Introduction

In the last lecture, we developed the simplest rectangular element. This element has 4 nodes and the corresponding shape functions are bi-linear. Since the degree of freedom per node is one, this element is called as the Lagrangian rectangular element, or to be precise, first order Lagrangian rectangular element. The corresponding shape functions are called as Lagrangian shape functions and the approximation is called as Lagrangian approximation. Thus, equations (24.12) represent the first order or bi-linear Lagrangian shape functions and equation (24.11) represents the first order or bi-linear Lagrangian approximation.

In this lecture, we shall develop the higher order Lagrangian rectangular elements using the approximations of order higher than bi-linear.