TY - JOUR
T1 - RMVT-based meshless collocation and element-free Galerkin methods for the quasi-3D free vibration analysis of multilayered composite and FGM plates
AU - Wu, Chih Ping
AU - Chiu, Kuan Hao
N1 - Funding Information:
This work is supported by the National Science Council of Republic of China through Grant NSC 97-2221-E006-128-MY3.
PY - 2011/4
Y1 - 2011/4
N2 - A meshless collocation (MC) and an element-free Galerkin (EFG) method, using the differential reproducing kernel (DRK) interpolation, are developed for the quasi-three-dimensional (3D) free vibration analysis of simply supported, multilayered composite and functionally graded material (FGM) plates. Based on the Reissner Mixed Variational Theorem (RMVT), the strong and weak formulations of this problem are derived, in which the material properties of each individual FGM layer, constituting the plate, are assumed to obey the power-law distributions of the volume fractions of the constituents. The system motion equations of both the RMVT-based MC and EFG methods are obtained using these strong and weak formulations, respectively, in combination with the DRK interpolation, in which the shape functions of the unknown functions satisfy the Kronecker delta properties, and the essential boundary conditions can be readily applied, exactly like the implementation in the finite element method. In the illustrative examples, the natural frequencies and their corresponding modal field variables varying along the thickness coordinate of the plate are studied. It is shown that the solutions obtained using these methods are in excellent agreement with the available 3D solutions, and their convergence rates are rapid.
AB - A meshless collocation (MC) and an element-free Galerkin (EFG) method, using the differential reproducing kernel (DRK) interpolation, are developed for the quasi-three-dimensional (3D) free vibration analysis of simply supported, multilayered composite and functionally graded material (FGM) plates. Based on the Reissner Mixed Variational Theorem (RMVT), the strong and weak formulations of this problem are derived, in which the material properties of each individual FGM layer, constituting the plate, are assumed to obey the power-law distributions of the volume fractions of the constituents. The system motion equations of both the RMVT-based MC and EFG methods are obtained using these strong and weak formulations, respectively, in combination with the DRK interpolation, in which the shape functions of the unknown functions satisfy the Kronecker delta properties, and the essential boundary conditions can be readily applied, exactly like the implementation in the finite element method. In the illustrative examples, the natural frequencies and their corresponding modal field variables varying along the thickness coordinate of the plate are studied. It is shown that the solutions obtained using these methods are in excellent agreement with the available 3D solutions, and their convergence rates are rapid.
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U2 - 10.1016/j.compstruct.2010.11.015
DO - 10.1016/j.compstruct.2010.11.015
M3 - Article
AN - SCOPUS:79955468849
SN - 0263-8223
VL - 93
SP - 1433
EP - 1448
JO - Composite Structures
JF - Composite Structures
IS - 5
ER -