In this study, we present a proper finite element model for the simulation of a single solid oxide fuel cell (SOFC) at the beginning of operation (warm-up). The SOFC comprises five layers: two ferrous base metal layers, one yttriastabilized zirconia (YSZ) electrolyte layer, one anode layer featuring a Ni/YSZ structure, and one cathode layer consisting of LSM. Our thermal-structural analysis considers crucial physical parameters, including the warm-up process, mechanical contact, and thermal contact. Zirconium oxide, renowned for its O₂- conductivity at the operating temperature of the fuel cell (800 ^◦C), serves as the chosen base material. As the SOFC heats up, thermal stresses emerge among these layers. To investigate the fracture procedure during warm-up, the finite element method is employed, examining various parameters such as the presence of mechanical contact, warm-up conditions (radiation or isothermal), and thermal contact resistance. Simplifications commonly employed in the finite element method, such as solving fields independently or simultaneously and defining material properties as layered elements, are also considered. The analyses and calculations are conducted using the ANSYS software. Our primary objective is to present a refined model that minimizes error and analysis time. Various conditions are examined, including layer slip effects, the use of composite or layered elements, the simplification of layer properties, the impact of contact resistance, and the investigation of simultaneous and indirect analyses, assessing their validity through a series of analyses.