C ******** FRAME2D ******** C ***** FRAME ANALYSIS BY FEM ***** DIMENSION X(100,2),NOC(100,2),MAT(100),PM(10,5),ARIN(100,2) DIMENSION NU(40),U(40),S(300,50),F(300),SEP(6,6),SE(6,6) DIMENSION MPC(20,2),BT(20,3),UDL(100),ALMBDA(6,6) DIMENSION ED(6),EDP(6),EF(6) CHARACTER*16 FILE1, FILE2 CHARACTER*81 DUMMY, TITLE IMAX = 300 PRINT *, '******** PROGRAM FRAME2D ********' PRINT *, '* 2-D FRAME ANALYSIS BY FEM *' PRINT *, '* T.R.Chandrupatla and A.D.Belegundu *' PRINT *, '*****************************************' PRINT *, 'Data File Name ' READ '(A)', FILE1 LINP = 10 OPEN (UNIT = 10, FILE = FILE1, STATUS = 'OLD') PRINT *, 'Output File Name' READ '(A)', FILE2 READ(LINP,'(A)') DUMMY READ(LINP,'(A)') TITLE READ(LINP,'(A)') DUMMY READ(LINP,*) NN, NE, NM, NDIM, NEN, NDN NQ = NDN * NN READ(LINP,'(A)') DUMMY READ(LINP,*) ND, NL, NMPC C --- Material property E NPR = 1 C ============ READ DATA FROM FILE =========== C ----- Coordinates ----- READ(LINP,'(A)') DUMMY DO 900 I = 1, NN 900 READ (LINP, *) N, X(N, 1), X(N, 2) C ----- Connectivity ----- READ(LINP,'(A)') DUMMY DO 1000 I=1,NE READ (LINP, *) N,NOC(N,1),NOC(N,2),MAT(N),ARIN(N,1),ARIN(N,2), 1UDL(N) 1000 CONTINUE C ----- Specified Displacements ----- READ(LINP,'(A)') DUMMY DO 1010 I = 1, ND 1010 READ (LINP, *) NU(I), U(I) C ----- Component Loads ----- READ(LINP,'(A)') DUMMY C ----- First initialize and then read loads ----- DO 1015 I=1, NQ 1015 F(I) = 0 DO 1020 I = 1, NL 1020 READ (LINP, *) N, F(N) C ----- Material Properties ----- READ(LINP,'(A)') DUMMY DO 1030 I = 1, NM 1030 READ (LINP, *) N, (PM(N, J), J = 1, NPR) C ----- Multi-point Constraints B1*Qi+B2*Qj=B0 IF (NMPC .GT. 0) THEN READ(LINP,'(A)') DUMMY DO 1040 I = 1, NMPC 1040 READ (LINP,*) BT(I,1),MPC(I,1),BT(I,2),MPC(I,2),BT(I,3) END IF CLOSE(LINP) C ----- Bandwidth Evaluation ----- NBW = 0 DO 1050 N = 1, NE NABS = NDN * (ABS(NOC(N, 1) - NOC(N, 2)) + 1) IF (NBW .LT. NABS) NBW = NABS 1050 CONTINUE DO 1060 I = 1, NMPC NABS = ABS(MPC(I, 1) - MPC(I, 2)) + 1 IF (NBW .LT. NABS) NBW = NABS 1060 CONTINUE PRINT *, 'Bandwidth = ', NBW C ----- First initialize stiffness matrix DO 1070 I = 1, NQ DO 1070 J = 1, NBW 1070 S(I,J) = 0 C ----- Global Stiffness Matrix DO 1090 N = 1, NE PRINT *, 'Forming Stiffness Matrix of Element ', N ISTF = 2 CALL ELSTIF(N,NOC,X,MAT,PM,ARIN,ALMBDA,SE,SEP,EL,ISTF) PRINT *, '.... Placing in Global Locations' DO 1090 II = 1, NEN NRT = NDN * (NOC(N, II) - 1) DO 1090 IT = 1, NDN NR = NRT + IT I = NDN * (II - 1) + IT DO 1090 JJ = 1, NEN NCT = NDN * (NOC(N, JJ) - 1) DO 1090 JT = 1, NDN J = NDN * (JJ - 1) + JT NC = NCT + JT - NR + 1 IF (NC .GT. 0) THEN S(NR, NC) = S(NR, NC) + SE(I, J) END IF 1090 CONTINUE C ----- Decide Penalty Parameter CNST ----- CNST = 0 DO 1100 I = 1, NQ IF (CNST .LT. S(I, 1)) CNST = S(I, 1) 1100 CONTINUE CNST = CNST * 10000 C ----- Loads due to uniformly distributed load on element DO 1130 N = 1, NE IF (ABS(UDL(N)) .GT. 0) THEN ISTF = 1 CALL ELSTIF(N,NOC,X,MAT,PM,ARIN,ALMBDA,SE,SEP,EL,ISTF) I1 = NOC(N, 1) I2 = NOC(N, 2) ED(1) = 0 ED(4) = 0 ED(2) = UDL(N) * EL / 2 ED(5) = ED(2) ED(3) = UDL(N) * EL ** 2 / 12 ED(6) = -ED(3) DO 1110 I = 1, 6 EDP(I) = 0 DO 1110 K = 1, 6 EDP(I) = EDP(I) + ALMBDA(K, I) * ED(K) 1110 CONTINUE DO 1120 I = 1, 3 F(3 * I1 - 3 + I) = F(3 * I1 - 3 + I) + EDP(I) F(3 * I2 - 3 + I) = F(3 * I2 - 3 + I) + EDP(I + 3) 1120 CONTINUE END IF 1130 CONTINUE C ----- Modify for Boundary Conditions ----- C --- Displacement BC --- DO 1140 I = 1, ND N = NU(I) S(N, 1) = S(N, 1) + CNST F(N) = F(N) + CNST * U(I) 1140 CONTINUE C --- Multi-point Constraints --- DO 1150 I = 1, NMPC I1 = MPC(I, 1) I2 = MPC(I, 2) S(I1, 1) = S(I1, 1) + CNST * BT(I, 1) * BT(I, 1) S(I2, 1) = S(I2, 1) + CNST * BT(I, 2) * BT(I, 2) IR = I1 IF (IR .GT.I2) IR = I2 IC = ABS(I2 - I1) + 1 S(IR, IC) = S(IR, IC) + CNST * BT(I, 1) * BT(I, 2) F(I1) = F(I1) + CNST * BT(I, 1) * BT(I, 3) F(I2) = F(I2) + CNST * BT(I, 2) * BT(I, 3) 1150 CONTINUE C ----- Equation Solving using Band Solver ----- CALL BAND(S, F, IMAX, NBW, NQ) LOUT = 11 OPEN (UNIT = 11, FILE = FILE2) WRITE(LOUT,'(1X,2A)') 'Output for Input Data from File ' ,FILE1 PRINT *, 'Output for Input Data from File ' ,FILE1 WRITE(LOUT,'(1X,A)') TITLE PRINT *, TITLE PRINT *, 'NODE# X-Displ. Y-Displ. Z-Rot.' WRITE(LOUT,'(1X,A)') 'NODE# X-Displ. Y-Displ. Z-Rot.' DO 1160 I = 1, NN I1 = 3 * I - 2 I2 = I1 + 1 I3 = I1 + 2 WRITE (*, '(I4,3E15.4)') I,F(I1),F(I2),F(I3) WRITE(LOUT, '(I4,3E15.4)') I,F(I1),F(I2),F(I3) 1160 CONTINUE C ----- Reaction Calculation ----- PRINT *, 'DOF# Reaction' WRITE(LOUT,'(1X,A)') 'DOF# Reaction' DO 1170 I = 1, ND N = NU(I) R = CNST * (U(I) - F(N)) WRITE(*,'(1X,I4,E15.4)') N, R WRITE(LOUT,'(1X,I4,E15.4)') N, R 1170 CONTINUE C ---- Member End-Actions WRITE(LOUT, '(1X,A)') ' Member End-Forces ' DO 1230 N = 1, NE ISTF = 1 CALL ELSTIF(N,NOC,X,MAT,PM,ARIN,ALMBDA,SE,SEP,EL,ISTF) I1 = NOC(N, 1) I2 = NOC(N, 2) DO 1180 I = 1, 3 ED(I) = F(3 * I1 - 3 + I) ED(I + 3) = F(3 * I2 - 3 + I) 1180 CONTINUE DO 1190 I = 1, 6 EDP(I) = 0 DO 1190 K = 1, 6 EDP(I) = EDP(I) + ALMBDA(I, K) * ED(K) 1190 CONTINUE C END FORCES DUE TO DISTRIBUTED LOADS IF (ABS(UDL(N)) .GT. 0) THEN ED(1) = 0 ED(4) = 0 ED(2) = -UDL(N) * EL / 2 ED(5) = ED(2) ED(3) = -UDL(N) * EL ** 2 / 12 ED(6) = -ED(3) ELSE DO 1200 K = 1, 6 1200 ED(K) = 0 END IF DO 1210 I = 1, 6 EF(I) = ED(I) DO 1210 K = 1, 6 EF(I) = EF(I) + SEP(I, K) * EDP(K) 1210 CONTINUE WRITE(LOUT,'(1X,A,I4)') ' Member #', N DO 1220 I = 1, 2 II = (I - 1) * 3 WRITE(LOUT, '(1X,3E15.4)') EF(II + 1), EF(II + 2), EF(II + 3) 1220 CONTINUE 1230 CONTINUE CLOSE(LOUT) END SUBROUTINE ELSTIF(N,NOC,X,MAT,PM,ARIN,ALMBDA,SE,SEP,EL,ISTF) C ===== SUBROUTINE ELEMENT STIFFNESS ===== DIMENSION X(100,2),NOC(100,2),MAT(100),PM(10,5),ARIN(100,2) DIMENSION SE(6,6),SEP(6,6),DCOS(3,3),ALMBDA(6,6) C----- Element Stiffness Matrix ----- I1 = NOC(N, 1) I2 = NOC(N, 2) M = MAT(N) X21 = X(I2, 1) - X(I1, 1) Y21 = X(I2, 2) - X(I1, 2) EL = SQRT(X21 * X21 + Y21 * Y21) EAL = PM(M, 1) * ARIN(N, 1) / EL EIZL = PM(M, 1) * ARIN(N, 2) / EL DO 3000 I = 1, 6 DO 3000 J = 1, 6 SEP(I, J) = 0 3000 CONTINUE SEP(1, 1) = EAL SEP(1, 4) = -EAL SEP(4, 4) = EAL SEP(2, 2) = 12 * EIZL / EL ** 2 SEP(2, 3) = 6 * EIZL / EL SEP(2, 5) = -SEP(2, 2) SEP(2, 6) = SEP(2, 3) SEP(3, 3) = 4 * EIZL SEP(3, 5) = -6 * EIZL / EL SEP(3, 6) = 2 * EIZL SEP(5, 5) = 12 * EIZL / EL ** 2 SEP(5, 6) = -6 * EIZL / EL SEP(6, 6) = 4 * EIZL DO 3010 I = 1, 6 DO 3010 J = I, 6 SEP(J, I) = SEP(I, J) 3010 CONTINUE C CONVERT ELEMENT STIFFNESS MATRIX TO GLOBAL SYSTEM DCOS(1, 1) = X21 / EL DCOS(1, 2) = Y21 / EL DCOS(1, 3) = 0 DCOS(2, 1) = -DCOS(1, 2) DCOS(2, 2) = DCOS(1, 1) DCOS(2, 3) = 0 DCOS(3, 1) = 0 DCOS(3, 2) = 0 DCOS(3, 3) = 1 DO 3020 I = 1, 6 DO 3020 J = 1, 6 ALMBDA(I, J) = 0 3020 CONTINUE DO 3030 K = 1, 2 IK = 3 * (K - 1) DO 3030 I = 1, 3 DO 3030 J = 1, 3 ALMBDA(I + IK, J + IK) = DCOS(I, J) 3030 CONTINUE IF (ISTF .EQ. 1) GO TO 3070 DO 3040 I = 1, 6 DO 3040 J = 1, 6 SE(I, J) = 0 DO 3040 K = 1, 6 SE(I, J) = SE(I, J) + SEP(I, K) * ALMBDA(K, J) 3040 CONTINUE DO 3050 I = 1, 6 DO 3050 J = 1, 6 SEP(I, J) = SE(I, J) 3050 CONTINUE DO 3060 I = 1, 6 DO 3060 J = 1, 6 SE(I, J) = 0 DO 3060 K = 1, 6 3060 SE(I, J) = SE(I, J) + ALMBDA(K, I) * SEP(K, J) 3070 CONTINUE RETURN END SUBROUTINE BAND(A, B, IMAX, NBW, N) C ----- Equation Solving Using Banded Storage DIMENSION A(IMAX,NBW), B(IMAX) N1 = N - 1 PRINT *, '*** FORWARD ELIMINATION ***' DO 2100 K = 1, N1 NK = N - K + 1 IF (NK .GT. NBW) NK = NBW DO 2100 I = 2, NK C1 = A(K, I) / A(K, 1) I1 = K + I - 1 DO 2000 J = I, NK J1 = J - I + 1 2000 A(I1, J1) = A(I1, J1) - C1 * A(K, J) 2100 B(I1) = B(I1) - C1 * B(K) PRINT *, '*** BACK SUBSTITUTION ***' B(N) = B(N) / A(N, 1) DO 2300 KK = 1, N1 K = N - KK C1 = 1 / A(K, 1) B(K) = C1 * B(K) NK = N - K + 1 IF (NK .GT. NBW) NK = NBW DO 2200 J = 2, NK B(K) = B(K) - C1 * A(K, J) * B(K + J - 1) 2200 CONTINUE 2300 CONTINUE RETURN END