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thesametanksize has n, =17 and nhg =3).
If the number of vertical stiffeners and horizontal girders increases, the man-hours required for the
construction of such transverse bulkheads increases. Such a design would be disadvantageous. Thus,
in this section, the results of optimization that take into consideration not only weight of the materid
but also the construction cost of the structures will be shown. To begin with, total cost C is defined as
the sum of the material cost and the construction cost as:
c = c, xw +c, x L, (9)
Here, c, is the cost of steel building material per Unit weight, and W is the total bulkhead weight.
The second term in the right hand-side of Eqn.9 is the cost of construction which is assumed to be in
proportion to the welding length De We can estimate L, by the number of vertical stiffeners and
horizontal girders. In this paper, c, and c, are assumed as:
c, = 70,OOOyen I ton and c, = 2,000yen I m .
The response surfaces of the total construction cost are obtained on the basis of these assumptions. The
third-order model is used. The obtained response surface of the total construction cost is shown in
Figure 8. To confirm the accuracy of the response surface, the exact solution is also shown in Figure
9. The response surface by the third-order model agrees quite well with the exact solution. The
results of both solutions are compared in Table 1. A slight difference between the two solutions
exists in the number of optimum horizontal girders, since in this example nvs and nhg are treated as
integers, while some errors due to polynomial approximation may also exist. However, the estimated
peak response (i.e., the optimal value of total cost) obtained using RSM agrees very closely with that
of the exact solution. As was indicated before, the actual ship with the same tank size has 17 vertical
stiffeners and 3 horizontal girders. It is considered that in the actual ship, the vertical stiffeners are
installed to correspond to the location of the longitudinal stiffeners, whose number is determined in
regard to the longitudinal strength of the hull structure. Therefore, the obtained number of vertical
stiffeners does not perfectly agree with the case regarding the actual ship; however, we can confirm
that the optimum solution arrived at using this analysis approaches to the actual design by introducing
the construction cost shown in Eqn.9.

TABLE 1
COMPARISON OF OPTIMUL
SOLUTIONS
1 I RSM IExacts0l.I

in Yen

Figure 8:Total construction cost Figure 9: Total construction cost
(1 O6 yen), RSM (IO6 yen), Exact solution
3.2 Optimization Based on the Stress blue of the Structure

As a second example of RSM application, a case is shown in which the maximum value of the stress
that will be occurred in horizontal girders is made to be an objective function. In this example, the
vertical positions of the horizontal girders (Figure 10) will be the design variables. In this study the