ABSTRACT
This chapter concentrates on the deep insights into the classic thin plate theory, which is known as the Kirchhoff thin plate theory. In this theory, the cross sections of the edges of the plate remain straight to the midplane of the plate after the deformation. The fundamental theory of plate element is also used for the shell element, which is considered as a very thin plate. Starting from the kinematic assumptions, the strains and stresses at an arbitrary location in the plate and shell element can be obtained. Then, the governing equations are derived using Hamilton’s principle, which takes the variational forms of energies of the plate. The series forms of Navier solutions for simply supported plates subjected to predefined loading conditions are given for comparison purpose. All the numerical examples are accompanied by their relevant and complete MATLAB® codes.
