Combining regular solutions of the Schaefer -Ignaczak thermodynamical behaviors relating to the first plane state of elastic strain of the micropolar body subjected to temperature field

Mountajab Al-Hasan

Department of Mathematics, AL Baath University, Homs, Syria

Email:  alhasanmountajab@gmail.com

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Abstract

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.    

Keywords: The superposition Method -The Hooke and Complementary Thermodynamical processes of Ignaczak Type – The Micropolar Elastic Solid  2D (E-N:5) subjected to temperature field- The first Plane State of Elastic Strain .