Harmonic differential quadrature-finite differences coupled approaches for geometrically nonlinear static and dynamic analysis of rectangular plates on elastic foundation

The geometrically nonlinear static and dynamic analysis of thin rectangular plates resting on elastic foundation has been studied. Winkler–Pasternak foundation model is considered. Dynamic analogues Von Karman equations are used. The governing nonlinear partial differential equations of the plate are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The analysis provides for both clamped and simply supported plates with immovable inplane boundary conditions at the edges. Various types of dynamic loading, namely a step function, a sinusoidal pulse and an N-wave, are investigated and the results are presented graphically. The accuracy of the proposed HDQ–FD coupled methodology is demonstrated by the numerical examples.