$ondollar title Dynamometer Ring (multiNLP) Example 8.2 of Rardin (1998)

$offsymxref offsymlist offuelxref offuellist offupper
option limrow = 0, limcol = 0;

option nlp = minos5;

scalar
capE      "Young modulus of elasticity" /2.1e6/,
sensconst "sensitivity constant" /0.7/;

free variables
sens     "sensitivity",
rigid    "rigidity";

positive variable w "width of the ring";
w.lo = 5.0;
w.up = 10.0;

positive variable t "thickness fo the outer surface";
t.lo = 0.1;
t.up = 2.0;

positive variable r "radius of the openings";
r.lo = 1.25;
r.up = 20.0;

equations
sensobj  "maximize sensitivity",
rigidobj "maximize rigidity";

sensobj..
sens =e= sensconst * r / ( capE * w * sqr(t) );

rigidobj..
rigid =e= capE * w * t**3 / r**3;

model dynaring /all/;

w.l = (w.lo + w.up)/2;
t.l = (t.lo + t.up)/2;
r.l = (r.lo + r.up)/2;

solve dynaring using nlp maximizing sens;

solve dynaring using nlp maximizing rigid;