For the eight-node element shown in Fig. P9.19, show that the x-coordinate along the side 1—2 is related to the ξ-coordinate by the relation

Thus, ∂uh/∂x grows at a rate of (xa)−1/2 as x approaches zero along the side 1—2. In other words, we have a x−1/2 singularity at node 1. Such elements are used to fracture mechanics problems.


The transformation equation for x is given by