Solution of the Föppl – von Kármán equations for square plates

The present paper develops an approach to obtaining solutions of the Föppl – von Kármán equations for square plates, which are based on direct algebraisation of the boundary-value problem. The solution is obtained in term of expansion into basis of the space of square-integrable function. The system of eigenfunction of a linear self-adjoined operator is used as the basis. The expansion coefficients are defined by the reduction method from an infinite-dimensional system of cubic equations. It allows one to consider the proposed solution as non-linear generalisation of classic Galerkin method.