The Boundary Element Method - Mechanics of Structures: Variational and Computational Methods - page 574

FIGURE 9.10
Boundary conditions and unknown variables for Example 9.5.

right-hand side of (10). This leads to a system of linear equations of the form of Eq. (9.95)
which can be solved for the quantities listed in (9).
The displacements at points a, b and c in the x 1 direction, computed using the three
meshes of Fig. 9.11, are given in the following table. The results are the numbers in the table
multiplied by 10 − 3 mm.

Nodes Mesh 1 Mesh 2 Mesh 3 Exact Solution

a 7.8781 8.0246 8.0350 8.0325

b 5.1668 5.2845 5.2928 5.2912

c 4.3896 4.4570 4.4631 4.4625

The boundary element solutions appear to converge to the exact solution. When a coarse
mesh like mesh 1 is used, the error of the boundary element solution is within 2.5%, and
when the mesh is refined to mesh 3, the error of the boundary element solution is reduced to
less than 0.015%. Since only 30 nodes are used in mesh 3, it would appear that the boundary
element solution is quite efficient for this accurate solution.