Nonlinear deflections of a circular plate with varying thickness

A theoretical analysis of large deflections and large strains in a circular plate with varying thickness and a circular membrane is considered.

The exact tensor first approximation equilibrium equations, converted into physical equations for a rotationally symmetric thin plate are used with the Alexander constitutive relations for a rubber-like material to analyze the deflections, stress resultants and change in the thickness for a plate clamped along the outer edge and deflected by a uniform pressure applied normal to the deformed surface. The equations are quasilinearized and solved numerically with the aid of a digital computer.

The thickness is allowed to vary in the radial direction but is held constant in the circumferential direction. Several variations in thickness were considered. The solutions found by using the Alexander constitutive relations were compared with the solutions using the Rivlin and Saunders constitutive relations and the Hart-Smith constitutive relations. Numerical results from the solution of a plate with uniform thickness were compared with those for a similar plate given by J. T. Oden.