1
Department of Mathematics, AL Baath University, Homs, Syria
(alhasanmountajab@gmail.com)
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 .
References :
[1] Al-Hasan M., Dyszlewicz J. Coupled , Dynamic Micropolar Problems of Thermoelasticity: Stress–Temperature Equations of Motion of Ignaczak Type. In: Hetnarski R.B. (eds) Encyclopedia of Thermal Stresses. Springer, Dordrecht,2014
[2]- Hetnarski, R.B., Ignaczak, J., Eslami, M.R., Noda, N., Sumi, N., and Tanigawa, Y. - Theory of Elasticity and Thermal Stresses, Springer Science+Business Media Dordrecht. 2013
[3] – Hetnarski, R.B., and Ignaczak, J., - The Mathematical Theory of Elasticity , Second Edition , CRC Press,Taylor & Francis Group,6000 Broken Sound Parkway NW, Suite 300,Boca Raton, FL 33487-2742. 2011
[4]- Ignaczak, J., Starzewski, M.O - Thermoelasticity with Finite Wave Speeds, Oxford University Press Inc., New York. 2010
[5]- Dyszlewicz , J, Micropolar Theory of Elasticity , in : Series Lectures. Notes in Applied and Computational Mechanics, Vol.15, 356 p, Springer . 2004
[6]–Dyszlewicz , J , Selected problems of linear asymmetrical thermoelasticity, Journal of Thermal Stresesses,19,1996
[7] –Nowacki, W , Theory of Asymmetric Elasticity , Warsaw , PWN, 1986
[8] – Eringen , A . C , Linear theory of micropolar elasticity, J.Math , 1966
[9] - Ignaczak , J Tensorial equations of motion for elastic materials with microstructure , in : Trends of Elasticity and Thermoelasticity, Witold Nowacki Ann.Volume , Wolters-Noordhoff Groningen , 1971
[10] – Debnath, L& Bhatta , D , Integral Transforms and their Applications, ( Second Edition), CRC Press, Boca Raton, Florida , 2007.
| Style | # |
|---|---|
| MLA | Mountajab Al-Hasan. "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." Prospects for Applied Mathematics and Data Analysis, Vol. 2, No. 1, 2023 ,PP. 27-41 (Doi : https://doi.org/10.54216/PAMDA.020103) |
| APA | Mountajab Al-Hasan. (2023). 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. Journal of Prospects for Applied Mathematics and Data Analysis, 2 ( 1 ), 27-41 (Doi : https://doi.org/10.54216/PAMDA.020103) |
| Chicago | Mountajab Al-Hasan. "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." Journal of Prospects for Applied Mathematics and Data Analysis, 2 no. 1 (2023): 27-41 (Doi : https://doi.org/10.54216/PAMDA.020103) |
| Harvard | Mountajab Al-Hasan. (2023). 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. Journal of Prospects for Applied Mathematics and Data Analysis, 2 ( 1 ), 27-41 (Doi : https://doi.org/10.54216/PAMDA.020103) |
| Vancouver | Mountajab Al-Hasan. 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. Journal of Prospects for Applied Mathematics and Data Analysis, (2023); 2 ( 1 ): 27-41 (Doi : https://doi.org/10.54216/PAMDA.020103) |
| IEEE | Mountajab Al-Hasan, 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, Journal of Prospects for Applied Mathematics and Data Analysis, Vol. 2 , No. 1 , (2023) : 27-41 (Doi : https://doi.org/10.54216/PAMDA.020103) |