A Dynamic Thermal-Mechanical Coupling Numerical Model to Solve the Deformation and Thermal Diffusion of Plates

Elastic materials include metal plates, rubber, foam, airbags and so on, which have a good buffer effect, toughness and strong recovery ability. In this paper, the deformation and thermal diffusion of 2D and 3D thin plates are studied. Two models are established for the deformation of 2D thin plates. The bending deformation equation of rectangular and circular plates is derived, and the semi-analytical solution of the deflection function w(x,y) is found through the Fourier series approximation in the polar coordinate. The consistencies of the numerical solution and the theoretical solution are verified by numerical method. Then, we find that the factors affecting the deformation are related to the Young’s modulus, load, plate length and deformation factor α of the material. In a separate temperature physics field, we establish a heat conduction model of 2D graphene film. Three numerical schemes of the transient heat conduction equation of FDM-FEM are given. In contrast, this paper uses the implicit Euler method to discrete the time term. Furthermore, we compared the difference between the adiabatic condition and the convection condition by the graphical method and the curve trend. The results show that the temperature near the adiabatic boundary is higher. Finally, we proposed a 3D dynamic thermal–mechanical coupling model (3D-DTMCM) that has been established. A laser heating monocrystalline silicon sheet with periodic motion formula is given. The temperature radiation of the laser heat source has Gaussian distribution characteristics. Our proposed model can dynamically determine Young’s modulus with a variable temperature. The numerical results show that the higher the temperature is, the higher the strain energy density of the plate is. In addition, the deformation amplitude of the plates in the coupling field is larger than that in the single mechanical field. Finally, we also discussed the stress field distribution of mixed cracks under high temperature and high load. Our research provides theoretical support for the deformation of different plates, and also reflects the value of the coupled model in practical applications.