aspg-34-1839-1791479306 20261008170826 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 2023 2 1 Mountajab Al-Hasan Department of Mathematics, AL Baath University, Homs, Syria The importance of results of this paper consist in supplying new analytical method for solving the Ignaczak tensorial equations, governing the thermodynamical plane state of small elastic strains of the homogeneous, isotropic, micropolar elastic solid of 5 material constants of Eringen-Nowacki type, which shortly called 2D (E-N:5) (Iron plates, copper plates, aluminum plates, .. etc.). The paper covers the mathematical model of the first plane state of small elastic strains of micropolar homogeneous and isotropic solid, of five material constants, subjected to temperature field, mathematically proposed by Eringen and Nowacki, and shortly called 2D (E-N:5). In paper, for the 2D (E-N:5) considerable body, we generalize the Schaefer vector method to: I) The Traditional Description of the 2D (E-N:5) considerable body, II) The Ignaczak Description of the 2D (E-N:5) considerable body. Subsequently, these results have important applications in material resistance, plate theory, industry ….etc. 2023 27 41 1839 https://creativecommons.org/licenses/by/4.0/ 10.54216/PAMDA.020103 https://www.americaspg.com/journal/34/article/1839 https://www.americaspg.com/storage/41701035691.pdf