Postprocessing - The Boundary Element Method with Programming - page 225

9
Postprocessing

Man soll auf alles achten, denn man kann alles deuten
(You should consider everything
because you can interpret everything)
H. Hesse

9.1 INTRODUCTION

In the previous Chapters we developed a general purpose computer program for the
analysis of two and three-dimensional problems in elasticity and potential flow. This
program only calculates the values of unknowns (temperature/displacements or
boundary flow/tractions) at the nodes of boundary elements. In this chapter we will
develop procedures for the calculation of other results which are of interest. These are
the flow vector or the stress tensor at the boundary and at points inside the domain.
There are two types of approximations involved in a boundary element analysis. The
first is that the distribution of temperature/displacement, or boundary flow/stress, is
approximated at the boundary by shape functions defined locally for each element. The
second approximation is that the theorem by Betti is only ensured to be satisfied at the
nodal points on the boundary elements (collocation points).
Because we use fundamental solutions, the variation of temperature/displacements
inside the domain is known in terms of boundary values. It is therefore possible to
compute the results at any point inside the domain as a postprocessing exercise, after the
analysis has been performed. This is in contrast to the FEM, where results are only
available at points inside finite elements. Now the results at interior points can be part of
a graphical postprocessor, with the option that the user may freely specify locations
where results are required. Instead of using interpolation between values at nodal points
of elements, we can use a direct procedure to determine the contour lines and this will be
discussed later.
In the discussion on the computation of results we distinguish between values inside
the domain and on the boundary. For the computation of results the integral equation for