Thin circular plate under a uniformly distributed load of the gravitational type

The problem of stability of shells and the problem of bending of columns are always relevant topics of the mechanics of deformable body, especially in the field of aviation and missile technology. The most common types of elements that are used in the automatic actuators of spacecrafts are flexible plates and shells. This article demonstrates an approach to the problem of bending of the thin circular plate under the constant distributed load of the gravitational type. The problem is presented in the form of nonlinear integral-differential equation that describes such bending. An approximate analytical solution that takes into account the geometric nonlinearity has been derived. The solution has been found under the condition that the deflection is sufficiently smaller than the radius of the plate. The shapes of the bent plate have been built.