Adomian’s Decomposition Method to Functionally Graded Thermoelastic Materials with Power Law
Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi
This paper presents an iteration method for the numerical solutions of a one-dimensional problem of generalized thermoelasticity with one relaxation time under given initial and boundary conditions. The thermoelastic material with variable properties as a power functional graded has been considered. Adomian’s decomposition techniques have been applied to the governing equations. The numerical results have been calculated by using the iterations method with a certain algorithm. The numerical results have been represented in figures, and the figures affirm that Adomian’s decomposition method is a successful method for modeling thermoelastic problems. Moreover, the empirical parameter of the functional graded, and the lattice design parameter have significant effects on the temperature increment, the strain, the stress, the displacement.
Keywords: Adomian, Decomposition Method, Generalized Thermoelasticity, algorithm, empirical parameter, lattice design.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 397
 Sweilam N. Harmonic wave generation in non-linear thermoelasticity by variational iteration method and Adomian's method. Journal of Computational and Applied Mathematics 2007;207:64-72.
 Adomian G. Solving Frontier Problems of Physics: The Decomposition Method. 1994. Klumer, Boston.
 Adomian G. Nonlinear stochastic systems theory and applications to physics: Springer Science & Business Media; 1988.
 Adomian G, Cherruault Y, Abbaoui K. A nonperturbative analytical solution of immune response with time-delays and possible generalization. Mathematical and computer modelling 1996;24:89-96.
 Ciarlet P, Jamelot E, Kpadonou F. Domain decomposition methods for the diffusion equation with low-regularity solution. 2016.
 Duz M. Solutions of Complex Equations with Adomian Decomposition Method. TWMS Journal of Applied and Engineering Mathematics 2017;7:66-73.
 El-Sayed SM, Kaya D. On the numerical solution of the system of two-dimensional Burgers' equations by the decomposition method. Applied Mathematics and Computation 2004;158:101-9.
 Górecki H, Zaczyk M. Decomposition method and its application to the extremal problems. Archives of Control Sciences 2016;26.
 Kaya D, El-Sayed SM. On the solution of the coupled Schrödinger–KdV equation by the decomposition method. Physics Letters A 2003;313:82-8.
 Kaya D, Inan IE. A convergence analysis of the ADM and an application. Applied Mathematics and computation 2005;161:1015-25.
 Kaya D, Yokus A. A decomposition method for finding solitary and periodic solutions for a coupled higher-dimensional Burgers equations. Applied Mathematics and Computation 2005;164:857-64.
 Lesnic D. Convergence of Adomian's decomposition method: periodic temperatures. Computers & Mathematics with Applications 2002;44:13-24.
 Lesnic D. Decomposition methods for non-linear, non-characteristic Cauchy heat problems. Communications in Nonlinear Science and Numerical Simulation 2005;10:581-96.
 Li L, Jiao L, Stolkin R, Liu F. Mixed second order partial derivatives decomposition method for large scale optimization. Applied Soft Computing 2017;61:1013-21.
 Mustafa I. Decomposition method for solving parabolic equations in finite domains. Journal of Zhejiang University-SCIENCE A 2005;6:1058-64.
 Vadasz P, Olek S. Convergence and accuracy of Adomian’s decomposition method for the solution of Lorenz equations. International Journal of Heat and Mass Transfer 2000;43:1715-34.
 Daftardar-Gejji V, Jafari H. Adomian decomposition: a tool for solving a system of fractional differential equations. Journal of Mathematical Analysis and Applications 2005;301:508-18.
 Ray SS, Bera R. An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method. Applied Mathematics and Computation 2005;167:561-71.
 Shawagfeh NT. Analytical approximate solutions for nonlinear fractional differential equations. Applied Mathematics and Computation 2002;131:517-29.
 Youssef HM, El-Bary AA. Thermoelastic material response due to laser pulse heating in context of four theorems of thermoelasticity. Journal of Thermal Stresses 2014; 37: 1379-89.