Elastoplastic Analysis of Frame Structures Using Radial Point Interpolation Meshless Methods

The need to design structures and structural elements that are more efficient in terms of performance is a key aspect of engineering. For a given material to be used at its maximum capacity, considering non-linear characteristics is mandatory. The non-linear regime is a subject of extreme interest for this reason and is an area with intense research activity. In this work, advanced discretization techniques (i.e., meshless methods) are applied in the elastoplastic analysis of 2D and 3D structural elements. The literature shows that meshless methods are capable of producing more accurate and smoother strain and stress fields, which are the variable fields required in the non-linear models describing elastoplasticity. Thus, in this study, the Radial Point Interpolation Method (RPIM) and the Natural Neighbor Radial Point Interpolation Method (NNRPIM) are combined with a non-linear iterative algorithm, fully developed by the authors, with the objective of analyzing for the first time the elastoplastic behavior of a two-bay asymmetric frame and bowstring bridge considering 2D and 3D analysis. The accuracy and robustness of the RPIM and the NNRPIM are shown in the end, comparing the obtained results with FEM solutions and the available literature.