Abstract
This work deals with applying the iteration method for the numerical solutions of a one-dimensional thermoelastic material. The governing equations have been constructed in the context of generalized thermoelasticity with one relaxation time model of Lord and Shulman (L-S). Some properties have been considered functional graded based on power law, and the lattice design parameter has been assumed. Adomian's decomposition method (ADM) and iteration techniques have been applied to solve the governing differential equations with an algorithm method. The numerical results have been represented in figures. The numerical results affirm that Adomian's decomposition method is a successful iteration method for solving and modeling thermoelastic problems. The lattice design parameter, empirical parameter, and ratio of the material properties significantly impact the temperature increment, strain, stress, displacement distributions, where they play vital roles in transferring the thermo-mechanical waves through the thermoelastic materials.