ship.gms : Structural Optimization
This model designs a vertically corrugated transverse bulkhead of an
oil tanker. The objective is to design for minimum weight and
meet stress, moment of inertia and plate thickness constraints.
Reference:
- Bracken, J, and McCormick, G P, Chapter 6. In Selected Applications of Nonlinear Programming. John Wiley and Sons, New York, 1968.
Small Model of Type: NLP
<![CDATA[
$Title Structural Optimization (SHIP,SEQ=22)
$Ontext
This model designs a vertically corrugated transverse bulkhead of an
oil tanker. The objective is to design for minimum weight and
meet stress, moment of inertia and plate thickness constraints.
Bracken, J, and McCormick, G P, Chapter 6. In Selected Applications of
Nonlinear Programming. John Wiley and Sons, New York, 1968.
$Offtext
Set s bulkhead sections / top, middle, bottom /; alias (s,sp)
Scalars gam specific gravity of water (kg cm-3) / .001 /
sig maximum bending stress (kg cm-2) / 1200 /
dnv det norske veritas factor / 3.9 /
ca corrosion allowance (cm) / na /
e flange effectiveness / na /
ha height above panel (cm) / 250 /
gamsteel specific weight of steel / .0078 /
width width of panel (m) / na /
tlow lower bound on t (cm) / na /
Parameters h(s) height at the middle of panel (cm)
hb(s) height at the base of panel (cm)
k1(s) constant number one
k2(s) constant number two
l(s) length of panel (cm)
/ top 495, middle 385, bottom 315 / ;
hb(s) = ha + sum(sp$(ord(sp) le ord(s)), l(sp));
h(s) = hb(s) - l(s)/2;
k1(s) = gam*h(s)*l(s)*l(s)/12/sig;
k2(s) = dnv*1.05e-4*sqrt(hb(s));
Display l, h, hb, k1, k2;
* the reference does not contain values for the parameters
* e, width, ca, and t.lo. from reported optimal solutions and
* using constraints stress and inertia a value for e can be calculated.
* the width is only a scaling constant and is set to 500. ca is assumed
* to be .2 and the lower bound of 1.05 on t was read out from
* solution values.
e = .8; width = 500; ca = .2; tlow = 1.05;
Variables z(s) module (cm3)
t(s) plate thickness (cm)
wl width of flange (cm)
lw length of web (cm)
d depth of corrugation (cm)
wc width of corrugation (cm)
w weight of structure (tons)
Equations zdef(s) module definition (cm3)
wdef width of corrugation - definition (cm)
stress(s) bending stress (kg cm-2)
inertia(s) moment of inertia (cm4)
platew(s) plate thickness - width of flange (cm)
platel(s) plate thickness - length of web (cm)
geom geometric constraint (cm)
weight total weight of structure (tons) ;
zdef(s).. z(s) =e= d*t(s)*(lw/3+wl*e)/2;
wdef.. wc =e= wl + sqrt(lw*lw-d*d);
stress(s).. z(s) =g= k1(s)*wc;
inertia(s).. z(s)*d/2 =g= 2.2*(k1(s)*wc)**(4/3);
platew(s).. t(s) =g= k2(s)*wl + ca ;
platel(s).. t(s) =g= k2(s)*lw + ca ;
geom.. lw =g= d ;
weight.. w =e= gamsteel*width*(wl+lw)*sum(s, t(s)*l(s))/wc/1000;
t.lo(s) = tlow;
t.l("top") = 1.2; t.l("middle") = 1.2; t.l("bottom") = 1.3;
wl.l = 45.8; lw.l = 43.2; d.l = 30.5;
wc.l = wl.l + sqrt(lw.l**2-d.l**2); display wc.l;
z.l(s) = d.l*t.l(s)*(lw.l/3+wl.l*e)/2; display z.l;
wc.lo = 1;
Model ship structural design of bulkhead / all /;
Solve ship minimizing w using nlp;
]]></plaintext></body></div>