NURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter
Source abstract
Abstract
In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material properties are assumed to be graded only in the thickness direction and the effective properties are computed either using the rule of mixtures or by Mori-Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation plate theory (FSDT). The shear correction factors are evaluated employing the energy equivalence principle and a simple modification to the shear correction factor is presented to alleviate shear locking. Static bending, mechanical and thermal buckling, linear free flexural vibration and supersonic flutter analysis of FGM plates are numerically studied. The accuracy of the present formulation is validated against available three-dimensional solutions. A detailed numerical study is carried out to examine the influence of the gradient index, the plate aspect ratio and the plate thickness on the global response of functionally graded material plates.
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Research context
OpenAlex topics: Composite Structure Analysis and Optimization · Structural Load-Bearing Analysis · Structural Analysis and Optimization
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References (55)
Show source-provided references
1. The concept of FGM
2. Analysis of functionally graded plates10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8 ↗
3. Vibration characteristic and transient response of shear-deformable functionally graded plates in thermal environments10.1006/jsvi.2001.4161 ↗
4. Nonlinear free flexural vibrations of functionally graded rectangular and skew plates under thermal environments10.1016/j.finel.2005.06.001 ↗
5. Static and dynamic deformations of thick functionally graded elastic plates by using higher order shear and normal deformable plate theory and meshless local Petrov Galerkin method10.1016/j.compositesb.2004.02.004 ↗
6. Natural frequencies of functionally graded plates by a meshless method10.1016/j.compstruct.2006.04.018 ↗
7. Bending and vibration of functionally graded material sandwich plates using an accurate theory10.1016/j.finel.2012.03.006 ↗
8. Influence of functionally graded material on buckling of skew plates under mechanical loads10.1061/(ASCE)0733-9399(2006)132:8(902) ↗
9. A four node plate bending element based on Mindlin–Reissner plate theory and mixed interpolation10.1002/nme.1620210213 ↗
10. A field-consistent four-noded laminated anisotropic plate/shell element10.1016/0045-7949(87)90127-1 ↗
11. Nonlinear flexural vibrations of laminated orthotropic plates10.1016/0045-7949(91)90211-4 ↗
12. A unified approach for shear-locking free triangular and rectangular shell finite elements
13. Locking-free stabilized conforming nodal integration for mesh-free Mindlin–Reissner plate formulation10.1016/j.cma.2003.12.006 ↗
14. A smoothed finite element method for shell analysis10.1016/j.cma.2008.05.029 ↗
15. A smoothed finite element method for plate analysis10.1016/j.cma.2007.10.008 ↗
16. On elimination of shear locking in the element-free Galerkin method10.1002/nme.223 ↗
17. Active control of FGM plates with integrated piezoelectric sensors and actuators10.1016/S0020-7683(00)00050-0 ↗
18. A solution method for analysis of cracked plates under vibration10.1016/0013-7944(94)90130-9 ↗
19. Effect of FGM materials on parametric response of plate structures10.1016/S0045-7825(99)00455-7 ↗
20. Dynamic response of initially stressed functionally graded rectangular thin plates10.1016/S0263-8223(01)00122-2 ↗
21. Free vibration and stability of functionally graded plates according to a 2D higher-order deformation theory10.1016/j.compstruct.2007.01.030 ↗
22. Exact solutions for thermoelastic deformations of functionally graded thick rectangular plates10.2514/2.1805 ↗
23. Three-dimensional exact solution for the vibration of functionally graded rectangular plates10.1016/S0022-460X(03)00412-7 ↗
24. Birman V. Buckling of functionally graded hybrid composite plates. In: Proceedings of 10th conference on engineering mechanics, vol. 2. 1995. p. 1199–202.
25. Buckling of functionally graded plates under in-plane compressive loading10.1002/1521-4001(200204)82:4<277::AID-ZAMM277>3.0.CO;2-Y ↗
26. Thermomechanical postbuckling analysis of functionally graded plates and shallow cylindrical shells10.1007/s00707-003-0035-4 ↗
27. Supersonic flutter characteristics of functionally graded flat panels including thermal effects10.1016/j.compstruct.2004.10.007 ↗
28. Nonlinear oscillations of a fluttering functionally graded plate10.1016/j.compstruct.2006.01.006 ↗
29. Structural stability of functionally graded panels subjected to aero-thermal loads10.1016/j.compstruct.2007.07.010 ↗
30. Nonlinear thermal flutter of functionally graded panels under a supersonic flow10.1016/j.compstruct.2008.04.016 ↗
31. Nonlinear dynamic response of a functionally graded plate with a through-width surface crack10.1007/s11071-009-9533-9 ↗
32. Nonlinear vibration of edge cracked functionally graded Timoshenko beams10.1016/j.jsv.2009.02.023 ↗
33. Linear free flexural vibration of cracked functionally graded plates in thermal environment10.1016/j.compstruc.2011.04.002 ↗
34. Natural frequencies of cracked functionally graded material plates by the extended finite element method10.1016/j.compstruct.2011.04.007 ↗
35. Linear buckling analysis of cracked plates by SFEM and XFEM10.2140/jomms.2011.6.1213 ↗
36. An iso-geometric method for the Reissner–Mindlin plate bending problem10.1016/j.cma.2011.10.009 ↗
37. On elimination of shear locking in the element-free Galerkin method10.1002/nme.223 ↗
38. An improved 4-node quadrilateral plate bending element of the reissne-mindlin type10.1007/s004660050405 ↗
39. Thermal buckling of a simply supported moderately thick rectangular FGM plate10.1016/j.compstruct.2003.08.004 ↗
40. Incremental finite element matrices10.1061/JSDEAG.0003667 ↗
41. Supersonic flutter of shear deformation laminated flat panel10.1016/0022-460X(90)90887-6 ↗
42. Supersonic flutter analysis of thermally stressed laminated composite flat panels10.1016/0263-8223(95)00148-4 ↗
43. Cottrell · 2009
44. Nguyen VP, Simpson RN, Bordas SP, Rabczuk T. An introduction to Isogeometric analysis with MATLAB implementation: FEM and XFEM formulations, in preparation.
45. Finite element analysis of functionally graded plates under transverse load10.1016/j.finel.2010.12.001 ↗
46. Analysis of thick functionally graded plates by using higher order shear and normal deformable plate theory and MLPG method with radial basis functions10.1016/j.compstruct.2006.07.007 ↗
47. Thermo-elastic analysis of functionally graded plates using the element free kp-Ritz method10.1088/0964-1726/18/3/035007 ↗
48. Analysis of functionally graded plates by an efficient finite element method with node-based strain smoothing10.1016/j.tws.2012.01.013 ↗
49. Static, free vibration and buckling analysis of laminated composite Reissner–Mindlin plates using NURBS based isogeometric approach10.1002/nme.4282 ↗
50. Finite elements for functionally graded Reissner–Mindlin plates10.1016/j.cma.2003.09.014 ↗
51. Geometrically nonlinear analysis of functionally graded plates using the element free kp-Ritz method10.1016/j.cma.2009.04.005 ↗
52. Analysis of functionally graded plates using an edge-based smoothed finite element method10.1016/j.compstruct.2011.04.028 ↗
53. Free vibration analysis of functionally graded plates using the element free kp-Ritz method10.1016/j.jsv.2008.06.025 ↗
54. A new exact analytical approach for free vibration of Reissne–Mindlin functionally graded rectangular plates10.1016/j.ijmecsci.2010.10.002 ↗
55. Thermal buckling of simply supported functionally graded skew plates10.1016/j.compstruct.2005.04.004 ↗