Free vibration analysis of moderately thick functionally graded plates by local Kriging meshless method
Source abstract
Abstract
Abstract This paper mainly Presents free vibration analyses of metal and ceramic functionally graded plates with the local Kriging meshless method. The Kriging technique is employed to construct shape functions which possess Kronecker delta function property and thus make it easy to implement essential boundary conditions. The eigenvalue equations of free vibration problems are based on the first-order shear deformation theory and the local Petrov–Galerkin formulation. The cubic spline function is used as the weight function which vanishes on internal boundaries of local quadrature domains and hence simplifies the implementation. Convergence studies are conducted to examine the stability of the present method. Three types of functionally graded plates – square, skew and quadrilateral plates – are considered as numerical examples to demonstrate the versatility of the present method for free vibration analyses.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Composite Structure Analysis and Optimization · Numerical methods in engineering · Fractional Differential Equations Solutions
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (56)
Show source-provided references
1. Meshless methods: an overview and recent developments10.1016/S0045-7825(96)01078-X ↗
2. Meshless methods: a review and computer implementation aspects10.1016/j.matcom.2008.01.003 ↗
3. Liu · 2010
4. Atluri S. The meshless method (MLPG) for domain and BIE discretizations. Tech Science Press; 2004.
5. Gu L. Some properties of Kriging based meshfree method. In: Proceedings of the program and abstracts for the 14th US national congress of theoretical and applied mechanics. Blacksburg (VA); 2002. p. 309–10.
6. Moving kriging interpolation and element-free Galerkin method10.1002/nme.553 ↗
7. Liu GR, Dai KY, Gu YT, Lim KM.A comparison between radial point interpolation method (RPIM) and Kriging based meshfree method. Advances in Meshfree and X-FEM Methods. In: Liu G, editor. Proceedings of the 1st Asian workshop on meshfree methods. Singapore: World Scientific; 2002. p. 29–34.10.1142/9789812778611_0007 ↗
8. Comparison between the radial point interpolation and the Kriging interpolation used in meshfree methods10.1007/s00466-003-0462-z ↗
9. A novel meshless approach – Local Kriging (LoKriging) method with two-dimensional structural analysis10.1007/s00466-003-0524-2 ↗
10. Development of a novel meshless Local Kriging (LoKriging) method for structural dynamic analysis10.1016/j.cma.2004.01.010 ↗
11. Analysis of microelectromechanical systems (MEMS) by meshless local kriging (Lokriging) method10.1080/02533839.2004.9670905 ↗
12. Further investigation of element-free Galerkin method using moving kriging interpolation10.1142/S0219876204000162 ↗
13. On the parametric refinement of moving Kriging interpolation for element-free Galerkin method
14. A moving Kriging interpolation-based meshless method for numerical simulation of Kirchhoff plate problems10.1002/nme.2462 ↗
15. A moving Kriging interpolation-based meshfree method for free vibration analysis of Kirchhoff plates10.1016/j.compstruc.2010.11.006 ↗
16. Eigenvalue analysis of thin plate with complicated shapes by a novel meshfree method10.1142/S1758825111000853 ↗
17. A meshless analysis of shells based on moving Kriging interpolation10.1142/S0219876207000935 ↗
18. A moving Kriging interpolation-based element-free Galerkin method for structural dynamic analysis10.1016/j.cma.2010.12.017 ↗
19. Sommanawat W, Kanok-Nukulchai W. Multiscale simulation based on moving Kriging method. In: 8th World congress on computational mechanics (WCCM8), 5th European congress on computational methods in applied sciences and Engineering (ECCOMAS 2008). Venice, Italy; 2008.
20. Fan C, Yang JY. Numerical modeling of Mode I crack propagation in rocks with meshless method. Controlling seismic hazard and sustainable development of deep mines. In: 7th International symposium on rockburst and seismicity in mines (Rasim7), vols. 1 and 2; 2009. p. 1235–8.
21. A meshless local Kriging method for large deformation analyses10.1016/j.cma.2006.09.017 ↗
22. Geometrically nonlinear analysis of microswitches using the local meshfree method10.1142/S0219876208001601 ↗
23. A local Petrov–Galerkin approach with moving Kriging interpolation for solving transient heat conduction problems
24. A Kriging-based error-reproducing and interpolating kernel method for improved mesh-free approximations10.1002/nme.2127 ↗
25. Fan C, Luan MT. Enriched kriging interpolation method based on finite covers and its application in engineering. In: CMESM 2006: Proceedings of the 1st international conference on enhancement and promotion of computational methods in engineering science and mechanics; 2006. p. 293–8.
26. A moving Kriging interpolation-based boundary node method for two-dimensional potential problems10.1088/1674-1056/19/12/120202 ↗
27. An enhancement of finite element method with moving Kriging shape functions10.1142/S0219876205000594 ↗
28. Wong F, Kanok-Nukulchai W. On alleviation of shear locking in the Kriging-based finite element method. In: International civil engineering conference towards sustainable civil engineering practice; 2006.
29. Wong F, Kanok-Nukulchai W. A Kriging-based finite element method for analysis of shell structures. In: 8th World congress on computational mechanics, 5th European congress on computational methods in applied sciences and engineer; 2008.
30. On the convergence of the Kriging-based finite element method10.1142/S0219876209001784 ↗
31. Kriging-based finite element method: element-by-element Kriging interpolation
32. Analysis of functionally graded plates10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8 ↗
33. Dynamic response of initially stressed functionally graded rectangular thin plates10.1016/S0263-8223(01)00122-2 ↗
34. Vibration characteristics and transient response of shear-deformable functionally graded plates in thermal environments10.1006/jsvi.2001.4161 ↗
35. Large amplitude vibration of thermo-electro-mechanically stressed FGM laminated plates10.1016/S0045-7825(03)00387-6 ↗
36. Nonlinear free and forced vibration analysis of thin circular functionally graded plates10.1016/j.jsv.2007.08.011 ↗
37. An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory10.1016/j.tws.2008.03.008 ↗
38. Thermal postbuckling and vibration analyses of functionally graded plates10.1016/j.jsv.2005.01.031 ↗
39. Free vibration of simply supported functionally graded and layered magneto–electro-elastic plates by finite element method10.1016/j.jsv.2005.12.030 ↗
40. 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 ↗
41. Natural frequencies of functionally graded plates by a meshless method10.1016/j.compstruct.2006.04.018 ↗
42. A radial basis function approach for the free vibration analysis of functionally graded plates using a refined theory10.1016/j.jsv.2006.08.037 ↗
43. A review of meshless methods for laminated and functionally graded plates and shells10.1016/j.compstruct.2011.02.018 ↗
44. A contouring program based on dual kriging interpolation10.1007/BF01206346 ↗
45. Post-processing of finite element stress fields using dual kriging based methods for structural analysis of concrete dams10.1016/j.finel.2005.10.004 ↗
46. Olea · 1999
47. Designs for computer experiments10.1080/00401706.1989.10488474 ↗
48. Design and analysis of computer experiments
49. Thermomechanical analysis of functionally graded cylinders and plates10.1080/01495739808956165 ↗
50. Reddy · 2003
51. Exact vibration analysis of variable thickness thick annular isotropic and FGM plates10.1016/j.jsv.2006.06.068 ↗
52. Free vibration analysis of functionally graded plates using the element-free kp-Ritz method10.1016/j.jsv.2008.06.025 ↗
53. Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory10.1016/j.compstruct.2007.01.030 ↗
54. Vibration of thick skew plates based on Mindlin shear deformation plate-theory10.1006/jsvi.1993.1361 ↗
55. Free vibration of skew Mindlin plates by p-version of FEM10.1016/S0022-460X(02)01536-5 ↗
56. Natural frequencies of thick arbitrary quadrilateral plates using the pb-2 Ritz method10.1006/jsvi.1996.0489 ↗