Nonlinear Problems - The Boundary Element Method with Programming - page 424

15.5 CONCLUSIONS

In this chapter we attempted to show that the treatment of nonlinear problems is almost
as straightforward as with the FEM. Only two types of nonlinear problems have been
discussed: plasticity and contact problems. In the first type, additional volume
discretisation is needed and the BEM looses a bit of its attraction. However, it was
pointed out that the internal cell discretisation does not add to the number of unknown
and that all the advantages of the BEM are still retained. It must be admitted, however,
that the effort in programming, especially dealing with hyper-singular integrations, is
rather involved.
We have also found that for contact problems the BEM is better suited than the FEM
because the interface stresses required for checking the yield conditions are directly
obtained from the solution. In the FEM these would have to be determined by
differentiation of the computed displacement field. The purpose of this chapter has been
to demonstrate that any type of nonlinear problem can be solved with the BEM.
However, the computer implementation has not been discussed in any detail here
because it would be beyond the scope of an introductory text.

15.6 REFERENCES

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10. Prager W. and Hodge P.G. (1951) Theory of Perfectly Plastic Solids. John Wiley &
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