Simplified theory and analytical solution for functionally graded thin plates with different moduli in tension and compression

• The simplified theory for a functionally graded thin plate with bimodular effect is proposed.
• The mechanical model based on subarea in tension and compression is established.
• The governing equation is derived via equilibrium and continuity conditions, respectively.
• The perturbation solution for the unknown neutral layer is obtained.
• The bending stiffness derived in this paper play an important role while solving similar problems.

In this study, a simplified theory for functionally graded thin plates with different moduli in tension and compression is proposed. Based on the classical Kirchhoff hypothesis, a mechanical model concerning tension-compression subzone is established, first. Using the geometrical and physical relations and equation of equilibrium, all stress components are expressed in terms of the deflection, in which modulus of elasticity in tensile and compressive zone are regarded as two different functions while Poisson's ratios are taken as two different constants. Via the equilibrium conditions and continuity conditions, the governing equation expressed in terms of the deflection as well as the unknown neutral layer are derived, respectively. Moreover, the application in polar coordinates, the strain energy and the perturbation solution for the unknown neutral layer, are discussed in detail. The results indicate that the bending stiffness derived in this study play an important role while contacting the classical problem and this problem. The analytical solutions from equilibrium conditions and continuity conditions are consistent. Analyses of more general cases for modulus of elasticity and Poisson's ratio also show the applicability of the simplified theory. This study provides a theoretical basis for the subsequent work.