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ROTDISC.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME ROTDISC
* Problem:
* ********
* Optimal design of a rotating disk of minimal weight, with constraints on
* stress and profile.
* The problem arise in the mechanical design of turbine where several disks
* are assembled, as in jet engines and steam turbines in power generation
* systems. The data correspond to the real design problem for the engine of
* a small civil jet.
* The problem has a linear objective function, linear constraints and
* quadratic equality constraints. The solution lies at a vertex of the
* feasible set.
* Source:
* B. Apraxine and E. Loute,
* "The optimal design of a rotating disk: a test case for nonlinear
* programming codes",
* Facultes Universitaires Saint Louis, Brussels, 1993.
* See also:
* J. P. Nigoghossian,
* "Problem: the optimization of jet engine discs",
* in "Optimisation and Design", M. Avriel, M. J. Rijckaert and D. J. Wilde,
* eds., Prentice Hall, Englewood Cliffs, 1973.
* SIF input : E. Loute and Ph. L. Toint, April 1993
* minor correction by Ph. Shott, Jan 1995.
* classification LQR2-RN-905-1081
IE K 180 $ number of intervals in discretization
RE rotspeed 22000.0 $ rotational speed (rpm)
RE ri 41.0 $ inner radius (mm)
RE ro 131.0 $ outer radius (mm)
RE rim 127.0 $ rim radius (mm)
RE rho 8200.0 $ specific weight (kg/m**3)
RE E 18525.0 $ elasticity modulus (hb)
RE epsc 14.0D-6 $ dilatation coefficient
RE nu 0.3 $ Poisson coefficient
RE wro 13.0 $ outer thickness
RE wmin 4.0 $ minimal thickness
RE wmax 34.0 $ maximal thickness
RE sigmaro 18.5 $ radial stress on outer radius
RE sigmari 0.0 $ radial stress on inner radius
RE sigmati 72.0 $ maximal radial stress on inner radius
RE sigmato 47.5 $ maximal radial stress on outer radius
RE sigmatA 66.0 $ maximal average tangential stress
RE sigmaru 55.0 $ maximal radial stress
* temperature law: t(r) = tempo + tempn * ( r / r0 )**n
RE tempo 450.0
RE tempn 150.0
IE n 4
* scaling constants
RE ech1 100.0
RE ech2 1.0E-13
RE ech3 1.0E-9
* useful parameters
IE 1 1
IE 0 0
IA K-1 K -1
RI RK K
R- Dr ro ri
R/ dr Dr RK
RE pi 3.1415926535
RM 2pi pi 2.0
R* aux1 2pi rotspeed
RE 60.0 60.0
R/ omega aux1 60.0
R* omega2 omega omega
R* romg2 rho omega2
RM romg2/2 romg2 0.5
R* aux2 romg2/2 ech2
RA 1+nu nu 1.0
RM 3nu nu 3.0
RA 1+3nu 3nu 1.0
RA 3+nu nu 3.0
RM (1+nu)/2 1+nu 0.5
RM (1+3nu)/2 1+3nu 0.5
RM (3+nu)/2 3+nu 0.5
R* pirho pi rho
RM dr/2 dr 0.5
R* aux3 aux2 dr
VARIABLES
DO k 0 K
* thickness
X w(k)
* tangential stress
X sigt(k)
* radial stress
X sigr(k)
* additional variables to handle average tangential stress
X x(k)
X y(k)
OD k
GROUPS
R= rk ri
RM -dr/2 dr/2 -1.0
R* rk2 rk rk
DO k 0 K-1
IA k+1 k 1
R+ rk+1 rk dr
* aux3 is ech2*rho*omega**2*dr/2
R* coef1 aux3 rk2
R* rk+1sq rk+1 rk+1
R* coef2 aux3 rk+1sq
ZE SR(k) 'SCALE' ech1
ZE SR(k) w(k) coef1
ZE SR(k) w(k+1) coef2
R* tmp1 (1+3nu)/2 rk
R* tmp2 (1+nu)/2 rk+1
R- tmp3 tmp1 tmp2
R/ coef3 tmp3 rk
ZE ST(k) sigr(k) coef3
R* tmp4 (3+nu)/2 rk
R* tmp5 (1+nu)/2 rk+1
R- tmp6 tmp5 tmp4
R/ coef4 tmp6 rk
ZE ST(k) sigt(k) coef4
R* tmp7 (1+3nu)/2 rk+1
R* tmp8 (1+nu)/2 rk
R- tmp9 tmp8 tmp7
R/ coef5 tmp9 rk+1
ZE ST(k) sigr(k+1) coef5
R* tmp10 (3+nu)/2 rk+1
R* tmp11 (1+nu)/2 rk
R- tmp12 tmp10 tmp11
R/ coef6 tmp12 rk+1
ZE ST(k) sigt(k+1) coef6
XE STAy(k) y(k+1) 1.0 y(k) -1.0
XE STAx(k) x(k+1) 1.0 x(k) -1.0
ZE STAx(k) w(k+1) -dr/2
ZE STAx(k) w(k) -dr/2
R= rk rk+1
R= rk2 rk+1sq
OD k
* objective function
R= rk-1 ri
R+ rk rk-1 dr
R* rk-1sq rk-1 rk-1
R* rk2 rk rk
R- aux3 rk-1sq rk2
R* aux4 aux3 pirho
R* coef1 aux4 ech3
RM -coef1 coef1 -1.0
ZN WEIGHT w(0) -coef1
DO k 1 K-1
IA k-1 k -1
R+ rk+1 rk dr
R* rk+1sq rk+1 rk+1
R- aux3 rk-1sq rk+1sq
R* aux4 aux3 pirho
R* coef1 aux4 ech3
RM -coef1 coef1 -1.0
ZE WEIGHT w(k) -coef1
R= rk-1sq rk2
R= rk rk+1
R= rk2 rk+1sq
OD k
R- aux3 rk-1sq rk2
R* aux4 pirho aux3
R* coef1 aux4 ech3
RM -coef1 coef1 -1.0
ZN WEIGHT w(K) -coef1
DO k 0 K-1
IA k+1 k 1
XL SLOP(k) w(k+1) 1.0 w(k) -1.0
XL SLOM(k) w(k+1) -1.0 w(k) 1.0
OD k
RM -sigmatA sigmatA -1.0
XL AVsigt y(K) 1.0
ZL AVsigt x(K) -sigmatA
CONSTANTS
* We compute in the loop the value of the temperature function
* tk = tempo + tempn*(rk/ro)**n (here n = 4)
R* Eepsc E epsc
R= rk ri
R/ aux1 rk ro
R* aux2 aux1 aux1
R* aux2 aux2 aux2
R* tmp1 aux2 tempn
R+ tk tmp1 tempo
DO k 0 K-1
R+ rk+1 rk dr
R/ aux1 rk+1 ro
R* aux2 aux1 aux1
R* aux2 aux2 aux2
R* tmp1 aux2 tempn
R+ tk+1 tmp1 tempo
R- tmp2 tk tk+1
R* coef1 tmp2 Eepsc
Z ROTDISC ST(k) coef1
R= rk rk+1
R= tk tk+1
OD k
RM 4dr dr 4.0
DO k 0 K-1
Z ROTDISC SLOP(k) 4dr
Z ROTDISC SLOM(k) 4dr
OD k
BOUNDS
FR ROTDISC 'DEFAULT'
ZX ROTDISC sigr(0) sigmari
ZU ROTDISC sigt(0) sigmati
XL ROTDISC sigt(0) -100.0
XX ROTDISC x(0) 0.0
XX ROTDISC y(0) 0.0
DO k 1 K
XL ROTDISC x(k) 0.0
OD k
DO k 1 K-1
XL ROTDISC sigr(k) 0.0
ZU ROTDISC sigr(k) sigmaru
XL ROTDISC sigt(k) -100.0
XU ROTDISC sigt(k) 100.0
OD k
* We express that thickness is constant on the rim and bounded outside
IA K-9 K -9
DO k 0 K-9
ZL ROTDISC w(k) wmin
ZU ROTDISC w(k) wmax
OD k
IA K-8 K -8
DO k K-8 K
ZX ROTDISC w(k) wro
OD k
ZU ROTDISC sigt(K) sigmato
ZX ROTDISC sigr(K) sigmaro
START POINT
* This starting point is slightly infeasible
* (the upper bound on sigr(k) is violated for some k)
ROTDISC w0 30.000000000
ROTDISC sigt0 70.224043123
ROTDISC sigr0 0.0
ROTDISC x0 0.0
ROTDISC y0 0.0
ROTDISC w1 30.000000000
ROTDISC sigt1 69.337178701
ROTDISC sigr1 .75150203489
ROTDISC x1 15.000000000
ROTDISC y1 1046.7091637
ROTDISC w2 30.000000000
ROTDISC sigt2 68.478656583
ROTDISC sigr2 1.4725717269
ROTDISC x2 30.000000000
ROTDISC y2 2080.3279283
ROTDISC w3 30.000000000
ROTDISC sigt3 67.647086003
ROTDISC sigr3 2.1645828149
ROTDISC x3 45.000000000
ROTDISC y3 3101.2709977
ROTDISC w4 30.000000000
ROTDISC sigt4 66.841155637
ROTDISC sigr4 2.8288294334
ROTDISC x4 60.000000000
ROTDISC y4 4109.9328100
ROTDISC w5 30.000000000
ROTDISC sigt5 66.059628152
ROTDISC sigr5 3.4665315686
ROTDISC x5 75.000000000
ROTDISC y5 5106.6886884
ROTDISC w6 30.000000000
ROTDISC sigt6 65.301335165
ROTDISC sigr6 4.0788400842
ROTDISC x6 90.000000000
ROTDISC y6 6091.8959133
ROTDISC w7 30.000000000
ROTDISC sigt7 64.565172618
ROTDISC sigr7 4.6668413532
ROTDISC x7 105.00000000
ROTDISC y7 7065.8947217
ROTDISC w8 30.000000000
ROTDISC sigt8 63.850096500
ROTDISC sigr8 5.2315615316
ROTDISC x8 120.00000000
ROTDISC y8 8029.0092401
ROTDISC w9 30.000000000
ROTDISC sigt9 63.155118892
ROTDISC sigr9 5.7739705049
ROTDISC x9 135.00000000
ROTDISC y9 8981.5483555
ROTDISC w10 30.000000000
ROTDISC sigt10 62.479304325
ROTDISC sigr10 6.2949855370
ROTDISC x10 150.00000000
ROTDISC y10 9923.8065296
ROTDISC w11 30.000000000
ROTDISC sigt11 61.821766398
ROTDISC sigr11 6.7954746441
ROTDISC x11 165.00000000
ROTDISC y11 10856.064560
ROTDISC w12 30.000000000
ROTDISC sigt12 61.181664651
ROTDISC sigr12 7.2762597204
ROTDISC x12 180.00000000
ROTDISC y12 11778.590293
ROTDISC w13 30.000000000
ROTDISC sigt13 60.558201672
ROTDISC sigr13 7.7381194336
ROTDISC x13 195.00000000
ROTDISC y13 12691.639290
ROTDISC w14 30.000000000
ROTDISC sigt14 59.950620407
ROTDISC sigr14 8.1817919107
ROTDISC x14 210.00000000
ROTDISC y14 13595.455456
ROTDISC w15 30.000000000
ROTDISC sigt15 59.358201664
ROTDISC sigr15 8.6079772309
ROTDISC x15 225.00000000
ROTDISC y15 14490.271621
ROTDISC w16 30.000000000
ROTDISC sigt16 58.780261800
ROTDISC sigr16 9.0173397415
ROTDISC x16 240.00000000
ROTDISC y16 15376.310097
ROTDISC w17 30.000000000
ROTDISC sigt17 58.216150564
ROTDISC sigr17 9.4105102106
ROTDISC x17 255.00000000
ROTDISC y17 16253.783190
ROTDISC w18 30.000000000
ROTDISC sigt18 57.665249095
ROTDISC sigr18 9.7880878301
ROTDISC x18 270.00000000
ROTDISC y18 17122.893688
ROTDISC w19 30.000000000
ROTDISC sigt19 57.126968056
ROTDISC sigr19 10.150642080
ROTDISC x19 285.00000000
ROTDISC y19 17983.835316
ROTDISC w20 30.000000000
ROTDISC sigt20 56.600745894
ROTDISC sigr20 10.498714467
ROTDISC x20 300.00000000
ROTDISC y20 18836.793171
ROTDISC w21 30.000000000
ROTDISC sigt21 56.086047224
ROTDISC sigr21 10.832820143
ROTDISC x21 315.00000000
ROTDISC y21 19681.944119
ROTDISC w22 30.000000000
ROTDISC sigt22 55.582361311
ROTDISC sigr22 11.153449416
ROTDISC x22 330.00000000
ROTDISC y22 20519.457183
ROTDISC w23 30.000000000
ROTDISC sigt23 55.089200663
ROTDISC sigr23 11.461069163
ROTDISC x23 345.00000000
ROTDISC y23 21349.493898
ROTDISC w24 30.000000000
ROTDISC sigt24 54.606099709
ROTDISC sigr24 11.756124148
ROTDISC x24 360.00000000
ROTDISC y24 22172.208651
ROTDISC w25 30.000000000
ROTDISC sigt25 54.132613569
ROTDISC sigr25 12.039038253
ROTDISC x25 375.00000000
ROTDISC y25 22987.749000
ROTDISC w26 30.000000000
ROTDISC sigt26 53.668316898
ROTDISC sigr26 12.310215632
ROTDISC x26 390.00000000
ROTDISC y26 23796.255979
ROTDISC w27 30.000000000
ROTDISC sigt27 53.212802809
ROTDISC sigr27 12.570041791
ROTDISC x27 405.00000000
ROTDISC y27 24597.864377
ROTDISC w28 30.000000000
ROTDISC sigt28 52.765681856
ROTDISC sigr28 12.818884596
ROTDISC x28 420.00000000
ROTDISC y28 25392.703012
ROTDISC w29 30.000000000
ROTDISC sigt29 52.326581096
ROTDISC sigr29 13.057095224
ROTDISC x29 435.00000000
ROTDISC y29 26180.894984
ROTDISC w30 30.000000000
ROTDISC sigt30 51.895143190
ROTDISC sigr30 13.285009049
ROTDISC x30 450.00000000
ROTDISC y30 26962.557916
ROTDISC w31 30.000000000
ROTDISC sigt31 51.471025575
ROTDISC sigr31 13.502946477
ROTDISC x31 465.00000000
ROTDISC y31 27737.804182
ROTDISC w32 30.000000000
ROTDISC sigt32 51.053899680
ROTDISC sigr32 13.711213727
ROTDISC x32 480.00000000
ROTDISC y32 28506.741121
ROTDISC w33 30.000000000
ROTDISC sigt33 50.643450190
ROTDISC sigr33 13.910103570
ROTDISC x33 495.00000000
ROTDISC y33 29269.471245
ROTDISC w34 30.000000000
ROTDISC sigt34 50.239374354
ROTDISC sigr34 14.099896013
ROTDISC x34 510.00000000
ROTDISC y34 30026.092429
ROTDISC w35 30.000000000
ROTDISC sigt35 49.841381338
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