/COM,ANSYS MEDIA REL. 2024R2 (05/10/2024) REF. VERIF. MANUAL: REL. 2024R2 /VERIFY,VM258 /TITLE,VM258,SPIN-UP MANEUVER OF A FLEXIBLE BEAM /COM, J.C. SIMO AND L. VU-QUOC /COM ON THE DYNAMICS IN SPACE OF RODS UNDERGOING LARGE MOTIONS- /COM, -A GEOMETRICALLY EXACT APPROACH /COM, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, VOL. 66, /COM, 125-161 (1988. /PREP7 ET,1,189 !3D QUADRATIC FINITE STRAIN BEAM ET,2,184,16 !JOINT ELEMENT TYPE GENERAL ET,3,184,6 !JOINT ELEMENT TYPE REVOLUTE KEYOPT,3,4,1 !Z-AXIS REVOLUTE JOINT N,1,0.0,0.0 !NODES FOR CANTILEVER BEAM N,9,10.0,0.0 FILL,1,9 SECT,1,GENB,ELASTIC !NONLINEAR GENERAL BEAM SECTION (ELASTIC) BSAX,0.0,0.0 !BEAM SECTION AXIAL STIFFNESS (AXIAL STRAIN/AXIAL FORCE) BSAX,1.0,2.8E7 BSM1,0.0,0.0 !BEAM SECTION BENDING STIFFNESS FOR PLANE XZ(CURVATURE/BENDING MOMENT) BSM1,1.0,1.4E4 BSM2,0.0,0.0 !BEAM SECTION BENDING STIFFNESS FOR PLANE XY(CURVATURE/BENDING MOMENT) BSM2,1.0,1.4E4 BSTQ,0.0,0.0 !BEAM SECTION TORSION STIFFNESS (TWIST/TORQUE) BSTQ,1.0,1.4E4 BSS1,0.0,0.0 !BEAM SECTION SHEAR STIFFNESS FOR PLANE XZ (SHEAR STRAIN/TRANSVERSE SHEAR FORCE) BSS1,1.0,1.0E7 BSS2,0.0,0.0 !BEAM SECTION SHEAR STIFFNESS FOR PLANE XY (SHEAR STRAIN/ TRANSVERSE SHEAR FORCE) BSS2,1.0,1.0E7 BSMD,1.2 !BEAM SECTION MASS DENSITY (MASS/LENGTH) TYPE,1 !BEAM ELEMENT DEFINITION SECNUM,1 EN,1,1,3,2 ENGEN,1,4,2,1 SECTYPE,2,JOIN,GENE,GENE !GENERAL JOINT SECTION SECJOIN, !LOCAL COORDINATE SYSTEM=GLOBAL CARTESIAN (DEFAULT) TYPE,2 !GENERAL JOINT ELEMENT DEFINITION SECNUM,2 EN,201,1,9 SECTYPE,3,JOIN,REVO,REVO !REVOLUTE JOINT SECTION SECJOIN, !LOCAL COORDINATE SYSTEM=GLOBAL CARTESIAN(DEFAULT) TYPE,3 !REVOLUTE JOINT ELEMENT DEFINITION SECNUM,3 EN,301, ,1 !GROUNDED JOINT ELEMENT C***DEFINE ROTATION ANGLE AS A FUNCTION OF TIME *DIM,FUNC1,TABLE,3001,1,1 !FIRST TABULAR LOAD: (6/15)*(((TIME*TIME)/2)+((15/(2*PI))^2)*(COS((2*TIME*PI)/15)-1)) FUNC1(0,0,1) = 0.0 FUNC1(0,1,1) = 0.0 PI = ACOS(-1.0) OM = (2.0*PI)/15.0 A = 0.4 B = 45.0/(2.0*PI*PI) *DO,II,1,3001 T1 = (II-1)*0.005 FUNC1(II,0,1) = T1 !TIME T2 = A*((T1*T1)/2.0) T3 = B*(COS(OM*T1)-1.0) FUNC1(II,1,1) = T2 + T3 !VALUE *END DO !SECOND TABULAR LOAD: 6*TIME-45 *DIM,FUNC2,TABLE,2,1,1 FUNC2(0,0,1) = 0.0 FUNC2(0,1,1) = 0.0 FUNC2(1,0,1) = 15.0 !TIME VALUES FUNC2(2,0,1) = 30.0 FUNC2(1,1,1) = 45 !ROTATION VALUES FUNC2(2,1,1) = 135.0 FINISH C*** PERFORM SOLUTION USING HHT ALGORITHM /SOLU ANTYPE,TRANS !TRANSIENT ANALYSIS NLGEOM,ON !LARGE DEFLECTION ! LOAD STEP 1--ROTATION WITH ANGULAR ACCELERATION (SMALL CENTRIFUGAL FORCE) DJ,301,ROTZ,%FUNC1% !APPLY FIRST TABULAR LOAD TRNOPT,FULL, , , , ,HHT !HHT TIME INTEGRATION SCHEME TINTP,0.1 !10% NUMERICAL DAMPING TIME,10 AUTOTS,ON !AUTO TIME STEPPING MIDTOL,ON,2 !MIDSTEP RESIDUAL CHECK DELTIM,0.005,0.002,0.02 OUTRES,ALL,2 !WRITE RESULTS EVERY 2 SUBSTEPS /OUT,SCRATCH SOLVE /OUT TIME,15 ! LOAD STEP 2--ROTATION WITH ANGULAR ACCELERATION (INTERMEDIATE CENTRIFUGAL FORCE) DELTIM,0.005,0.005,0.01 OUTRES,ALL,2 /OUT,SCRATCH SOLVE /OUT ! LOAD STEP 3--STEADY MOTION AT CONSTANT ANGULAR VELOCITY DJ,301,ROTZ,%FUNC2% !APPLY SECOND TABULAR LOAD TIME,18 OUTRES,ALL,2 /OUT,SCRATCH SOLVE /OUT FINISH ! EXTRACT TIME POINTS FROM Mechanical APDL RESULTS CLOSEST TO THE REFERENCE TIME DATA *DIM,TIME2,ARRAY,12 /POST1 *DO,K,1,12,1 T = K*1.5 SET,NEAR, , , ,T *GET,TIME2(K),ACTIVE,0,SET,TIME *END DO FINISH /POST26 ESOL,2,201,9,SMISC,61,U1 !AXIAL DISPLACEMENT OF BEAM TIP ESOL,3,201,9,SMISC,62,U2 !TRANSVERSE DISPLACEMENT OF BEAM TIP NSOL,4,9,ROT,Z,ROTZ9 !ROTATION OF BEAM BASE NSOL,5,1,ROT,Z,ROTZ1 !ROTATION OF BEAM TIP ! ROTATION OF BEAM TIP RELATIVE TO BASE--CONVERTED TO DEGREES ADD,6,5,4,,ROTZ, , ,57.2957795131,-57.2957795131,0 /OUT /TITLE,SPIN-UP OF A FLEXIBLE BEAM: ROTATION ANGLE VS. TIME /AXLAB,Y,ROTATION ANGLE PLVAR,5 /TITLE, TIME HISTORY OF AXIAL DISPLACEMENT OF BEAM TIP /AXLAB,Y,AXIAL DISPLACEMENT PLVAR,2 !COMPARE THIS PLOT WITH FIGURE 6 IN REFERENCE /TITLE,TIME HISTORY OF TRANSVERSE DISPLACEMENT OF BEAM TIP /AXLAB,Y,TRANSVERSE DISPLACEMENT PLVAR,3 !COMPARE THIS PLOT WITH FIGURE 6 IN REFERENCE /TITLE,TIME HISTORY OF RELATIVE ROTATION OF BEAM TIP /AXLAB,Y,RELATIVE ROTATION PLVAR,6 !COMPARE THIS PLOT WITH FIGURE 6 IN REFERENCE *GET,UXMIN,VARI,2,EXTREM,VMIN ! MIN AXIAL DISPLACEMENT AT BEAM TIP *GET,TXMIN,VARI,2,EXTREM,TMIN ! TIME CORRESPONDING TO MIN AXIAL DISPLACEMENT *GET,UYMIN,VARI,3,EXTREM,VMIN ! MIN TRANSVERSE DISPLACEMENT AT BEAM TIP *GET,TYMIN,VARI,3,EXTREM,TMIN ! TIME CORRESPONDING TO MIN TRANSVERSE DISPLACEMENT *GET,ROTZMAX,VARI,6,EXTREM,VMAX ! MAX RELATIVE ROTATION *GET,TZMAX,VARI,6,EXTREM,TMAX ! TIME CORRESPONDING TO MAXIMUM RELATIVE ROTATION *GET,UXMAX,VARI,2,EXTREM,VMAX ! MAX STRETCH *GET,TXMAX,VARI,2,EXTREM,TMAX ! TIME CORRESPONDING TO MAX STRETCH *DIM,LABEL1,CHAR,2,2 *DIM,VALUE1,,2,3 LABEL1(1,1) = 'TIME','TIP DISP' LABEL1(1,2) = ' (sec)','UX ' *VFILL,VALUE1(1,1),DATA,6.7,-0.019 *VFILL,VALUE1(1,2),DATA,TXMIN,UXMIN *VFILL,VALUE1(1,3),DATA,ABS(TXMIN/6.7),ABS(UXMIN/(-0.019)) FINISH SAVE,TABLE_1 /POST26 *DIM,LABEL2,CHAR,2,2 *DIM,VALUE2,,2,3 LABEL2(1,1) = 'TIME','TIP DISP' LABEL2(1,2) = ' (sec)','UY ' *VFILL,VALUE2(1,1),DATA,6.85,-0.575 *VFILL,VALUE2(1,2),DATA,TYMIN,UYMIN *VFILL,VALUE2(1,3),DATA,ABS(TYMIN/6.85),ABS(UYMIN/(-0.575)) FINISH SAVE,TABLE_2 /POST26 *DIM,LABEL3,CHAR,2,2 *DIM,VALUE3,,2,3 LABEL3(1,1) = 'TIME','REL' LABEL3(1,2) = ' (sec)','ROTZ(deg)' *VFILL,VALUE3(1,1),DATA,6.7,4.424 *VFILL,VALUE3(1,2),DATA,TZMAX,ROTZMAX *VFILL,VALUE3(1,3),DATA,ABS(TZMAX/6.7),ABS(ROTZMAX/4.424) FINISH SAVE,TABLE_3 /POST26 *DIM,LABEL4,CHAR,2,2 *DIM,VALUE4,,2,3 LABEL4(1,1) = 'TIME','STRETCH' LABEL4(1,2) = ' (sec)','UX' *VFILL,VALUE4(1,1),DATA,16,5.14E-4 *VFILL,VALUE4(1,2),DATA,TXMAX,UXMAX *VFILL,VALUE4(1,3),DATA,ABS(TXMAX/16),ABS(UXMAX/5.14E-4) FINISH SAVE,TABLE_4 RESUME,TABLE_1 /COM /OUT,vm258,vrt /COM,------------------- VM258 RESULTS COMPARISON -------------- /COM, /COM, | TARGET | Mechanical APDL | RATIO /COM, /COM,PEAK AXIAL DISPLACEMENT *VWRITE,LABEL1(1,1),LABEL1(1,2),VALUE1(1,1),VALUE1(1,2),VALUE1(1,3) (1X,A8,A8,' ',F10.4,' ',F14.4,' ',1F15.3) /NOPR RESUME,TABLE_2 /GOPR /COM, /COM,PEAK TRANSVERSE DISPLACEMENT *VWRITE,LABEL2(1,1),LABEL2(1,2),VALUE2(1,1),VALUE2(1,2),VALUE2(1,3) (1X,A8,A8,' ',F10.4,' ',F14.4,' ',1F15.3) /NOPR RESUME,TABLE_3 /GOPR /COM, /COM,PEAK RELATIVE ROTATION *VWRITE,LABEL3(1,1),LABEL3(1,2),VALUE3(1,1),VALUE3(1,2),VALUE3(1,3) (1X,A8,A8,' ',F10.4,' ',F14.4,' ',1F15.3) /NOPR RESUME,TABLE_4 /GOPR /COM, /COM,STEADY-STATE STRETCH *VWRITE,LABEL4(1,1),LABEL4(1,2),VALUE4(1,1),VALUE4(1,2),VALUE4(1,3) (1X,A8,A8,' ',F10.4,' ',F14.4,' ',1F15.3) /COM,----------------------------------------------------------- /COM, /OUT FINISH *LIST,vm258,vrt /DELETE,TABLE_1 /DELETE,TABLE_2 /DELETE,TABLE_3 /DELETE,TABLE_4