Bending and free vibration and analysis of laminated plates on Winkler foundations based on meshless layerwise theory

Free vibration and bending of laminated plates on Winkler foundations are investigated based on a combination of generalized layerwise theory (LW) for higher-order shear deformation theory (HSDT) and the meshless radial point interpolation method (RPIM). The shape function of the meshless radial interpolation method is used to discretize the weak form control equations derived from the principle of virtual work. The shape functions have the properties of Kronecker functions. The slope components associated with the first-order derivatives of the transverse displacements are defined as approximate variables. The transverse shear stresses at each layer interface are continuous. A comparative study with literature solutions verified the numerical stability and applicability of the combined generalized LW-HSDT and meshless RPIM methods. The effect of Winkler modulus parameters on the vibration performance and bending performance of the laminated plate was investigated. The results of bending, vibration frequencies and modes of the laminated plates on different Winkler foundations are presented. It is found that initially, the Winker foundation had a significant effect on the frequency magnitude and bending deformation, but little influence on vibration mode. After the influence of the foundation on the frequency enters the stable period, the influence of foundation on the mode shape will be significant. With the relaxation of the boundary conditions, the vibration mode will still be affected when the foundation parameters are small.