A simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates
Source abstract
Abstract
Abstract This paper presents a simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates. Unlike the conventional first-order shear deformation theory, the present first-order shear deformation theory contains only four unknowns and has strong similarities with the classical plate theory in many aspects such as governing equations of motion, boundary conditions, and stress resultant expressions. Equations of motion and boundary conditions are derived from Hamilton’s principle. Closed-form solutions of simply supported plates are obtained and the results are compared with the exact 3D and quasi-3D solutions and those predicted by other plate theories. Comparison studies show that the present theory can achieve the same accuracy of the conventional first-order shear deformation theory which has more number of unknowns.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Composite Structure Analysis and Optimization · Structural Load-Bearing Analysis · Structural Analysis and Optimization
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (47)
Show source-provided references
1. A critical review of recent research on functionally graded plates10.1016/j.compstruct.2012.09.001 ↗
2. Analysis of functionally graded plates10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8 ↗
3. A simple higher-order theory for laminated composite plates10.1115/1.3167719 ↗
4. A nth-order shear deformation theory for the bending analysis on the functionally graded plates10.1016/j.euromechsol.2012.08.005 ↗
5. A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates10.1016/j.compstruct.2011.05.022 ↗
6. An efficient and simple refined theory for bending and vibration of functionally graded plates10.1016/j.compstruct.2009.05.008 ↗
7. A general nonlinear third-order theory of functionally graded plates10.3850/S201042861100002X ↗
8. Vibration and stability of functionally graded plates based on a higher-order deformation theory10.1177/0731684408088884 ↗
9. Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation10.1016/j.jsv.2008.03.056 ↗
10. Static response and free vibration analysis of FGM plates using higher order shear deformation theory10.1016/j.apm.2010.03.034 ↗
11. Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique10.1016/j.compositesb.2012.01.089 ↗
12. Generalized shear deformation theory for bending analysis of functionally graded plates10.1016/j.apm.2005.03.009 ↗
13. A new higher order shear deformation theory for sandwich and composite laminated plates10.1016/j.compositesb.2011.07.017 ↗
14. A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates10.1016/j.ijsolstr.2011.09.008 ↗
15. Bending response of functionally graded plates by using a new higher order shear deformation theory10.1016/j.compstruct.2011.09.007 ↗
16. Generalized hybrid quasi-3D shear deformation theory for the static analysis of advanced composite plates10.1016/j.compstruct.2012.02.019 ↗
17. Analysis of laminated shells by a sinusoidal shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations10.1016/j.compositesb.2011.01.031 ↗
18. A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates10.1016/j.compositesb.2011.08.009 ↗
19. A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates10.1016/j.compstruct.2011.12.005 ↗
20. Response of elastic columns to axial pulse loading10.2514/3.2000 ↗
21. Flexure of composite plates10.1016/0263-8223(87)90027-4 ↗
22. Buckling of shear-deformable plates10.2514/3.48742 ↗
23. Refined plate theory and its variants10.2514/2.1622 ↗
24. Buckling analysis of plates using the two variable refined plate theory10.1016/j.tws.2008.08.002 ↗
25. A two variable refined plate theory for laminated composite plates10.1016/j.compstruct.2008.07.017 ↗
26. Free vibration of laminated composite plates using two variable refined plate theory10.1016/j.ijmecsci.2010.01.002 ↗
27. A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates10.1016/j.apm.2012.08.008 ↗
28. A refined plate theory for functionally graded plates resting on elastic foundation10.1016/j.compscitech.2011.08.016 ↗
29. Levy-type solution for buckling analysis of orthotropic plates based on two variable refined plate theory10.1016/j.compstruct.2011.01.012 ↗
30. A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates10.1016/j.compstruct.2012.08.025 ↗
31. An efficient and simple refined theory for buckling analysis of functionally graded plates10.1016/j.apm.2011.07.062 ↗
32. A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation10.1016/j.compositesb.2011.11.062 ↗
33. A nonlocal beam theory for bending, buckling, and vibration of nanobeams10.1016/j.ijengsci.2011.11.011 ↗
34. Levy-type solution for free vibration analysis of orthotropic plates based on two variable refined plate theory10.1016/j.apm.2011.11.003 ↗
35. Analytical solution of a two variable refined plate theory for bending analysis of orthotropic Levy-type plates10.1016/j.ijmecsci.2011.11.007 ↗
36. Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories10.1016/j.ijmecsci.2012.05.014 ↗
37. Free vibration of axially loaded rectangular composite beams using refined shear deformation theory10.1016/j.compstruct.2012.05.012 ↗
38. Vibration and buckling of composite beams using refined shear deformation theory10.1016/j.ijmecsci.2012.06.001 ↗
39. Static behavior of composite beams using various refined shear deformation theories10.1016/j.compstruct.2012.02.010 ↗
40. An efficient shear deformation theory for vibration of functionally graded plates10.1007/s00419-012-0642-4 ↗
41. A simple quasi-3D sinusoidal shear deformation theory for functionally graded plates10.1016/j.compstruct.2012.11.030 ↗
42. Average stress in matrix and average elastic energy of materials with misfitting inclusions10.1016/0001-6160(73)90064-3 ↗
43. Variable kinematic model for the analysis of functionally graded material plates10.2514/1.32490 ↗
44. Effects of thickness stretching in functionally graded plates and shells10.1016/j.compositesb.2010.10.005 ↗
45. Three-dimensional exact solution for the vibration of functionally graded rectangular plates10.1016/S0022-460X(03)00412-7 ↗
46. Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory10.1016/j.compstruct.2007.01.030 ↗
47. A new exact analytical approach for free vibration of Reissner–Mindlin functionally graded rectangular plates10.1016/j.ijmecsci.2010.10.002 ↗