...
0
x
H
,
0y
H
388 The Boundary Element Method with Programming
The Hankel functions can be expanded to
4
(14.12)
where
0.57721
J
(Euler constant) and here only the first terms of the expansion ... continuous elements and then with the program prog111_discont, the
discontinuous version of the multi-region program. If we compare the tractions at
inte...
... 212
8. 3 PROGRAM 8. 2 : Replacing assembly by element- by -element procedure 213
8. 3.1 Sample input file 219
8. 3.2 Sample output file 219
16 The Boundary Element Method with Programming
When the ... 203
8. 1 The Element by Element Concept 204
8. 1.1 Element- by -element storage requirements 206
8. 2 PROGRAM 8. 1 : Replacing direct by iterative solution 206...
... side of the beam
are the same and agree very well with the analytical solution, except for the coarse mesh
with continuous elements. For the discontinuous mesh with 3 elements and for the
continuous ...
332 The Boundary Element Method with Programming
We now investigate the other possibilities for the location of
i
P .
i
P is located at one...
... previously if the point
a
P is
not one of the cell nodes. If
P
a
coincides with the nodes of cells, then the integrand tends
to infinity with
o(r
2
) for 2-D and o(r
3
) for 3-D problems and special ...
()ut
4 38 The Boundary Element Method with Programming
Figure 16.2 Interface between finite element and boundary regions showing interface forces...
... linear elements
(c) one quadratic element
40 The Boundary Element Method with Programming
If the element shape functions for the quadratic element are derived from Lagrange
polynomials, then there ... is substituted for i,j and
(4. 58)
is the
Kronecker Delta.
For the boundary element method we also need the solutions for the boundary str...
... be written and used for numerical experiments. As the
1 38 The Boundary Element Method with Programming
We see that since R cancels out, the integral is valid for any radius of the circle, ... 1.0 0.7
18
0. -5 .
0. -4 .5
0. -4 .
0. -3 .5
0. -3 .
0. -2 .5
0. -2 .
0. -1 .5
BOUNDARY INTEGRAL EQUATIONS 117
or in discretised form u...
... matrices and
then solve for the boundary unknowns and another where the assembly and solution are
intermixed. The analogy to this in the FEM is the direct solution and the Element by
Element ... So the information that is needed for the assembly is the
Connectivity or Destination vector and the boundary code for each element. Note that
the bo...