Assembly and Solution - The Boundary Element Method with Programming - page 195

the boundary/boundary stresses. The computation of the complete flow vectors/stress
tensor at the boundary, as well as the computation of values inside the domain is
discussed in Chapter 9.

7.6 EXERCISES

Exercise 7.1
Using Program 7.1 compute the problem of flow past a cylindrical isolator, find out the
influence of the following on the accuracy of results:

(a) when linear and quadratic boundary elements are used.
(b) when the number of elements is 8,16 and 32.

Plot the error in the computation of maximum temperature against number of elements.

Exercise 7.2
Modify the problem computed in Exercise 7.1 by changing the shape of the isolator, so
that it has an elliptical shape, with a ratio vertical to horizontal axis of 2.0. Comment on
the changes in the boundary values due to the change in shape.

Exercise 7.3
Using Program 7.1, compute the problem of a circular excavation in a plane strain
infinite pre-stressed domain Figure 7.10, find out the influence of the following on the
accuracy of results:

(a) when linear and quadratic boundary elements are used.
(b) when the number of elements is 8,16 and 32.

Plot the error against the number of elements.

Hint: This is the elasticity problem equivalent to the heat flow problem in Exercise 7.1.
The problem is divided into two:
1. Continuum with no hole and the initial stresses only
2. Continuum with a hole and Neuman boundary conditions. The boundary conditions
are computed in such a way that when stresses at the boundary of problem 1 are added
to the ones at problem 2, zero values of boundary tractions are obtained. To compute
the boundary tractions equivalent to the initial stresses use equation (4.28).