Buckling of compressed rectangular orthotropic plate resting on elastic foundation with nonlinear change of transverse displacement over the thickness

Abstract

Results of investigation of buckling behaviour of an orthotropic composite plate resting on elastic orthotropic foundation with nonlinear change of transverse displacement over the thickness, using the Ritz method are reported in the paper. The foundation has the form of a parallelepiped with the fully fixed bottom plane. A model of the foundation, linking its transverse displacement with the plate deflection, is developed in this work. According to this model, the transverse displacement of the foundation varies nonlinearly over the thickness as opposed to the traditional Winkler-Pasternak model. The proposed method of calculation of critical buckling load is based on a one-dimensional minimisation procedure with respect to the parameter characterising the decay of the transverse displacement of the foundation over its thickness. Using this method, the effects of plate and foundation thicknesses, and moduli of elasticity of the foundation material on the critical buckling load are analysed. It is found that the values of critical loads calculated using the proposed model are lower than those calculated based on the Winkler-Pasternak model. The verification of the results obtained based on the different models of deformed foundation is performed using the finite element method. The finite-element model was composed of three-dimensional elements. The analysis confirmed the validity of the calculations of critical load. The study has shown that the model of the foundation deformation developed in this work enables more accurate calculations of the critical load to be performed compared with those based on the conventional Winkler-Pasternak model.