On convergence of interpolated-iterative method of geometrically nonlinear equations of circular plates (Q1121717)

The von Kármán equation for geometrically nonlinear circular plates is solved using the interpolated-iterative method. Some solution methods proposed in the literature are efficient only in the case of weak nonlinearities and only for such cases proofs of convergence exist. The authors try to find the connection between the nonlinear bending theory of thin plates and the theory of membrane. A strict proof of existence and convergence of the solution of the von Kármán plate equation for the arbitrary unilateral load is presented. The initial problem is reduced to the integral equations equivalent to the boundary value problem. The load under consideration is proposed as a uniform, point concentrated or linear function or their combinations. Finally the iterative procedure with parameters from the range zero-one enables to solve the equation. Indications for the selection of the interpolated parameters are given. Purely analytical considerations concern one particular problem of the plate. The lack of solution examples unables to estimate accuracy of the approach for highly nonlinear cases, when the iterative process is carried on by the computer means. The work may be interesting for those working in the field of the mathematical treatment of mechanical or physical equations.