Civil Engineering Reference
In-Depth Information
FIGURE 6.4
Comparison of temperature fields corresponding to prototype cross sections which show a high level
of similarity.
parameters for this weld are given in data set 1 of Appendix A. This set of data includes information
concerning projections onto the transverse cross section of the weld of the solidification boundary and
of the
Ac
1
and
Ac
3
isotherms. Shown in
Fig. 6.8
are solidification boundaries at the top surface and
transverse cross sections for a bead-in-groove weld having essentially a flat surface. The process param-
eters for this weld are given in data set 2 of Appendix A. This set of data includes, in addition to
information concerning the shape of the solidification boundary, information concerning the projection
of the
Ac
1
isotherm onto the transverse cross section.
Prototype case study 1. General procedure for constrained optimization of discrete temperature
field—
For the present case study we consider a prototype analysis of the weld whose cross section is shown
in
Fig. 6.7
and whose process parameters are given in data set 1 of Appendix A. For this analysis only the
transverse cross section of the solidification boundary is adopted as a constraint based on experimental
measurements. We adopt as an objective function the expression defined by Eq. (6.32). Minimization
of the value of this function represents an optimization of the energy per distance for a finite region of
the weld spanning the calculated temperature field which does not totally include the energy source. This
region does, however, include a large fraction of the weld, i.e., the region defined by
L
S
in
Fig. 6.6
.
For
this analysis we adopt a three-dimensional solution domain defined by six boundaries which enclose a
finite section of the total region spanning the pseudo steady state.
Figure 6.1
provides a two-dimensional
schematic representation of the top view of this model system. The upstream boundary is considered to
be either in close proximity or partially within the region of the weld within which there is energy deposition.
One of the longitudinal boundaries corresponds to the midplane of the weld. The top surface boundary
corresponds to the top surface of the workpiece and represents an approximation since for this weld
(data set 1 of Appendix A) there is substantial reinforcement extending above the workpiece surface. Three
of the boundaries are adopted as downstream boundaries on the solution domain.
