Generalization of a sandwich structure model: Analytical studies of bending and buckling problems of rectangular plates

The paper is devoted to generalization of the analytical model of sandwich structures. The continuous variation of mechanical properties in thickness direction of the structure wall is proposed. The individual nonlinear theory of deformation of the straight line normal to the neutral surface is developed. This analytical model of sandwich structures is presented in detail for the example rectangular plate. Based on the principle of stationary potential energy two differential equations of equilibrium of the plate are obtained. The system of equations is analytically solved. The maximum deflection and critical loads of the example plates are derived. Results of these analytical studies are presented in Figures and Tables.

Automated summary

The paper presents the analytical model of sandwich structures, proposing a continuous variation of mechanical properties in the thickness direction of the structure wall and developing an individual nonlinear theory of deformation normal to the neutral surface. Using the principle of stationary potential energy, two differential equations of equilibrium for the plate are obtained and analytically solved, deriving the maximum deflection and critical loads of the example plates. The results of these analytical studies are presented in Figures and Tables.