Nonlinear bending analysis of functionally graded plates with complex shape resting on elastic foundations

摘要

Nonlinear bending of functionally graded plates under transverse and in-plane loads and resting on two-parameter elastic foundations (Winkler-Pasternak type) is investigated. Mathematical statement of the problem is based on classical plate theory taking into account geometrical nonlinearity in the Von Karman sense and plate-foundation interaction. Material properties are assumed to be temperature dependent and varied in the thickness direction according to Voigt's law. The increment loading method, Newton-Raphson iteration scheme and Ritz's method in conjunction with the R-functions theory are employed in the present analysis. The load-deflection and load-bending dependence for plates with complex form are obtained. A comparison of the presented results with available findings is carried out for rectangular plates with different boundary conditions. Good agreement confirms the validation of the proposed method.