Test Examples - The Boundary Element Method with Programming - page 269

The internal results along a horizontal line are shown in Figure 10.8. It can be seen that
there is good agreement even for coarse meshes.

9

8

4 elements
8 elements
16 elements
Ex a c t

Mesh 1
Mesh 2
Mesh 3

7

6

5

4

0 0,1 0,2 0,3 0,4 0,5

distance (m)

Figure 10.8

Distribution of vertical stress along a horizontal line

10.3.4 Comparison with FEM

The problem was analysed with the FEM with 3 different meshes of finite elements with
quadratic shape function, as shown in Figure 10.9. Symmetry was considered by
appropriate boundary conditions at the symmetry planes. This discretisation has the same
variation of displacements along the excavation boundary as the boundary element mesh.
Note that in the FEM we have to truncate the mesh at some distance away from the
excavation. A truncation of 2 diameters away from the excavation is used here. At the
truncation surface all displacements are assumed to be fixed. In order to eliminate the
truncation error, coupled analyses were also made, where boundary elements were used
at the edge of the FE mesh (see Chapter 16 on methods of coupling)

u

x ,

0

y

or BEM

Mesh 2 Mesh 3

Mesh 1

Figure 10.9 Finite element meshes used