An Optimized Shape Parameter Radial Basis Function Formulation for Composite and Sandwich Plates using Higher Order Formulations

The purpose of this work is to use a meshless collocation method with multiquadric radial basis functions (RBFs) and optimal values of the shape parameter in the RBFs to analyze static deformations of sandwich and composite plates. Two shear deformation theories with the same number of degrees of freedom are tested (the third-order shear deformation theory of Reddy (TSDT) and a trigonometric layerwise theory). Although the TSDT proved to be most adequate for the analysis of composite plates, the same is not true for sandwich plates, specially in the case of large ratios of material properties between the core and face sheets. The trigonometric layerwise theory produced excellent results for both sandwich and composite plates. The multiquadric RBF method was introduced by Kansa [1,2] for solving boundary-value problems governed by partial differential equations. Here we show that this method with optimal values of the shape parameter gives deflections of sandwich and composite plates that agree very well with analytical solutions, for regular and irregular grids. An advantage of the meshless method is that it requires very little input data, thus the time required for preparing the data can be significantly reduced.