Civil Engineering Reference
In-Depth Information
13
Body Forces
Gravitation is not responsible
for people falling in love
J. Keppler
13.1
INTRODUCTION
The advantages of the boundary element method over the FEM that no elements are
required inside the domain, also has some disadvantages: loading may only be applied at
the boundary, but not inside the domain. A number of problems exist where applying
loading inside the domain is necessary, for example
x
where sources (of heat or water) or forces have to be considered inside the domain
x
where self weight or centrifugal forces have to be considered
x
where initial strains are applied inside the domain, for example when material is
subjected to swelling.
In addition, as we will see later, for the analysis of domains exhibiting nonlinear
material behaviour, for which we cannot find fundamental solutions, the problem can be
considered as one where initial stresses are generated inside the domain.
In this chapter we will discuss methods which allow us to consider such loads
commonly known as
body forces
. Here we will distinguish between those which are
constant, such as for example, self weight and those which vary inside the domain. We
will find that we can deal with constant body forces in a fairly straightforward way since
the volume integrals which occur can be transformed into surface integrals. In the case
where they are not constant, however, the only way to deal with volume integration is by
providing additional volume discretisation.
We will start this chapter by revisiting Betti's theorem as derived for integral
equations but now we will consider the additional effect of body forces.
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