It is noted that the mesh is refined in the near of the reentrant corner.
The numerical results for the first normal stress [[tau].sub.xx], first normal stress difference [N.sub.1], and second normal stress difference [N.sub.2] near the reentrant corner are illustrated in Figures 2(a), 2(b), and 2(c), respectively.
finite difference finite element and boundary integral equation methods have limitations when the solution has the singularity on the boundary which is due to either a reentrant corner or to an abrupt change of boundary condition.
They also described how the approximation may be post-processed in the neighbourhood of a reentrant corner singularity in order to obtain an improved and more rapidly converging representation.
This example presents an analysis of the waveguide containing boundary singularities such as a reentrant corner
in a L-shaped waveguide.
Suppose only one of the vertex of T is a reentrant corner
[c.sub.l] of [omega].
For example, a surface flaw may propagate into the reentrant corner
of a reactor pressure vessel's primary coolant pipe during severe thermal shock conditions when there is a loss of coolant within the pressure vessel.
In (4.1), (r, [theta]) denotes polar coordinates with respect to the reentrant corner
, and [eta](r) is a smooth cut-off function with 0 [less than or equal to] [eta] [less than or equal to] 1, [eta] = 1 for 0 [less than or equal to] r [less than or equal to] [r.sub.0]/3, [eta] = 0 for r [geater than or equal to] 2[r.sub.0] singular parts of the solution holds s [member of] [H.sup.1+[lambda]-[epsilon]] ([OMEGA]) with any [epsilon] > 0.
A noteworthy aspect of this method is its use of singular (Fourier-Bessel) functions in the expansion to incorporate, for example, reentrant corners
. Improvements have been made by including points on the interior of the domain where the condition that the eigenfunction is nonzero is enforced .
However, problems with non-convex boundaries (useful for scatters with reentrant corners
in order to minimize the number of unknowns) does not follow the convergence behavior described above.
Good coverage also avoids reentrant corners
such as recessed doorways in corridors where an inmate can hide.
The high interfacial energy between inclusions and molten aluminum causes reentrant corners
to collect H from the melt as [H.sub.2] in a reversible reaction: