Thermal Stresses in Plates

This chapter presents the derivations of the equilibrium equations of rectangular and circular plates in terms of the lateral deflection, using the classical first-order theory under the mechanical and thermal loads. The classical solutions of the plates under the simply supported boundary conditions are given by Navier and Levy. These two methods of solutions for rectangular plates are discussed in this chapter. The chapter continues to derive the equilibrium equations of composite rectangular plates using the classical plate theory. Assuming the simply supported boundary conditions at two opposite edges, the Levy solution is applied to obtain the lateral deflection. The first-order shear deformation theory is then considered with five partial differential equations for five dependent functions and, with the assumption of two opposite simply supported boundary conditions, the analytical Levy solution is employed to obtain the lateral deflection. It is therefore concluded that once two opposite edges are simply supported, the Levy solution to derive analytical solutions is applicable for the rectangular plates. Plate’s material properties are indifferent for application of the Navier or Levy solutions, as long as the types of boundary conditions are those assumed by the Navier or Levy. When none of the boundaries are assumed according to the Navier or Levy assumptions, the numerical solution methods may be essential for the analysis, such as the problem given in Sect. 3.12 of this chapter.