Ritz Variational Method for the Flexural Analysis of Rectangular Kirchhoff Plate on Winkler Foundation

Abstract

In this study, the Ritz variational method has been applied to solve the bending problem of rectangular Kirchhoff plate resting on Winkler foundation for the case of simply supported edges and transverse distributed load. The problem was presented in variational form using energy principles to obtain the total potential energy functional. Ritz technique was then used to find the generalised displacement parameters which minimized the total potential energy functional; where basis functions were choose to apriori satisfy the boundary conditions. Analytical solutions were obtained which were found to be identical with Navier’s series solutions for the general case of arbitrary distributed transverse load, as well as the specific cases of point loads, sinusoidal load, uniform and linearly distributed loads.

Keywords

• Ritz variational method
• Kirchhoff plate
• Winkler foundation
• total potential energy functional
• generalised displacement parameters
• displacement basis functions