Energy based approach for shape parameter selection in radial basis functions collocation method

The accuracy of the multiquadratic radial basis functions collocation method in performing elasto-static analyses of multilayer composite plates is strongly affected by the shape parameter, a value that dominates the shape of the radial basis functions. The selection of an optimal value of the shape parameter is still an open problem and several approaches have been proposed in the open literature. In this paper, a novel algorithm based on the Principle of Minimum of the Total Potential Energy is presented. The effectiveness of this algorithm is assessed by static analysis of a laminated composite plate simply supported on all edges. Comparison with other algorithms for the selection of the shape parameter is made. The radial basis functions collocation method coupled with the present algorithm results very accurate in predicting maximum deflections and stresses in the range of the span-to-thickness ratio values considered.