Civil Engineering Reference
In-Depth Information
FIGURE 6.15
Cross-sections of estimated temperature field calculated by means of a generating function extending
over the entire solution domain. Discretization of temperature field is not uniformly distributed throughout solution
domain.
level of discretization of the temperature field depending upon characteristic maximum of the temper-
ature gradient associated with a given subdomain. That is to say, this property provides the basis for a
discretization of the temperature field by means of a nested set of embedded meshes of progressively
finer resolution. As an example, consider the constrained optimization leading to the discrete temperature
field whose two dimensional cross sections are shown in
Figs. 6.15
through
6.19
is with respect to a set
of embedded meshes whose discretization lengths are 4
0.2 mm.
Shown in
Fig. 6.15
are two-dimensional cross-sections of an estimated temperature field calculated
by means of a generating function
T
E
(
x
). For this calculation the generating function consists of a sum
of Rosenthal solutions of the type given by Eq. (6.B1) in Appendix B. The energy per distance corre-
l
, 2
l
, and
l
, where
l
