RBF-based meshless method for large deflection of elastic thin plates on nonlinear foundations

A simple, yet efficient method for the analysis of thin plates resting on nonlinear foundations and undergoing large deflection is presented. The method is based on collocation with the multiquadric radial basis function. In order to address the in-plane edge conditions, two formulations, namely w–F and u–v–w are considered for the movable and immovable edge conditions, respectively. The resulted coupled nonlinear equations for the two cases are solved using an incremental-iterative procedure. Three foundation models are considered, namely Winkler, nonlinear Winkler and Pasternak. The accuracy and efficiency of the method is verified through several numerical examples.