ABSTRACT

This chapter begins with an explanation of the finite element method used for determining the value of “phi” by calculating the area of a circle in the finite element concept. Next, the details of derivations and formulations of both types of Kirchhoff and Mindlin plate and shell elements in the finite element context are given systematically. To construct the exact stiffness, mass matrices, and loading vector, the shape functions of the plate and shell element are the crucial components to be considered in the formulations. The shape functions of both the thin and thick plate and shell elements are derived from their homogeneous governing equations. Thus, the exact solution of static problems can be obtained by using only one plate and shell element. The construction of stiffness, mass matrices, and loading vector is given clearly. All the numerical examples are accompanied by their relevant and complete MATLAB® codes.