set materials := NYLON TEFLON STEEL CARBON ALUM EPOXYN EPOXYP ; set epoxy := EPOXYN EPOXYP ; param N := 20; # max number of intercepts. param THOT := 300; # temperature at the hottest end. param TCOLD := 4.2; # temperature at the coldest end. param M := 10; # max mass of the system. param F := 250000; # max allowed force on the system. param DELTA := 5; # max % expansion allowed. param L := 100; # length of the system. param SIGMAX := 130000; param SIGMIN := 1000; #param C := 1 5.0 # 2 4.0 # 3 2.5; param: RHO D := NYLON 0.0010 33 TEFLON 0.0015 33 STEEL 0.0078 33 CARBON 0.0078 33 ALUM 0.0027 33 EPOXYN 0.0018 21 EPOXYP 0.0018 21 ; # lookup table data for Temperature param T := [EPOXYP, *] 1 0 2 4.2 3 20 4 23.92 5 43.64 6 63.36 7 77 8 83.08 9 102.8 10 122.52 11 142.24 12 161.96 13 181.68 14 195 15 201.4 16 221.12 17 240.84 18 260.56 19 280.28 20 297 21 300 [EPOXYN, *] 1 0 2 4.2 3 20 4 23.92 5 43.64 6 63.36 7 77 8 83.08 9 102.8 10 122.52 11 142.24 12 161.96 13 181.68 14 195 15 201.4 16 221.12 17 240.84 18 260.56 19 280.28 20 297 21 300 [NYLON, *] 1 0 2 4 3 4.2 4 22.222222 5 23.92 6 43.64 7 44.444444 8 55.555556 9 63.36 10 77.777778 11 83.08 12 100 13 102.8 14 111.11111 15 122.52 16 133.33333 17 142.24 18 155.55556 19 161.96 20 166.66667 21 181.68 22 188.88889 23 201.4 24 211.11111 25 221.12 26 222.22222 27 240.84 28 244.44444 29 260.56 30 266.66667 31 277.77778 32 280.28 33 300 [TEFLON, *] 1 0 2 4 3 4.2 4 22.222222 5 23.92 6 43.64 7 44.444444 8 55.555556 9 63.36 10 77.777778 11 83.08 12 100 13 102.8 14 111.11111 15 122.52 16 133.33333 17 142.24 18 155.55556 19 161.96 20 166.66667 21 181.68 22 188.88889 23 201.4 24 211.11111 25 221.12 26 222.22222 27 240.84 28 244.44444 29 260.56 30 266.66667 31 277.77778 32 280.28 33 300 [ALUM, *] 1 0 2 4 3 4.2 4 22.222222 5 23.92 6 43.64 7 44.444444 8 55.555556 9 63.36 10 77.777778 11 83.08 12 100 13 102.8 14 111.11111 15 122.52 16 133.33333 17 142.24 18 155.55556 19 161.96 20 166.66667 21 181.68 22 188.88889 23 201.4 24 211.11111 25 221.12 26 222.22222 27 240.84 28 244.44444 29 260.56 30 266.66667 31 277.77778 32 280.28 33 300 [STEEL, *] 1 0 2 4 3 4.2 4 22.222222 5 23.92 6 43.64 7 44.444444 8 55.555556 9 63.36 10 77.777778 11 83.08 12 100 13 102.8 14 111.11111 15 122.52 16 133.33333 17 142.24 18 155.55556 19 161.96 20 166.66667 21 181.68 22 188.88889 23 201.4 24 211.11111 25 221.12 26 222.22222 27 240.84 28 244.44444 29 260.56 30 266.66667 31 277.77778 32 280.28 33 300 [CARBON, *] 1 0 2 4 3 4.2 4 22.222222 5 23.92 6 43.64 7 44.444444 8 55.555556 9 63.36 10 77.777778 11 83.08 12 100 13 102.8 14 111.11111 15 122.52 16 133.33333 17 142.24 18 155.55556 19 161.96 20 166.66667 21 181.68 22 188.88889 23 201.4 24 211.11111 25 221.12 26 222.22222 27 240.84 28 244.44444 29 260.56 30 266.66667 31 277.77778 32 280.28 33 300 ; # lookup table data for Thermal Conductivity param K := [EPOXYP, *] 1 0 2 0.00047068659 3 0.002 4 0.0022647305 5 0.0028865448 6 0.0027777209 7 0.0026 8 0.002554026 9 0.0025855456 10 0.0028351456 11 0.0032273821 12 0.0036868113 13 0.0041379893 14 0.0044 15 0.0045060506 16 0.0047531189 17 0.0049000151 18 0.0049727725 19 0.0049974241 20 0.005 21 0.005000003 [EPOXYN, *] 1 0 2 0.00035204819 3 0.0015 4 0.0017009599 5 0.0021897161 6 0.0021303491 7 0.002 8 0.0019613012 9 0.0019491657 10 0.0020756954 11 0.0022958458 12 0.002564573 13 0.0028368325 14 0.003 15 0.0030679163 16 0.0032346044 17 0.003347777 18 0.0034213419 19 0.0034692068 20 0.0035 21 0.0035052797 [NYLON, *] 1 0 2 0.00012459291 3 0.00013184246 4 0.0011074925 5 0.0012036277 6 0.0021304792 7 0.0021630714 8 0.0025610765 9 0.0027412462 10 0.002941777 11 0.0030109431 12 0.0032013456 13 0.0032187803 14 0.0032532593 15 0.003303029 16 0.0033570867 17 0.0034014376 18 0.0034609142 19 0.0034838097 20 0.0034955233 21 0.003500089 22 0.0034955233 23 0.0034940673 24 0.0034955233 25 0.0034955612 26 0.0034955233 27 0.0034954861 28 0.0034955233 29 0.0034955388 30 0.0034955233 31 0.0034955233 32 0.0034955245 33 0.0034955233 [TEFLON, *] 1 0 2 0.00046030158 3 0.00048106375 4 0.0014795408 5 0.0015304168 6 0.0020110956 7 0.0020246348 8 0.0021630714 9 0.0022313406 10 0.0023361171 11 0.0023736496 12 0.0024572491 13 0.0024601492 14 0.0024572491 15 0.0024602217 16 0.0024745536 17 0.0024916906 18 0.0025264673 19 0.0025468823 20 0.0025610765 21 0.0025898968 22 0.0025956856 23 0.0025971549 24 0.0025956856 25 0.0025956473 26 0.0025956856 27 0.0025957231 28 0.0025956856 29 0.00259567 30 0.0025956856 31 0.0025956856 32 0.0025956844 33 0.0025956856 [ALUM, *] 1 0 2 0.34609142 3 0.36343602 4 1.8169799 5 1.9282547 6 2.7220907 7 2.7341222 8 2.7514268 9 2.6424909 10 2.3534216 11 2.2637737 12 2.0938531 13 2.0812711 14 2.0592439 15 2.0393883 16 2.0246348 17 2.0151141 18 2.0073302 19 2.0069699 20 2.0073302 21 2.0075113 22 2.0073302 23 2.0072725 24 2.0073302 25 2.0073317 26 2.0073302 27 2.0073287 28 2.0073302 29 2.0073308 30 2.0073302 31 2.0073302 32 2.0073303 33 2.0073302 [STEEL, *] 1 0 2 0.0024226399 3 0.0025596054 4 0.021803759 5 0.024081437 6 0.050917187 7 0.051913712 8 0.064026912 9 0.070783375 10 0.080985391 11 0.08446992 12 0.095002094 13 0.096579226 14 0.098982145 15 0.093856403 16 0.090675951 17 0.097028107 18 0.11299885 19 0.1185228 20 0.121132 21 0.12401044 22 0.124939 23 0.12898224 24 0.13220692 25 0.13393813 26 0.13411042 27 0.13803373 28 0.13878266 29 0.14163227 30 0.14293576 31 0.14587753 32 0.14648171 33 0.15003063 [CARBON, *] 1 0 2 0.02941777 3 0.031164935 4 0.25956856 5 0.27878958 6 0.42894737 7 0.43434473 8 0.51048484 9 0.55070313 10 0.59527724 11 0.60604822 12 0.62988638 13 0.63281552 14 0.64026912 15 0.64731199 16 0.65065186 17 0.65123907 18 0.65065186 19 0.65059977 20 0.65065186 21 0.65067805 22 0.65065186 23 0.65064351 24 0.65065186 25 0.65065208 26 0.65065186 27 0.65065165 28 0.65065186 29 0.65065195 30 0.65065186 31 0.65065186 32 0.65065187 33 0.65065186; # lookup table data for Expansion param E := [EPOXYP, *] 1 0 2 1.1652557e-06 3 4.926e-06 4 5.5630013e-06 5 6.9188219e-06 6 6.3175679e-06 7 5.564e-06 8 5.28881e-06 9 4.7562973e-06 10 4.6396229e-06 11 4.7639126e-06 12 4.9542924e-06 13 5.0358883e-06 14 4.9412e-06 15 4.8352651e-06 16 4.2710452e-06 17 3.4079341e-06 18 2.323609e-06 19 1.0957467e-06 20 0 21 -1.9797554e-07 [EPOXYN, *] 1 0 2 8.7214031e-07 3 3.6945e-06 4 4.1767501e-06 5 5.2363293e-06 6 4.8319525e-06 7 4.28e-06 8 4.0706371e-06 9 3.6263995e-06 10 3.4555525e-06 11 3.4468903e-06 12 3.4892067e-06 13 3.4712959e-06 14 3.369e-06 15 3.282857e-06 16 2.8714996e-06 17 2.2767299e-06 18 1.5462137e-06 19 7.2761706e-07 20 -4.2351647e-22 21 -1.3139415e-07 [NYLON, *] 1 0 2 1.8036817e-06 3 1.9085251e-06 4 1.5914668e-05 5 1.7278861e-05 6 2.9950954e-05 7 3.0369522e-05 8 3.5240412e-05 9 3.7173043e-05 10 3.865495e-05 11 3.9023044e-05 12 3.9472591e-05 13 3.9327059e-05 14 3.8583655e-05 15 3.733428e-05 16 3.6189395e-05 17 3.5357521e-05 18 3.388235e-05 19 3.2897989e-05 20 3.2088904e-05 21 2.9318429e-05 22 2.7894276e-05 23 2.5291087e-05 24 2.3210275e-05 25 2.1041958e-05 26 2.0798364e-05 27 1.6428458e-05 28 1.5520123e-05 29 1.1229535e-05 30 9.5427786e-06 31 6.4317629e-06 32 5.7200108e-06 33 0 [TEFLON, *] 1 0 2 1.2362043e-05 3 1.2918577e-05 4 3.9104264e-05 5 4.036514e-05 6 5.1610661e-05 7 5.189139e-05 8 5.4379614e-05 9 5.5285017e-05 10 5.6206977e-05 11 5.6443376e-05 12 5.6148141e-05 13 5.5824631e-05 14 5.4575502e-05 15 5.2972754e-05 16 5.1643934e-05 17 5.0591232e-05 18 4.9013466e-05 19 4.8222781e-05 20 4.7584801e-05 21 4.4977601e-05 22 4.3373907e-05 23 4.0053317e-05 24 3.7170218e-05 25 3.40866e-05 26 3.3743913e-05 27 2.7797956e-05 28 2.6579821e-05 29 2.1011027e-05 30 1.9078289e-05 31 1.5340502e-05 32 1.4124273e-05 33 0 [ALUM, *] 1 0 2 0.001491654 3 0.0015664163 4 0.0078311835 5 0.0083101742 6 0.011657841 7 0.011702043 8 0.011638535 9 0.011069819 10 0.0096254945 11 0.0091482554 12 0.0080613343 13 0.0079415007 14 0.007639795 15 0.0072353799 16 0.0068432656 17 0.0065210333 18 0.006042064 19 0.0058117714 20 0.0056405979 21 0.0050759959 22 0.0047975192 23 0.0043063549 24 0.0039142939 25 0.0034986684 26 0.003452608 27 0.0026662195 28 0.0025091628 29 0.0017835813 30 0.0015054977 31 0.0010036651 32 0.00089083258 33 0 [STEEL, *] 1 0 2 7.3696222e-06 3 7.786199e-06 4 6.6523269e-05 5 7.351706e-05 6 0.000155417 7 0.00015838874 8 0.0001934253 9 0.00021155931 10 0.00023566749 11 0.00024292391 12 0.00026030574 13 0.00026196231 14 0.00026032304 15 0.00023652218 16 0.00021671552 17 0.00022079605 18 0.00023955756 19 0.00024190923 20 0.00023984135 21 0.00021989818 22 0.00020864813 23 0.00019345462 24 0.00018112348 25 0.00016424323 26 0.00016227361 27 0.00012895158 28 0.00012212874 29 8.9040562e-05 30 7.575595e-05 31 5.1057136e-05 32 4.5400015e-05 33 0 [CARBON, *] 1 0 2 6.1777318e-05 3 6.5445812e-05 4 0.00054509398 5 0.00058550081 6 0.00089697456 7 0.00090778048 8 0.0010567036 9 0.0011306607 10 0.0011965072 11 0.0012050798 12 0.0011967841 13 0.0011915717 14 0.0011716925 15 0.0011356483 16 0.0010930951 17 0.0010523427 18 0.00098248431 19 0.00094546867 20 0.00091741913 21 0.00082589778 22 0.00078078224 23 0.00070065965 24 0.00063763883 25 0.00057306664 26 0.00056606712 27 0.00044369471 28 0.00041641719 29 0.00028115058 30 0.00023423467 31 0.00016266297 32 0.00014617537 33 0 ; # lookup table data for Stress param SIGMA := [EPOXYP, *] 1 80668.692 2 80580.682 3 80668.692 4 80888.59 5 82995.835 6 85377.052 7 86184.5 8 86140.405 9 84333.842 10 80563.009 11 75580.098 12 70137.298 13 64986.798 14 62052.84 15 60874.795 16 58163.887 17 56607.964 18 55906.865 19 55760.425 20 55847.556 21 55868.485 [EPOXYN, *] 1 80668.692 2 80580.682 3 80668.692 4 80888.59 5 82995.835 6 85377.052 7 86184.5 8 86140.405 9 84333.842 10 80563.009 11 75580.098 12 70137.298 13 64986.798 14 62052.84 15 60874.795 16 58163.887 17 56607.964 18 55906.865 19 55760.425 20 55847.556 21 55868.485 [NYLON, *] 1 20615.332 2 20546.385 3 20543.46 4 20408.49 5 20390.249 6 20074.543 7 20063.752 8 19925.856 9 19754.315 10 19305.328 11 19132.383 12 18615.852 13 18536.562 14 18271.114 15 17751.654 16 17236.9 17 16909.189 18 16478.476 19 16227.53 20 15995.843 21 14985.612 22 14478.996 23 13757.953 24 13306.887 25 12824.309 26 12755.306 27 11177.567 28 10893.721 29 9913.966 30 9445.8212 31 8273.712 32 8010.0853 33 6205.284 [TEFLON, *] 1 12962.149 2 12824.254 3 12817.534 4 12272.673 5 12223.17 6 11610.259 7 11583.197 8 11169.511 9 10813.112 10 10204.245 11 10060.598 12 9583.7164 13 9446.718 14 8963.188 15 8346.0023 16 7928.974 17 7725.0619 18 7308.4456 19 6928.85 20 6618.9696 21 5844.9874 22 5653.7032 23 5540.3054 24 5240.0176 25 4497.6765 26 4412.6464 27 3425.6276 28 3309.4848 29 2887.877 30 2688.9564 31 2206.3232 32 2096.1488 33 1310.0044 [ALUM, *] 1 35163.276 2 34473.8 3 34435.423 4 29647.468 5 29160.482 6 24908.815 7 24821.136 8 24131.66 9 23541.672 10 22063.232 11 21540.15 12 20339.542 13 20233.406 14 19994.804 15 19604.096 16 19305.328 17 19245.246 18 19305.328 19 19310.658 20 19305.328 21 19302.649 22 19305.328 23 19306.182 24 19305.328 25 19305.306 26 19305.328 27 19305.35 28 19305.328 29 19305.319 30 19305.328 31 19305.328 32 19305.327 33 19305.328 [STEEL, *] 1 134792.56 2 134447.82 3 134432.49 4 133758.34 5 133724.95 6 133109.21 7 133068.87 8 132379.39 9 131830.01 10 131000.44 11 130831.99 12 130310.96 13 130147.24 14 129621.49 15 129215.28 16 128932.01 17 128564.2 18 128242.54 19 128325.57 20 128242.54 21 126402.01 22 125484.63 23 124966.97 24 124795.16 25 124183.8 26 124105.68 27 122940.86 28 122726.73 29 121730.67 30 121347.78 31 120658.3 32 120503.34 33 119279.35 [CARBON, *] 1 70326.552 2 68947.6 3 68878.17 4 63431.792 5 63118.704 6 60191.904 7 59984.412 8 56537.032 9 55123.349 10 53779.128 11 52941.414 12 49642.272 13 49241.671 14 48263.32 15 46769.33 16 45505.416 17 44836.837 18 43436.988 19 42217.983 20 41368.56 21 40237.487 22 39989.608 23 39046.921 24 37921.18 25 36660.594 26 36542.228 27 35336.443 28 35163.276 29 34195.196 30 33784.324 31 33094.848 32 32974.087 33 32405.372 ; # ... initialize integer variables let n := 10; let {i in 1..n+1} y[i] := 1; let {i in 1..n+1, j in materials} z[i,j] := y[i]/card(materials); display n, y, z; # ... initialize continuous variables let {i in 1..n+1} x[i] := L/(n+1); let {i in 0..n+1} t[i] := TCOLD + i*(THOT - TCOLD)/(n+1); let {i in 1..n+1} a[i] := 10; display x, t, a, v, z; # ... compute derived variables let {i in 1..n+1} u[i] := ( sum{k in materials} w[i,k]*z[i,k] ) / ( sum{k in materials} v[i,k]*z[i,k] ); let {i in 1..n+1} q[i] := a[i] * sum{j in materials} v[i,j]*z[i,j] / x[i]; display u,q;