Derivation of the equations of motion and boundary conditions of a thin plate via the variational method

Small deflections in both a thin rectangular plate and a thin circular plate are studied via the variational method. In order to apply Hamilton’s principle to this system, the potential energy is expressed in terms of strain and stress tensors. Quantities such as the gradient displacement tensor and the traction vector are reviewed. It is showed the advantage of the variational method as a technique which allows to obtain the equations of motion and the boundary conditions simultaneously.

Keywords
Stress; strain; thin plate; Hamilton Principle