Large deflection analysis of functionally graded carbon nanotube-reinforced composite plates by the element-free kp-Ritz method

Computer Methods in Applied Mechanics and Engineering

Volumn 256, Issue , 2013, Pages 189-199

  Lei, Z X ^a,b,c   Liew, K M ^a,c   Yu, J L ^b,c  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^c City University of Hong Kong Joint Advanced Research Center   (China)

Author keywords

Carbon nanotube; Composite; Element free; First order shear deformation theory; Kp Ritz; Nonlinear

Indexed keywords

BENDING STIFFNESS; COMPOSITE PLATES; EFFECTIVE MATERIAL PROPERTY; ELEMENT-FREE; EQUIVALENT CONTINUUM; FIRST-ORDER SHEAR DEFORMATION; FIRST-ORDER SHEAR DEFORMATION THEORY; FUNCTIONALLY GRADED; GOVERNING EQUATIONS; INTEGRATION METHOD; INTEGRATION SCHEME; INVESTIGATE EFFECTS; KP-RITZ; LARGE DEFLECTION ANALYSIS; MESHFREE; NON-LINEAR RESPONSE; NONLINEAR; NONLINEAR BEHAVIOR; NUMERICAL RESULTS; PLATE ASPECT RATIO; SHEAR-LOCKING; SMALL STRAINS; THICKNESS DIRECTION; THIN PLATE; TWO-DIMENSIONAL DISPLACEMENT; WIDTH-TO-THICKNESS RATIO;

ASPECT RATIO; CARBON NANOTUBES; COMPOSITE MATERIALS; COMPUTATIONAL MECHANICS; CONTINUUM MECHANICS; NANOCOMPOSITES; NONLINEAR ANALYSIS; REINFORCEMENT; SINGLE-WALLED CARBON NANOTUBES (SWCN);

NONLINEAR EQUATIONS;

EID: 84873166115     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2012.12.007     Document Type: Article

References (47)

1. Thostenson E.T., Li C., Chou T.W. Nanocomposites in context. Compos. Sci. Technol. 2005, 65:491-516.
2. Lau A.K.T., Hui D. The revolutionary creation of new advanced materials-carbon nanotube composites. Compos. Part B 2002, 33:263-277.
3. Harris P.J.F. Carbon nanotubes and related structures: new materials for the twenty-first century 2001, Cambridge University Press.
4. Bokobza L. Multiwall carbon nanotube elastomeric composites: A review. Polymer 2007, 48:4907-4920.
5. Qian D., Dickey E.C., Andrews R., Rantell T. Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites. Appl. Phys. Lett. 2000, 76:2868-2870.
6. Pötschke P., Fornes T.D., Paul D.R. Rheological behavior of multiwalled carbon nanotube/polycarbonate composites. Polymer 2002, 43:3247-3255.
7. Fidelus J.D., Wiesel E., Gojny F.H., Schulte K., Wagner H.D. Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites. Compos. Part A 2005, 36:1555-1561.
8. Anumandla V., Gibson R.F. A comprehensive closed form micromechanics model for estimating the elastic modulus of nanotube-reinforced composites. Compos. Part A 2006, 37:2178-2185.
9. Han Y., Elliott J. Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites. Comput. Mater. Sci. 2007, 39:315-323.
10. Shen H.S. Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells. Compos. Struct. 2011, 93:2096-2108.
11. Shen H.S. Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells. Compos. Struct. 2011, 93:2096-2108.
12. G. Formica, W. Lacarbonara, Eshelby-like equivalent continuum modeling of carbon nanotube-based composites, in: Proceedings of 7th EUROMECH Solid Mechanics Conference, Lisbon, September 2009.
13. Shi D.L., Feng X.Q., Huang Y.Y., Hwang K.C., Gao H.J. The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites. J. Eng. Mater. Technol. 2004, 126:250-257.
14. Li X., Gao H., Scrivens W.A., Fei D., Xu X., Sutton M.A., Reynolds A.P., Myrick M.L. Reinforcing Mechanisms of Single-Walled Carbon Nanotube-Reinforced Polymer Composites. J. Nanosci. Nanotechnol. 2007, 7:2309-2317.
15. Shen H.S. Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments Part I: Axially-loaded shells. Compos. Struct. 2011, 93:2096-2108.
16. Koizumi M. The concept of FGM, ceramic transactions. Funct. Gradient Mater. 1993, 34:3-10.
17. Zhu P., Lei Z.X., Liew K.M. Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory. Compos. Struct. 2012, 94:1450-1460.
18. Shen H.S. Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Compos. Struct. 2009, 91:9-19.
19. Ke L.L., Yang J., Kitipornchai S. Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams. Compos. Struct. 2010, 92:676-683.
20. Aragh B.S., Barati A.H.N., Hedayati H. Eshelby-Mori-Tanaka approach for vibrational behavior of continuously graded carbon nanotube-reinforced cylindrical panels. Compos. Part B 2012, 43:1943-1954.
21. Formica G., Lacarbonara W., Alessi R. Vibrations of carbon nanotube-reinforced composites. J. Sound Vib. 2010, 329:1875-1889.
22. Mehrabadi S.J., Aragh B.S., Khoshkhahesh V., Taherpour A. Mechanical buckling of nanocomposite rectangular plate reinforced by aligned and straight single-walled carbon nanotubes. Compos. Part B 2012, 43:2031-2040.
23. Shen H.S. Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells. Compos. Struct. 2011, 93:2096-2108.
24. Shen H.S. Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part II: Pressure-loaded shells. Compos. Struct. 2011, 93:2496-2503.
25. Shen H.S., Zhang C.L. Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates. Mater. Des. 2010, 31:3403-3411.
26. Zhao X., Li Q., Liew K.M., Ng T.Y. The element-free -Ritz method for free vibration analysis of conical shell panels. J. Sound Vib. 2006, 295:906-922.
27. Liew K.M., Wang J., Tan M.J., Rajendran S. Postbuckling analysis of laminated composite plates using the mesh-free kp-Ritz method. Comput. Methods Appl. Mech. Eng. 2006, 195:551-570.
28. Zhao X., Liew K.M., Ng T.Y. Vibration analysis of laminated composite cylindrical panels via a meshfree approach. Int. J. Solids Struct. 2003, 40:161-180.
29. Liew K.M., Ng T.Y., Zhao X., Reddy J.N. Harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells. Comput. Methods Appl. Mech. Eng. 2002, 191:4141-4157.
30. Mori T., Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 1973, 21:571-574.
31. Benveniste Y. A new approach to the application of Mori-Tanaka's theory in composite materials. Mech. Mater. 1987, 6:147-157.
32. Mura T. Micromechanics of defects in solids 1987, Martinus Nijhoff, The Netherlands. second ed.
33. Reddy J.N. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis 2004, CRC Press, Boca Raton, FL. second ed.
34. Efraim E., Eisenberger M. Exact vibration analysis of variable thickness thick annular isotropic and FGM plates. J. Sound Vib. 2007, 299:720-738.
35. Chen J.S., Pan C., Wu C.T., Liu W.K. Reproducing Kernel Particle Methods for large deformation analysis of non-linear structures. Comput. Methods Appl. Mech. Eng. 1996, 139:195-227.
36. Liu W.K., Jun S., Zhang Y.F. Reproducing kernel particle methods. Int. J. Numer. Meth. FL 1995, 20:1081-1106.
37. Beissel S., Belytschko T. Nodal integration of the element-free Galerkin method. Comput. Methods Appl. Mech. Eng. 1996, 139:49-74.
38. Chen J.S., Wu C.T., Yoon S., You Y. A stabilized conforming nodal integration for Galerkin mesh-free methods. Int. J. Numer. Methods Eng. 2001, 50:435-466.
39. Dolbow J., Belytschko T. Numerical integration of the Galerkin weak form in meshfree methods. Comput. Mech. 1999, 23:219-230.
40. Chang T.C., Geng J.Y., Guo X.M. Chirality- and size-dependent elastic properties of single-walled carbon nanotubes. Appl. Phys. Lett. 2005, 87.
41. Elliott J.A., Sandler J.K.W., Windle A.H., Young R.J., Shaffer M.S.P. Collapse of Single-Wall Carbon Nanotubes is Diameter Dependent. Phys. Rev. Lett. 2004, 92:095501.
42. Jin Y., Yuan F.G. Simulation of elastic properties of single-walled carbon nanotubes. Compos. Sci. Technol. 2003, 63:1507-1515.
43. Liew K.M., Yan J.W., Sun Y.Z., He L.H. Investigation of temperature effect on the mechanical properties of single-walled carbon nanotubes. Compos. Struct. 2011, 93:2208-2212.
44. Popov V.N., Doren V.E.V., Balkanski M. Elastic properties of crystals of single-walled carbon nanotubes. Solid State Commun. 2000, 114:395-399.
45. Shen H.S. Nonlinear bending of shear deformable laminated plates under transverse and in-plane loads and resting on elastic foundations. Compos. Struct. 2000, 50:131-142.
46. Zaghloul S.A., Kennedy J.B. Nonlinear behavior of symmetrically laminated plates. J. Appl. Mech.-Trans. ASME 1975, 42:234-236.
47. Wu T.L., Shukla K.K., Huang J.H. Nonlinear static and dynamic analysis of functionally graded plates. Int. J. Appl. Mech. Eng. 2006, 11:679-698.