Universal Journal of Computational Mathematics Vol. 5(2), pp. 34 - 43
DOI: 10.13189/ujcmj.2017.050204
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Mathematical and Numerical Modeling of the Coupled Dynamic Thermoplastic Problem


Yusupov Y. 1,*, Khaldjigitov A.A. 2
1 Faculty of Mathematics, National University of Uzbekistan, Uzbekistan
2 Samarkand Branch of Tashkent University of Information technologies, Uzbekistan

ABSTRACT

Using the strain space and deformation thermoplasticity theories the coupled dynamic thermoplastic boundary value problems are formulated. Strain space thermoplasticity theory, in contrast to the deformation one, allows formulating the coupled thermoplastic boundary value problems for the displacement and temperature increments. As an example, in one-dimensional case, the explicit and implicit types of finite difference equations are constructed. The numerical solution of the explicit finite difference equations reduced to the application of the recurrent formulas, whereas the implicit scheme reduced to the application of the elimination method. Comparison shows that the numerical results obtained using explicit and implicit scheme coincides.

KEYWORDS
Finite Difference, Elimination Method, Coupled, Thermoplastic, Dynamic, Strain Space Theory, Deformation Theory, Displacement, Temperature, Explicit, Implicit

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Yusupov Y. , Khaldjigitov A.A. , "Mathematical and Numerical Modeling of the Coupled Dynamic Thermoplastic Problem," Universal Journal of Computational Mathematics, Vol. 5, No. 2, pp. 34 - 43, 2017. DOI: 10.13189/ujcmj.2017.050204.

(b). APA Format:
Yusupov Y. , Khaldjigitov A.A. , (2017). Mathematical and Numerical Modeling of the Coupled Dynamic Thermoplastic Problem. Universal Journal of Computational Mathematics, 5(2), 34 - 43. DOI: 10.13189/ujcmj.2017.050204.