discrete layer approach. Compos Part B: Eng 2006, 37:10-20.
9. Ramirez F., Heyliger P.R., Pan E. Discrete layer solution to free vibrations of functionally graded magneto-electro-elastic plates. Mech Adv Mater Struct 2006, 13:249-266.
10. Hussein M., Heyliger P.R. Discrete layer analysis of axisymmetric vibrations of laminated piezoelectric cylinders. J Sound Vib 1996, 192:995-1013.
11. Saravanos D.A., Heyliger P.R., Hopkins D.A. Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates. Int J Solids Struct 1997, 34:359-378.
12. Reissner E. On a certain mixed variational theory and a proposed applications. Int J Numer Methods Eng 1984, 20:1366-1368.
13. Reissner E. On a mixed variational theorem and on a shear deformable plate theory. Int J Numer Methods Eng 1986, 23:193-198.
14. Carrera E. Developments, ideas, and evaluations based upon Reissner's mixed variational theorem in the modeling of multilayered plates and shells. Appl Mech Rev 2001, 54:301-329.
15. Murakami H. Laminated composite plate theory with improved in-plane responses. J Appl Mech 1986, 53:661-666.
16. Toledano A., Murakami H. A high-order laminated plate theory with improved in-plane responses. Int J Solids Struct 1987, 23:111-131.
17. Carrera E. An assessment of mixed and classical theories on global and local response of multilayered orthotropic plates. Compos Struct 2000, 50:183-198.
18. Carrera E. An assessment of mixed and classical theories for the thermal stress analysis of orthotropic multilayered plates. J Therm Stress 2000, 23:797-831.
19. Carrera E. Mixed layer-wise models for multilayered plates analysis. Compos Struct 1998, 43:57-70.
20. Carrera E. Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarks. Arch Comput Methods Eng 2003, 10:215-296.
21. Carrera E., Ciuffreda A. A unified formulation to assess theories of multilayered plates for various bending problems. Compos Struct 2005, 69:271-293.
22. Brischetto S., Leetsch R., Carrera E., Wallmersperger T., Kroplin B. Thermo-mechanical bending of functionally graded plates. J Therm Stress 2008, 31:286-308.
23. Brischetto S., Carrera E. Refined 2D models for the analysis of functionally graded piezoelectric plates. J Intell Mater Sys Struct 2009, 20:1783-1797.
24. Carrera E., Brischetto S., Robaldo A. Variable kinematic model for the analysis of functionally graded material plates. AIAA J 2008, 46:194-203.
25. Brischetto S., Carrera E. Advanced mixed theories for bending analysis of functionally graded plates. Comput Struct 2008, 10.1016/j.compstruc.2008.04.004.
26. Demasi L. ∞6 mixed plate theories based on the generalized unified formulation. Part I: Governing equations. Compos Struct 2009, 87:1-11.
27. Demasi L. ∞6 mixed plate theories based on the generalized unified formulation. Part II: Layerwise theories. Compos Struct 2009, 87:12-22.
28. Demasi L. ∞6 mixed plate theories based on the generalized unified formulation. Part III: Advanced mixed high order shear deformation theories. Compos Struct 2009, 87:183-194.
29. Demasi L. ∞6 mixed plate theories based on the generalized unified formulation. Part IV: Zig-zag theories. Compos Struct 2009, 87:195-205.
30. Demasi L. ∞6 mixed plate theories based on the generalized unified formulation. Part V: Results. Compos Struct 2009, 88:1-16.
31. Cheung Y.K. Finite strip method in structural analysis 1976, Pergamon Press, Oxford.
32. Cheung Y.K., Jiang C.P. Finite layer method in analysis of piezoelectric composite laminates. Comput Methods Appl Mech Eng 2001, 191:879-901.
33. Akhras G., Li W.C. Three-dimensional static, vibration and stability analysis of piezoelectric composite plates using a finite layer method. Smart Mater Struct 2007, 16:561-569.
34. Akhras G., Li W.C. Three-dimensional thermal buckling analysis of piezoelectric composite plates using the finite layer method. Smart Mater Struct 2008, 17:1-8.
35. Carrera E., Demasi L. Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 1: Derivation of finite element matrices. Int J Numer Methods Eng 2002, 55:191-231.
36. Carrera E., Demasi L. Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 2: Numerical implementations. Int J Numer Methods Eng 2002, 55:253-291.
37. Demasi L. Treatment of stress variables in advanced multilayered plate elements based upon Reissner's mixed variational theorem. Comput Struct 2006, 84:1215-1221.
38. Pan E. Exact solution for functionally graded anisotropic elastic composite laminates. J Compos Mater 2003, 37:1903-1920.
39. Pan E., Han F. Exact solution for functionally graded and layered magneto-electro-elastic plates. Int J Eng Sci 2005, 43:321-339.
40. Pan E., Heyliger P.R. Free vibration of simply supported and multilayered magneto-electro-elastic plates. J Sound Vib 2002, 252:429-442.
41. Kashtalyan M. Three-dimensional elasticity solution for bending of functionally graded rectangular plates. Eur J Mech A Solids 2004, 23:853-864.
42. Wu C.P., Syu Y.S. Exact solutions of functionally graded piezoelectric shells under cylindrical bending. Int J Solids Struct 2007, 44:6450-6472.
43. Wu C.P., Tsai Y.H. Static behavior of functionally graded magneto-electro-elastic shells under electric displacement and magnetic flux. Int J Eng Sci 2007, 45:744-769.
44. Tsai Y.H., Wu C.P. Dynamic responses of functionally graded magneto-electro-elastic shells with open-circuit surface conditions. Int J Eng Sci 2008, 46:843-857.
45. Wu C.P., Tsai Y.H. Cylindrical bending vibration of functionally graded piezoelectric shells using the method of perturbation. Int J Eng Math 2009, 63:95-119.
46. Wu C.P., Liu K.Y. A state space approach for the analysis of doubly curved functionally graded elastic and piezoelectric shells. Comput Mater Continua 2007, 6:177-199.
47. Wu C.P., Chen S.J., Chiu K.H. Three-dimensional static behavior of functionally graded magneto-electro-elastic plates using the modified Pagano method. Mech Res Commun 2010, 37:54-60.
48. Wu C.P., Lu Y.C. A modified Pagano method for the 3D dynamic responses of functionally graded magneto-electro-elastic plates. Compos Struct 2009, 90:363-372.
49. Wu C.P., Huang S.E. Three-dimensional solutions of functionally graded piezo-thermo-elastic shells and plates using a modified Pagano method. Comput Mater Continua 2009, 12:251-282.
50. Wu C.P., Chiu K.H., Wang Y.M. A review on the three-dimensional analytical approaches of multilayered and functionally graded piezoelectric plates and shells. Comput Mater Continua 2008, 18:93-132.
51. Pagano N.J. Exact solutions for rectangular bidirectional composites and sandwich plates. J Compos Mater 1970, 4:20-34.
52. Wu C.P., Li H.Y. An RMVT-based third-order shear deformation theory of multilayered functionally graded material plates. Compos Struct 2010, 10.1016/j.compstruct.2010.01.022.
53. Zenkour A. Generalized shear deformation theory for bending analysis of functionally graded plates. Appl Math Modeling 2006, 30:67-84.