ABSTRACT
Various theories of plate and shell elements are given as the introduction in this chapter. This chapter focuses on the classic thick plate theory. When the thickness of the plate and shell element is considerably thick compared to the plane dimension of the plate, the edges of the plate are not remaining straight to the midplane of the plate after the deformation. In this chapter, the first-order shear deformation theory, which is proposed by Mindlin, is considered. Starting from the kinematic assumptions, the strains and stresses at an arbitrary location in the plate and shell element are used to derive the governing equations using Hamilton’s principle. The series forms of Navier solutions for simply supported plates subjected to predefined loading conditions are presented for comparison purpose. All the numerical examples are accompanied by their relevant and complete MATLAB® codes.
