Classical Theory of Plates

In this chapter, the authors consider bodies where more than one geometric dimension dominates the configuration. Specifically, they are interested in bodies bounded by surfaces whose lateral dimensions are large compared to the separation between these surfaces. When the bounding surfaces are flat the body is called a plate; when the surfaces are curved the body is called a shell. The authors present the explanation set forth by Thomson and Tait in their classical treatise Natural Philosophy. They show that their natural boundary conditions render the effective shear force intensity equal to zero. Thus by the method of minimum total potential energy we have generated the entire boundary-value problem for the classical thin plate theory. The authors consider examples illustrating certain aspects of the classical theory of plates. They also examine the case of the axisymmetric circular plate.