L. Verduzco Martnez “The idealized Smeared Reinforcement (ISR) method for the optimization of concrete sections: a survey of the state-of-the-art and analysis of potential computational approaches”, Revista Mexicana de Mtodos Numricos (2021), Vol. 5, 1 1 Introduction Ever since Whitney and Cohen [Whitney & Cohen, 1956] many years ago in 1956 proposed a guide to de- sign reinforcing steel in concrete structures subject to axial force and bending moment by ultimate strength based on the ACI code many different approaches have taken place from that point on to design optimally reinforced concrete sections. What Whitney and Cohen presented then was a series of charts based on N- M interaction diagrams normalized considering symmetric and uniform reinforcement over a cross section. In recent years however, new more realistic considerations for the design and analysis have been carried on, for instance, influence of confinement and flexural behaviour [Au FTK, Bai ZZ, 2006], or non-symmetric rein- forcement [Walther & Miehlbardt, 1990] in which a particular solution of a problem is provided for elements subjected to flexure-compression stresses. Also, the concept of strength design has been challenged by new design approaches [H. Montes, 2005] which generate a family of solutions for arbitrary combinations of imposed axial load and moment, requiring even a non-symmetric distribution of reinforcement over the cross section. Correspondence: Luis Fernando Verduzco Martnez (lf.verduzcomartinez@ugto.mx). This is an article distributed under the terms of the Creative Commons BY-NC-SA-licence https://www.scipedia.com/public/Verduzco_Martinez_2021a 1