Abstract
The quantites determined for an infinite plate resting on a nonlinear foundation of the Winkler type are the deflections, bending moments and shear forces. The solution is obtained by iteration.The convergence of the iteration process is shown and the error is estimated by reducing the quasi-linear equation of the plate (2.2) to a nonlinear integral equation of the Hammerstein type, the solution of which is based on the theorem of Banach-Cacciopoli on the invariant point. The problem of a plate resting on an analytic foundation and loaded by a concentrated force is studied in detail. A numerical example is done, giving diagrams of deflection and section forces.
The problem considered is of importance for the analysis of the state of stress in road and runway plates.
References
1. [in Russian]
2. [in Russian]
3. N. W. McLACHLAN, Funkcje Bessela dla inżynierów, PWN, Warszawa 1964.
4. W. POGORZELSKI, Równania całkowe i ich zastosowanie, t. II, PWN, Warszawa 1958.
5. [in Russian]
6. S. TIMOSZENKO, S. WOJNOWSKY-KRIEGER, Teoria płyt i powłok, Arkady, Warszawa 1962.
2. [in Russian]
3. N. W. McLACHLAN, Funkcje Bessela dla inżynierów, PWN, Warszawa 1964.
4. W. POGORZELSKI, Równania całkowe i ich zastosowanie, t. II, PWN, Warszawa 1958.
5. [in Russian]
6. S. TIMOSZENKO, S. WOJNOWSKY-KRIEGER, Teoria płyt i powłok, Arkady, Warszawa 1962.
