Introduction

Determination of the element stiffness matrix and the element force vector and their assembly into the global stiffness matrix and global force vector were discussed in the last lecture. Before solving the (global) finite element equations, the essential or the Dirichlet boundary condition (i.e., the boundary condition on the primary variable) needs to be applied. This lecture discusses the procedure of the application of the essential boundary condition.

Note that, in the Ritz Method or in the Weighted Residual Method, the basis functions , j = 0,.., N are chosen such that the approximate solution (equations 3.2 and 3.69)

(7.1)

satisfies the essential boundary condition automatically. Thus, this boundary condition is applied in the beginning itself. It is applied even before developing the algebraic equations for the unknown coefficients .However, in the finite element formulation, the chosen basis functions do not satisfy the essential boundary condition automatically (see equations 5.5 and 6.3). Therefore, this boundary condition needs to be applied before solving the (global) finite element equations.