Iranian Journal of Numerical Analysis and Optimization Vol. 11, No. 2, (2021), pp 437-483 DOI:10.22067/ijnao.2021.11336.0 ———————————————————————————————————— Research Article Review of the strain-based formulation for analysis of plane structures Part I: Formulation of basics and the existing elements M. Rezaiee-Pajand ∗ , N. Gharaei-Moghaddam and M. Ramezani Abstract Since the introduction of the fnite element approach, as a numerical solu- tion scheme for structural and solid mechanics applications, various for- mulation methodologies have been proposed. These ways ofer difer- ent advantages and shortcomings. Among these techniques, the stan- dard displacement-based approach has attracted more interest due to its straightforward scheme and generality. Investigators have proved that the other strategies, such as the force-based, hybrid, assumed stress, and as- sumed strain provides special advantages in comparison with the classic fnite elements. For instance, the mentioned techniques are able to solve difculties, like shear locking, shear parasitic error, mesh sensitivity, poor convergence, and rotational dependency. The main goal of this two-part study is to present a brief yet clear portrait of the basics and advantages of the direct strain-based method for development of high-performance plane fnite elements. In this article, which is the frst part of this study, assump- tions and the basics of this method are introduced. Then, a detailed review of all the existing strain-based membrane elements is presented. Although the strain formulation is applicable for diferent types of structures, most of the existing elements pertain to the plane structures. The second part of this study deals with the application and performance of the reviewed elements in the analysis of plane stress/strain problems. AMS subject classifcations (2020): 74K15, 74G15. * Corresponding author Received 25 October 2020; revised 8 June 2021; accepted 9 June 2021 Mohammad Rezaiee-Pajand Professor of Civil Engineering, School of Engineering, Ferdowsi University of Mashhad, Iran. e-mail: Rezaiee@um.ac.ir, Tel/fax: +98-51-38412912 Nima Gharaei-Moghaddam PhD of Structural Engineering, School of Engineering, Ferdowsi University of Mashhad, Iran. e-mail: Nima.Gharaei@gmail.com, Tel: +98-915-1589342 Mohammadreza Ramezani PhD Student of Structural Engineering, School of Engineering, Ferdowsi University of Mashhad, Iran. e-mail: Mohammadrezaramezani1994@gmail.com, Tel: +98-915- 1076010 437