RBF- based Meshless Method for Free Vibration Analysis of Laminated Composite Plates
The governing differential equations of laminated
plate utilizing trigonometric shear deformation theory are derived
using energy approach. The governing differential equations
discretized by different radial basis functions are used to predict the
free vibration behavior of symmetric laminated composite plates.
Effect of orthotropy and span to thickness ratio on frequency
parameter of simply supported laminated plate is presented.
Numerical results show the accuracy and good convergence of radial
basis functions.
[1] E.J. Kansa, Multiquadrics a scattere ddat aapproximation scheme with
applications to computational fluid dynamics, i:Surface approximations
and partial derivative estimates, Comput. Math. Appl. 19 (8/9) (1990)
127-145.
[2] Liew K.M. Xin Zhao, Antonio J.M. Ferreira, A review of meshless
methods for laminated and functionally graded plates and shells,
Composite Structures, 93, 8, 2031-2041
[3] Xiang S, Ke-ming Wang, Yan-ting Ai, Yun-dong Sha, Shi H. Analysis
of isotropic, sandwich and laminated plates by a meshless method and
various shear deformation theories. Composite Structures 91(2009) 31-
37.
[4] Xiang S, Ke-ming Wang. Free vibration analysis of symmetric
laminated composite plates by trigonometric shear deformation theory
and inverse multiquadrics RBF. Thin-Walled Structures 47(2009) 304-
310
[5] Castro LMS, Ferreira AJM, Bertoluzza S, Batra RC, Reddy JN. A
wavelet collocation method for the static analysis of sandwich plates
using a layerwise theory. Composite Structures 92 (2010) 1786-179
[6] Ferreira AJM, Castro LM, Roque CMC, Reddy JN, Bertoluzza S.
Buckling analysis of laminated plates by wavelets. Article in Press.
Computers and Structures (2011)
[7] Ferreira AJM, Roque CMC, Neves AMA, Jorge RMN, Soares CMM,
Liew KM. Buckling and vibration analysis of isotropic and laminated
plates by radial basis functions. Composites: Part B: Engineering 42
(2011) 592-606
[8] Liew KM, Huang YQ. Bending and buckling of thick symmetric
rectangular laminates using the moving least-squares differential
quadrature method. International Journal of Mechanical Sciences 45
(2003) 95-114
[9] Liew KM, Chen XL, Reddy JN. Meshfree radial basis function method
for buckling analysis of non-uniformly loaded arbitrarily shaped shear
deformable plates. Computer Methods in Applied Mechanics
Engineering 193 (2004) 205-224
[10] Liew KM, Wang J, Ng TY, Tan MJ. Free vibration and buckling
analyses of shear-deformable plates based on FSDT meshfree method
Journal of Sound and Vibration 276 (2004) 997-1017
[1] E.J. Kansa, Multiquadrics a scattere ddat aapproximation scheme with
applications to computational fluid dynamics, i:Surface approximations
and partial derivative estimates, Comput. Math. Appl. 19 (8/9) (1990)
127-145.
[2] Liew K.M. Xin Zhao, Antonio J.M. Ferreira, A review of meshless
methods for laminated and functionally graded plates and shells,
Composite Structures, 93, 8, 2031-2041
[3] Xiang S, Ke-ming Wang, Yan-ting Ai, Yun-dong Sha, Shi H. Analysis
of isotropic, sandwich and laminated plates by a meshless method and
various shear deformation theories. Composite Structures 91(2009) 31-
37.
[4] Xiang S, Ke-ming Wang. Free vibration analysis of symmetric
laminated composite plates by trigonometric shear deformation theory
and inverse multiquadrics RBF. Thin-Walled Structures 47(2009) 304-
310
[5] Castro LMS, Ferreira AJM, Bertoluzza S, Batra RC, Reddy JN. A
wavelet collocation method for the static analysis of sandwich plates
using a layerwise theory. Composite Structures 92 (2010) 1786-179
[6] Ferreira AJM, Castro LM, Roque CMC, Reddy JN, Bertoluzza S.
Buckling analysis of laminated plates by wavelets. Article in Press.
Computers and Structures (2011)
[7] Ferreira AJM, Roque CMC, Neves AMA, Jorge RMN, Soares CMM,
Liew KM. Buckling and vibration analysis of isotropic and laminated
plates by radial basis functions. Composites: Part B: Engineering 42
(2011) 592-606
[8] Liew KM, Huang YQ. Bending and buckling of thick symmetric
rectangular laminates using the moving least-squares differential
quadrature method. International Journal of Mechanical Sciences 45
(2003) 95-114
[9] Liew KM, Chen XL, Reddy JN. Meshfree radial basis function method
for buckling analysis of non-uniformly loaded arbitrarily shaped shear
deformable plates. Computer Methods in Applied Mechanics
Engineering 193 (2004) 205-224
[10] Liew KM, Wang J, Ng TY, Tan MJ. Free vibration and buckling
analyses of shear-deformable plates based on FSDT meshfree method
Journal of Sound and Vibration 276 (2004) 997-1017
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:62954", author = "Jeeoot Singh and Sandeep Singh and K. K. Shukla", title = "RBF- based Meshless Method for Free Vibration Analysis of Laminated Composite Plates", abstract = "The governing differential equations of laminated
plate utilizing trigonometric shear deformation theory are derived
using energy approach. The governing differential equations
discretized by different radial basis functions are used to predict the
free vibration behavior of symmetric laminated composite plates.
Effect of orthotropy and span to thickness ratio on frequency
parameter of simply supported laminated plate is presented.
Numerical results show the accuracy and good convergence of radial
basis functions.", keywords = "Composite plates, Meshfree method, free vibration,Shear deformation, RBFs", volume = "5", number = "7", pages = "1520-6", }
