ABSTRACT
We often encounter situations in which the degrees of freedom D are not independent or they are limited in range. This is often expressible as a constraint of the form of n linear equations:
CD – Q = 0, (14.1)
where matrices C and Q are constant. For example, consider the axially loaded rod in which one element is modeled as a rigid body (Figure 14.1). This condition can be applied as a constraint on the nodal displacements:
u1 – u2 = 0. (14.2)
The constraints could be applied directly to the assembled finite element equations to reduce the number of independent variables. However, it is more convenient to incorporate the constraints 14.1 indirectly in order to provide for the general situation. There are two commonly used methods to do this: Lagrange multipliers and the penalty method.
