WANG Wei, YI Shi-chao, YAO Lin-quan. An Effective Meshfree Method for Bending and Vibration Analyses of Laminated Composite Plates[J]. Applied Mathematics and Mechanics, 2015, 36(12): 1274-1284. doi: 10.3879/j.issn.1000-0887.2015.12.006
 Citation: WANG Wei, YI Shi-chao, YAO Lin-quan. An Effective Meshfree Method for Bending and Vibration Analyses of Laminated Composite Plates[J]. Applied Mathematics and Mechanics, 2015, 36(12): 1274-1284.

# An Effective Meshfree Method for Bending and Vibration Analyses of Laminated Composite Plates

##### doi: 10.3879/j.issn.1000-0887.2015.12.006
Funds:  The National Natural Science Foundation of China（11172192；11572210）
• Rev Recd Date: 2015-10-23
• Publish Date: 2015-12-15
• Numerical analysis of laminated plates’ bending and vibration problems was presented based on the high order shear and normal deformation plate theory (HOSNDPT) with the meshless method. For the usual radial point interpolation method (RPIM), the inverses of the moment matrices are required for each Gauss point or calculation point, and are limited by the radius of the domain. For the weighted node radial point interpolation method (WN-RPIM), the number of the inverses of the system matrices is equal to the number of nodes in the problem domain, which is far less than the number of Gauss points, so the WN-RPIM can greatly reduce the computation complexity of the moment matrices and overcome the limitations on the RPIM. First, the 3D plate displacement was decomposed into the product of the thickness-direction and in-plane displacements, and the orthogonal Legendre polynomials were used as basis functions in the thickness direction, the WN-RPIM was employed in plane to construct the shape functions. Then, the numerical calculation of the bending problems of laminated plates verified the accuracy and stability of the WN-RPIM. At last, the proposed method was extended to the numerical calculation of the vibration problems of laminated plates with different boundary conditions, different thickness-to-span ratios and different laying patterns. The numerical results show the applicability and effectiveness of the proposed method.
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