Application of Displacement (or Dirichlet) Boundary Condition

For piece-wise linear Lagrangian shape functions Lecture 7 discusses the algorithm of applying the displacement (or Dirichlet) boundary condition at the end , i.e., at the first node . This algorithm does not depend on the order p of the approximation. Instead, it depends on the number of degrees of freedom per node. Since, we are still using the Lagrangian approximation, the number of degrees of freedom per node remains the same. Therefore the algorithm of section 7.1 of applying the displacement (or Dirichlet) boundary condition remains valid even for higher order Lagrangian approximations. This algorithm, as given by equations (7.14-7.15), can be written as :

	(9.16)

Here, is the value of the displacement at the end x = 0, i.e. at the first node.

Algorithm for solving the modified equations will be discussed in a separate Lecture.