General perturbation solution of large-deflection circular plate with different moduli in tension and compression under various edge conditions

摘要

The large deflection problem for a thin circular plate with different moduli in tension and compression has dually non-linear characteristics. In this paper, we use perturbation technique to obtain a general analytical solution of thin circular plate with different moduli in tension and compression, in which four edge conditions including rigidly clamped, clamped but free to slip, simply hinged and simply supported are considered. Because the perturbation solution is expanded in ascending powers of a known perturbation parameter (central deflection, for example) and the unknown constants and functions in the solution are gradually determined by decomposing boundary conditions and governing equation, the constants and functions obtained in such a manner have an inherent consistency concerning material properties. The results show that via construction of some parameters reflecting materials properties, not only the solution based on bimodular elasticity theory may regress to that on classical theory with singular modulus, but also the solution obtained under simply hinged edge may serve as a general solution to describe other three edge conditions. Via the general solution, the relations of load vs. central deflection, the plate-membrane transition for bimodular problem and the radial membrane stresses and bending stresses at the center and edge of the plate, are also discussed. Moreover, the comparison between the analytical solutions and numerical results indicates that the perturbation solutions based on the central deflection are overall valid. This work will be helpful for analyzing the mechanical behaviors of flexible layer structures while considering large deformation and bimodular effect.