構造力学 構造工学特論
ＢＡＳＩＣプログラム
そりねじりの格子桁（剛性マトリックス法）
10 REM SAVE "WGRILL",A
1000 REM "GRILLWARP"
1010 REM GRILLAGE GIRDER
1020 REM WARPING TORSION , DD: DOUBLE PRECISION
1030 REM 1984.3.2
1040 DIM KAKOM(30,2),X(20),Y(20),SM(8,8),TSM(40,40),F(40),NOKW(18)
1050 DIM NOKXX(18),NOKYY(18),NOKZ(18),INDEX(40),REAC(40),DIS(40)
1060 DIM STRE#(30,8),SST(40,40),QI(30),QJ(30),STR(8,8),WD(40),CM(30)
1070 DIM NONGL(18),ANGL(18),W(4,4),SSM(8,8)
1080 CLS
1090 DATA 9, 8, 6, 0, 6, 0, 6, 2.1E+7, 8.1E+6
1100 DATA 1, 2, 1.167E-3, 2.048E-6, 2.185E-5
1110 DATA 2, 3, 1.167E-3, 2.048E-6, 2.185E-5
1120 DATA 4, 5, 1.167E-3, 2.048E-6, 2.185E-5
1130 DATA 5, 6, 1.167E-3, 2.048E-6, 2.185E-5
1140 DATA 7, 8, 1.167E-3, 2.048E-6, 2.185E-5
1150 DATA 8, 9, 1.167E-3, 2.048E-6, 2.185E-5
1160 DATA 2, 5, 1.167E-3, 2.048E-6, 2.185E-5
1170 DATA 5, 8, 1.167E-3, 2.048E-6, 2.185E-5
1180 DATA 0.0, 2.58819, 0.0, 0.0, 0.0, 0.0
1190 DATA 9.65926, 0.0, 1.0, 0.0, 0.0, 0.0
1200 DATA 19.31852, 2.58819, 0.0, 0.0, 0.0, 0.0
1210 DATA 0.96593, 5.32937, 0.0, 0.0, 0.0, 0.0
1220 DATA 9.65926, 3.0, 0.0, 0.0, 0.0, 0.0
1230 DATA 18.35259, 5.32937, 0.0, 0.0, 0.0, 0.0
1240 DATA 1.93185, 8.07055, 0.0, 0.0, 0.0, 0.0
1250 DATA 9.65926, 6.0, 0.0, 0.0, 0.0, 0.0
1260 DATA 17.38667, 8.07055, 0.0, 0.0, 0.0, 0.0
1270 DATA 1, -15.0000
1280 DATA 3, 15.0000
1290 DATA 4, -15.0000
1300 DATA 6, 15.0000
1310 DATA 7, -15.0000
1320 DATA 9, 15.0000
1330 DATA 1, 3, 4, 6, 7, 9
1340 DATA 1, 3, 4, 6, 7, 9
1350 READ NODT,NELT,KOZ,KOYY,KOXX,KOW,NANGL,E,G
1360 FOR I=1 TO NELT
1370 FOR J=1 TO 2
1380 READ KAKOM(I,J):NEXT J:READ QI(I),QJ(I),CM(I)
1390 NEXT I
1400 FOR I=1 TO NODT
1410 I1=4*I-3
1420 I2=4*I-2
1430 I3=4*I-1
1440 I4=4*I
1450 READ X(I),Y(I),F(I1),F(I2),F(I3),F(I4)
1460 NEXT I
1470 IF NANGL=0 THEN 1510
1480 FOR I=1 TO NANGL
1490 READ NONGL(I),ANGL(I)
1500 NEXT I
1510 FOR I=1 TO KOZ
1520 READ NOKZ(I)
1530 NEXT I
1540 IF KOYY=0 THEN 1580
1550 FOR I=1 TO KOYY
1560 READ NOKYY(I)
1570 NEXT I
1580 IF KOXX=0 THEN 1620
1590 FOR I=1 TO KOXX
1600 READ NOKXX(I)
1610 NEXT I
1620 IF KOW=0 THEN 1660
1630 FOR I=1 TO KOW
1640 READ NOKW(I)
1650 NEXT I
1660 NT=NODT*4
1670 FOR I=1 TO NT
1680 FOR J=1 TO NT
1690 TSM(I,J)=0 :NEXT J,I
1700 PRINT:PRINT "剛性マトリックスの計算中"
1710 FOR NE=1 TO NELT
1720 GOSUB *GRILL
1730 IF NANGL=0 THEN 1820
1740 FOR NNN=1 TO NANGL
1750 IF NONGL(NNN)=II THEN 1770
1760 NEXT NNN : GOTO 1780
1770 GOSUB *SLOPE
1780 FOR NNN=1 TO NANGL
1790 IF NONGL(NNN)=JJ THEN 1810
1800 NEXT NNN : GOTO 1820
1810 GOSUB *SLOPE
1820 PRINT " NE=";NE;SPC(5) "I=";KAKOM(NE,1);SPC(5) "J=";KAKOM(NE,2)
1830 ' LPRINT " NE=";NE;SPC(5) "I=";KAKOM(NE,1);SPC(5) "J=";KAKOM(NE,2)
1840 ' FOR I=1 TO 8
1850 ' FOR J=1 TO 8
1860 ' AA=13*(J-1):AA=AA-104*INT(AA/104)
1870 ' LPRINT TAB(AA);USING "##.####^^^^";SM(I,J);
1880 ' NEXT J:LPRINT
1890 ' NEXT I
1900 GOSUB *ASMAT
1910 NEXT NE
1920 PRINT:PRINT "支点処理の作業中"
1930 FOR I=1 TO NT
1940 DIS(I)=0
1950 INDEX(I)=I:NEXT I
1960 FOR I=1 TO KOZ
1970 N=4*NOKZ(I)-3
1980 INDEX(N)=0 :NEXT I
1990 IF KOYY=0 THEN 2040
2000 FOR I=1 TO KOYY
2010 N=4*NOKYY(I)-2
2020 INDEX(N)=0
2030 NEXT I
2040 IF KOXX=0 THEN 2080
2050 FOR I=1 TO KOXX
2060 N=4*NOKXX(I)-1
2070 INDEX(N)=0: NEXT I
2080 IF KOW=0 THEN 2120
2090 FOR I=1 TO KOW
2100 N=4*NOKW(I)
2110 INDEX(N)=0: NEXT I
2120 MM=0
2130 FOR I=1 TO NT
2140 IF INDEX(I)=0 THEN 2170
2150 MM=MM+1
2160 INDEX(MM)=INDEX(I)
2170 NEXT I
2180 FOR I=1 TO MM
2190 IA=INDEX(I)
2200 F(I)=F(IA)
2210 FOR J=1 TO MM
2220 JA=INDEX(J)
2230 TSM(I,J)=TSM(IA,JA)
2240 NEXT J
2250 NEXT I
2260 FOR I=1 TO MM
2270 FOR J=1 TO MM
2280 SST(I,J)=TSM(I,J)
2290 NEXT J
2300 NEXT I
2310 PRINT:PRINT "逆マトリックスの計算中"
2320 GOSUB *MATI
2330 ' PRINT :LPRINT :LPRINT "***** SHITENSHORI *****"
2340 ' FOR I=1 TO MM
2350 ' FOR K=1 TO MM
2360 ' AA=13*(K-1):AA=AA-130*INT(AA/130)
2370 ' LPRINT TAB(AA);USING "##.####^^^^";SST(I,K);
2380 ' NEXT K:LPRINT
2390 ' NEXT I
2400 ' LPRINT :LPRINT "********** GYAKU **********"
2410 ' FOR K=1 TO MM
2420 ' FOR J=1 TO MM
2430 ' AA=13*(J-1):AA=AA-130*INT(AA/130)
2440 ' LPRINT TAB(AA);USING "##.####^^^^";TSM(K,J);
2450 ' NEXT J:LPRINT
2460 ' NEXT K
2470 FOR I=1 TO MM
2480 REAC(I)=0
2490 FOR K=1 TO MM
2500 REAC(I)=REAC(I)+TSM(I,K)*F(K)
2510 NEXT K
2520 NEXT I
2530 FOR I=1 TO MM
2540 IA=INDEX(I)
2550 DIS(IA)=REAC(I)
2560 NEXT
2570 FOR I=1 TO NT
2580 FOR J=1 TO NT
2590 TSM(I,J)=0
2600 NEXT J
2610 NEXT I
2620 PRINT:PRINT "剛性マトリックスの再計算中"
2630 FOR NE=1 TO NELT
2640 GOSUB *GRILL
2650 IF NANGL=0 THEN 2740
2660 FOR NNN=1 TO NANGL
2670 IF NONGL(NNN)=II THEN 2690
2680 NEXT NNN : GOTO 2700
2690 GOSUB *SLOPE
2700 FOR NNN=1 TO NANGL
2710 IF NONGL(NNN)=JJ THEN 2730
2720 NEXT NNN : GOTO 2740
2730 GOSUB *SLOPE
2740 GOSUB *ASMAT
2750 NEXT NE
2760 FOR I=1 TO NT
2770 REAC(I)=0
2780 FOR K=1 TO NT
2790 REAC(I)=REAC(I)+TSM(I,K)*DIS(K)
2800 NEXT K
2810 NEXT I
2820 ' LPRINT
2830 ' LPRINT " ********** DISPLACEMENT AND REACTION **********"
2840 ' LPRINT "NODE No. V YY XX XY RZ RYY RXX RXY"
2850 ' FOR I=1 TO NODT
2860 ' LPRINT TAB(3);I;
2870 ' LPRINT TAB(8);USING "##.####^^^^";DIS(4*I-3);
2880 ' LPRINT TAB(20);USING "##.####^^^^";DIS(4*I-2);
2890 ' LPRINT TAB(32);USING "##.####^^^^";DIS(4*I-1);
2900 ' LPRINT TAB(44);USING "##.####^^^^";DIS(4*I);
2910 ' LPRINT TAB(56);USING "##.####^^^^";REAC(4*I-3);
2920 ' LPRINT TAB(68);USING "##.####^^^^";REAC(4*I-2);
2930 ' LPRINT TAB(80);USING "##.####^^^^";REAC(4*I-1);
2940 ' LPRINT TAB(92);USING "##.####^^^^";REAC(4*I);
2950 ' NEXT
2960 LPRINT:LPRINT
2970 LPRINT " ********** MOMENTS AND SHEARS **********"
2980 LPRINT "NELT No. SI MI TI MWI SJ MJ TJ MWJ"
2990 PRINT "応力マトリックスの計算中"
3000 FOR NE=1 TO NELT
3010 PRINT " NE=";NE;SPC(5) "I=";KAKOM(NE,1);SPC(5) "J=";KAKOM(NE,2)
3020 GOSUB *STRESS
3030 IF NANGL=0 THEN 3120
3040 FOR NNN=1 TO NANGL
3050 IF NONGL(NNN)=II THEN 3070
3060 NEXT NNN : GOTO 3080
3070 GOSUB *SLOPEX
3080 FOR NNN=1 TO NANGL
3090 IF NONGL(NNN)=JJ THEN 3110
3100 NEXT NNN : GOTO 3111
3110 GOSUB *SLOPEX
3111 FOR I=1 TO 8
3112 FOR J=1 TO 8
3113 AA=13*(J-1):AA=AA-104*INT(AA/104)
3114 LPRINT TAB(AA);USING "##.####^^^^";STR(I,J);
3115 NEXT J:LPRINT
3116 NEXT I
3120 FOR I=1 TO 2
3130 IA=KAKOM(NE,I)
3140 WD(4*I-3)=DIS(4*IA-3)
3150 WD(4*I-2)=DIS(4*IA-2)
3160 WD(4*I-1)=DIS(4*IA-1)
3170 WD(4*I)=DIS(4*IA)
3180 NEXT I
3190 FOR I=1 TO 8
3200 STRE#(NE,I)=0
3210 FOR K=1 TO 8
3220 STRE#(NE,I)=STRE#(NE,I)+STR(I,K)*WD(K)
3230 NEXT K
3240 NEXT I
3250 LPRINT TAB(2);NE;SPC(1);
3260 FOR I=1 TO 8
3270 LPRINT SPC(1);USING "##.####^^^^";STRE#(NE,I);
3280 NEXT I
3290 NEXT NE
3300 END
3310 *GRILL
3320 DEF FNSINH#(X)=(EXP(X)-EXP(-X))/2
3330 DEF FNCOSH#(X)=(EXP(X)+EXP(-X))/2
3340 DEF FNTANH#(X)=(1-EXP(-2*X))/(1+EXP(-2*X))
3350 II=KAKOM(NE,1)
3360 JJ=KAKOM(NE,2)
3370 XI=X(II)
3380 XJ=X(JJ)
3390 YI=Y(II)
3400 YJ=Y(JJ)
3410 AL=SQR((XJ-XI)^2+(YJ-YI)^2)
3420 RA=SQR(G*QJ(NE)/(E*CM(NE)))
3430 RL=RA*AL
3440 DD#=RL*FNSINH#(RL)-2*FNCOSH#(RL)+2
3450 SN=(YJ-YI)/AL
3460 CS=(XJ-XI)/AL
3470 'PRINT "RL";RL;"EXP(RL)";EXP(RL);"FNSINH";FNSINH#(RL);"FNCOSH";FNCOSH#(RL);"FNTANH";FNTANH#(RL);"DD";DD#
3480 C1=12*E*QI(NE)/AL^3
3490 C2=6*E*QI(NE)/AL^2
3500 C3=4*E*QI(NE)/AL
3510 C4=2*E*QI(NE)/AL
3520 C5=E*CM(NE)/DD#*RA^3*FNSINH#(RL)
3530 C6=E*CM(NE)/DD#*RA^2*(FNCOSH#(RL)-1)
3540 C7=E*CM(NE)/DD#*RA*(RL*FNCOSH#(RL)-FNSINH#(RL))
3550 C8=E*CM(NE)/DD#*RA*(RL-FNSINH#(RL))
3560 'PRINT "DD";DD#;"C5";C5;"C6";C6;"C7";C7;"C8";C8
3570 SM(1,1)=C1
3580 SM(1,2)=CS*C2
3590 SM(1,3)=-SN*C2
3600 SM(1,4)=0
3610 SM(1,5)=-C1
3620 SM(1,6)=CS*C2
3630 SM(1,7)=-SN*C2
3640 SM(1,8)=0
3650 SM(2,2)=CS*CS*C3+SN*SN*C5
3660 SM(2,3)=-CS*SN*C3+CS*SN*C5
3670 SM(2,4)=SN*C6
3680 SM(2,5)=-CS*C2
3690 SM(2,6)=CS*CS*C4-SN*SN*C5
3700 SM(2,7)=-CS*SN*C4-CS*SN*C5
3710 SM(2,8)=SN*C6
3720 SM(3,3)=SN*SN*C3+CS*CS*C5
3730 SM(3,4)=CS*C6
3740 SM(3,5)=SN*C2
3750 SM(3,6)=-CS*SN*C4-CS*SN*C5
3760 SM(3,7)=SN*SN*C4-CS*CS*C5
3770 SM(3,8)=CS*C6
3780 SM(4,4)=C7
3790 SM(4,5)=0
3800 SM(4,6)=-SN*C6
3810 SM(4,7)=-CS*C6
3820 SM(4,8)=-C8
3830 SM(5,5)=C1
3840 SM(5,6)=-CS*C2
3850 SM(5,7)=SN*C2
3860 SM(5,8)=0
3870 SM(6,6)=CS^2*C3+SN^2*C5
3880 SM(6,7)=CS*SN*(-C3+C5)
3890 SM(6,8)=-SN*C6
3900 SM(7,7)=SN^2*C3+CS^2*C5
3910 SM(7,8)=-CS*C6
3920 SM(8,8)=C7
3930 FOR I=2 TO 8
3940 I1=I-1
3950 FOR J=1 TO I1
3960 SM(I,J)=SM(J,I)
3970 NEXT J,I
3980 RETURN
3990 *ASMAT
4000 FOR I=1 TO 2
4010 FOR J=1 TO 2
4020 KI=(KAKOM(NE,I)-1)*4
4030 KJ=(KAKOM(NE,J)-1)*4
4040 IS=(I-1)*4
4050 JS=(J-1)*4
4060 FOR K=1 TO 4
4070 FOR L=1 TO 4
4080 KIK=KI+K
4090 KJL=KJ+L
4100 ISK=IS+K
4110 JSL=JS+L
4120 TSM(KIK,KJL)=TSM(KIK,KJL)+SM(ISK,JSL)
4130 NEXT L,K
4140 NEXT J,I
4150 RETURN
4160 *MATI
4170 DIM IND(40)
4180 FOR KO=1 TO MM
4190 IND(KO)=KO:NEXT
4200 FOR KO=1 TO MM
4210 W=0
4220 FOR IO=KO TO MM
4230 IF ABS(TSM(IO,1))=IND(IO) THEN 4530
4510 IR=IO
4520 GOTO 4540
4530 NEXT IO
4540 FOR JO=1 TO MM
4550 W=TSM(JO,KO)
4560 TSM(JO,KO)=TSM(JO,IR)
4570 TSM(JO,IR)=W:NEXT
4580 IND(IR)=IND(KO):IND(KO)=KO
4590 NEXT KO
4600 RETURN
4610 *STRESS
4620 DEF FNSINH#(X)=(EXP(X)-EXP(-X))/2
4630 DEF FNCOSH#(X)=(EXP(X)+EXP(-X))/2
4640 II=KAKOM(NE,1)
4650 JJ=KAKOM(NE,2)
4660 XI=X(II)
4670 XJ=X(JJ)
4680 YI=Y(II)
4690 YJ=Y(JJ)
4700 AL=SQR((XJ-XI)^2+(YJ-YI)^2)
4710 RA=SQR(G*QJ(NE)/(E*CM(NE)))
4720 RL=RA*AL
4730 DD#=RL*FNSINH#(RL)-2*FNCOSH#(RL)+2
4740 SN=(YJ-YI)/AL
4750 CS=(XJ-XI)/AL
4760 C1=12*E*QI(NE)/AL^3
4770 C2=6*E*QI(NE)/AL^2
4780 C3=4*E*QI(NE)/AL
4790 C4=2*E*QI(NE)/AL
4800 C5=E*CM(NE)/DD#*RA^3*FNSINH#(RL)
4810 C6=E*CM(NE)/DD#*RA^2*(FNCOSH#(RL)-1)
4820 C7=E*CM(NE)/DD#*RA*(RL*FNCOSH#(RL)-FNSINH#(RL))
4830 C8=E*CM(NE)/DD#*RA*(RL-FNSINH#(RL))
4840 STR(1,1)=C1
4850 STR(1,2)=CS*C2
4860 STR(1,3)=-SN*C2
4870 STR(1,4)=0
4880 STR(1,5)=-C1
4890 STR(1,6)=CS*C2
4900 STR(1,7)=-SN*C2
4910 STR(1,8)=0
4920 STR(2,1)=C2
4930 STR(2,2)=CS*C3
4940 STR(2,3)=-SN*C3
4950 STR(2,4)=0
4960 STR(2,5)=-C2
4970 STR(2,6)=CS*C4
4980 STR(2,7)=-SN*C4
4990 STR(2,8)=0
5000 STR(3,1)=0
5010 STR(3,2)=SN*C5
5020 STR(3,3)=CS*C5
5030 STR(3,4)=C6
5040 STR(3,5)=0
5050 STR(3,6)=-SN*C5
5060 STR(3,7)=-CS*C5
5070 STR(3,8)=C6
5080 STR(4,1)=0
5090 STR(4,2)=SN*C6
5100 STR(4,3)=CS*C6
5110 STR(4,4)=C7
5120 STR(4,5)=0
5130 STR(4,6)=-SN*C6
5140 STR(4,7)=-CS*C6
5150 STR(4,8)=-C8
5160 STR(5,1)=-C1
5170 STR(5,2)=-CS*C2
5180 STR(5,3)=SN*C2
5190 STR(5,4)=0
5200 STR(5,5)=C1
5210 STR(5,6)=-CS*C2
5220 STR(5,7)=SN*C2
5230 STR(5,8)=0
5240 STR(6,1)=C2
5250 STR(6,2)=CS*C4
5260 STR(6,3)=-SN*C4
5270 STR(6,4)=0
5280 STR(6,5)=-C2
5290 STR(6,6)=CS*C3
5300 STR(6,7)=-SN*C3
5310 STR(6,8)=0
5320 STR(7,1)=0
5330 STR(7,2)=-SN*C5
5340 STR(7,3)=-CS*C5
5350 STR(7,4)=-C6
5360 STR(7,5)=0
5370 STR(7,6)=SN*C5
5380 STR(7,7)=CS*C5
5390 STR(7,8)=-C6
5400 STR(8,1)=0
5410 STR(8,2)=SN*C6
5420 STR(8,3)=CS*C6
5430 STR(8,4)=-C8
5440 STR(8,5)=0
5450 STR(8,6)=-SN*C6
5460 STR(8,7)=-CS*C6
5470 STR(8,8)=C7
5540 RETURN
5550 '
5560 *SLOPE
5570 ANGLR=ANGL(NNN)*3.1416/180!
5580 FOR I=1 TO 4
5590 FOR J=1 TO 4
5600 W(I,J)=0!
5610 NEXT J,I
5620 W(1,1)=1!
5630 W(2,2)=COS(ANGLR)
5640 W(2,3)=SIN(ANGLR)
5650 W(3,2)=-SIN(ANGLR)
5660 W(3,3)=COS(ANGLR)
5670 W(4,4)=1!
5680 NI=1
5690 IF NONGL(NNN)=JJ THEN NI=2
5700 FOR NJ=1 TO 2
5710 FOR I=1 TO 4
5720 FOR J=1 TO 4
5730 JA=(NJ-1)*4+J
5740 SSM(I,J)=0!
5750 FOR K=1 TO 4
5760 KA=(NI-1)*4+K
5770 SSM(I,J)=SSM(I,J)+W(K,I)*SM(KA,JA)
5780 NEXT K,J,I
5790 FOR I=1 TO 4
5800 IA=(NI-1)*4+I
5810 FOR J=1 TO 4
5820 JA=(NJ-1)*4+J
5830 SM(IA,JA)=SSM(I,J)
5840 NEXT J,I,NJ
5850 NJ=1
5860 IF NONGL(NNN)=JJ THEN NJ=2
5870 FOR NI=1 TO 2
5880 FOR I=1 TO 4
5890 IA=(NI-1)*4+I
5900 FOR J=1 TO 4
5910 SSM(I,J)=0!
5920 FOR K=1 TO 4
5930 KA=(NJ-1)*4+K
5940 SSM(I,J)=SSM(I,J)+SM(IA,KA)*W(K,J)
5950 NEXT K,J,I
5960 FOR I=1 TO 4
5970 IA=(NI-1)*4+I
5980 FOR J=1 TO 4
5990 JA=(NJ-1)*4+J
6000 SM(IA,JA)=SSM(I,J)
6010 NEXT J,I,NI
6020 RETURN
6030 '
6040 *SLOPEX
6050 ANGLR=ANGL(NNN)*3.1416/180!
6060 FOR I=1 TO 4
6070 FOR J=1 TO 4
6080 W(I,J)=0!
6090 NEXT J,I
6100 W(1,1)=1!
6110 W(2,2)=COS(ANGLR)
6120 W(2,3)=SIN(ANGLR)
6130 W(3,2)=-SIN(ANGLR)
6140 W(3,3)=COS(ANGLR)
6150 W(4,4)=1!
6160 NJ=1
6170 IF NONGL(NNN)=JJ THEN NJ=2
6180 FOR NI=1 TO 2
6190 FOR I=1 TO 4
6200 IA=(NI-1)*4+I
6210 FOR J=1 TO 4
6220 SSM(I,J)=0!
6230 FOR K=1 TO 4
6240 KA=(NJ-1)*4+K
6250 SSM(I,J)=SSM(I,J)+STR(IA,KA)*W(K,J)
6260 NEXT K,J,I
6270 FOR I=1 TO 4
6280 IA=(NI-1)*4+I
6290 FOR J=1 TO 4
6300 JA=(NJ-1)*4+J
6310 STR(IA,JA)=SSM(I,J)
6320 NEXT J,I,NI
6330 RETURN