Prospects for Applied Mathematics and Data Analysis

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Volume 2 , Issue 1 , PP: 27-41, 2023 | Cite this article as | XML | Html | PDF | Full Length Article

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 1 *

  • 1 Department of Mathematics, AL Baath University, Homs, Syria - (alhasanmountajab@gmail.com)
  • Doi: https://doi.org/10.54216/PAMDA.020103

    Received: August 19, 2022 Accepted: February 23, 2023
    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 &ndash , 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.

    Cite This Article As :
    Al-Hasan, Mountajab. 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. , no. , 2023, pp. 27-41. DOI: https://doi.org/10.54216/PAMDA.020103
    Al-Hasan, M. (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. Prospects for Applied Mathematics and Data Analysis, (), 27-41. DOI: https://doi.org/10.54216/PAMDA.020103
    Al-Hasan, Mountajab. 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 , no. (2023): 27-41. DOI: https://doi.org/10.54216/PAMDA.020103
    Al-Hasan, M. (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. Prospects for Applied Mathematics and Data Analysis , () , 27-41 . DOI: https://doi.org/10.54216/PAMDA.020103
    Al-Hasan M. [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. Prospects for Applied Mathematics and Data Analysis. (): 27-41. DOI: https://doi.org/10.54216/PAMDA.020103
    Al-Hasan, M. "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. , no. , pp. 27-41, 2023. DOI: https://doi.org/10.54216/PAMDA.020103