# Elastoplastic Analysis of Frame Structures Using Radial Point Interpolation Meshless Methods
## 5 Conclusions  
In this work, the Radial Point Interpolation Method (RPIM) and the Natural Neighbor Radial Point Interpolation Method (NNRPIM) were used in the elastoplastic analysis of 2D and 3D structural elements. A selected example from [PERSON] et al. and a novel example by the authors are presented. It is concluded that for the two-bay asymmetric frame, considering both 2D and 3D analyses, the FEM, the RPIM, and the NNRPIM reach a good agreement with the reference solution. The three methods reach the same results not only in terms of order but also in terms of the location of the plastic connections. For the 3D case, a higher nodal density for a more accurate analysis is needed, with this fact being dependent on the computational power that is available. For the bowstring bridge, excellent agreement for all three methods is reached, with the RPIM for the 2D case not reaching the load input to match the other methods. In both 2D and 3D examples, the development of the plastic hinges and overall material plasticity is broader in the 3D case, mainly due to the lower nodal density used. The numerical studies developed throughout this work show that the RPIM and NNRPIM reach good results not only when compared to the FEM but with the reference solutions presented, showing their accuracy and capabilities to analyze the same kind of engineering problems analyzed with the FEM until the present day and even more problems for which the FEM may not be the most suitable tool--such as a large deformations formulation. It was shown that these meshless methods behave better than the FEM for low nodal densities, with the NNRPIM having a disadvantage in terms of preprocessing time. The RPIM, depending on the Gauss quadrature chosen, has a low preprocessing time phase. J.B. Conceptualization; J.B., methodology; J.B. and D.E.S.R., software; M.A. and J.B., validation; M.A. and J.B., formal analysis; J.B., investigation, J.B., resources; J.B. and D.E.S.R., data curation; M.A. and D.E.S.R., writing--original draft preparation; J.B. and D.E.S.R., writing--review and editing; J.B. and D.E.S.R., visualization; J.B. and D.E.S.R., supervision; J.B., project administration; J.B., funding acquisition. All authors have read and agreed to the published version of the manuscript. The authors acknowledge the funding provided by Ministerio da Ciencia, Tecnologia e Ensino Superior--Fundacao para a Ciencia e a Tecnologia (Portugal) and LAETA, under internal project UIDB/50022/2020. Data Availability StatementData are contained within the article. The authors declare no conflict of interest. +++ ==WARNING: Truncated because of repetitions==
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