/COM,ANSYS MEDIA REL. 2024R2 (05/10/2024) REF. VERIF. MANUAL: REL. 2024R2 /VERIFY,VM312 /TITLE,VM312, ELECTROSTATIC-STRUCTURAL ANALYSIS OF A SPHERICAL CAPACITOR /COM, /COM, REF: ANY ELECTROSTATICS TEXTBOOK /COM, /OUT,vm312_scratch _GEOMGEN=0 ! SET THIS TO 1 TO UPDATE CDB FILE *IF,_GEOMGEN,EQ,1,THEN PI=ACOS(-1) A=1 ! INNER RADIUS, UM B=2 ! OUTER RADIUS, UM K=60 ! SPRING CONSTANT, KG/S^2 M=1E-4 ! MASS, KG PER=8.854E-6 ! FREE SPACE PERMITTIVITY, PF/UM VDC=397 ! DC-BIAS VOLTAGE, VOLT VLP=20 ! VOLTAGE APPLIED IN LP ANALYSIS, VOLT ULP=0.02 ! RADIAL DISPLACEMENT APPLIED IN LP ANALYSIS, UM FLP=1.3 ! FORCE APPLIED IN LP HARMONIC ANALYSIS, UN FRQ=50 ! FREQUENCY OF HARMONINC LOAD, HZ NDIV1=3 ! NUMBER OF ELEMENTS ALONG RADIUS NDIV2=10 ! NUMBER OF ELEMENTS ALONG CIRCUMFERENCE NS=25 ! TOTAL NUMBER OF SUBSTEPS FOR NONLINEAR STATIC ANALYSIS NS2=19 ! SUBSTEP TO RESTART FROM IN LP ANALYSIS ! TO CREATE WHITE BACKGROUND /RGB,INDEX,100,100,100, 0 /RGB,INDEX, 80, 80, 80, 13 /RGB,INDEX, 60, 60, 60, 14 /RGB,INDEX, 0, 0, 0, 15 /PREP7 ET,1,226,1001 KEYOP,1,4,1 SPHERE,A,B,0,90 SPHERE,A,B,90,180 SPHERE,A,B,180,270 SPHERE,A,B,270,360 NUMMRG,KP VSBW,ALL,,DELETE CSYS,2 LSEL,S,LOC,X,A+(B-A)/2 LESIZE,ALL,,,NDIV1 LSEL,INVE LESIZE,ALL,,,NDIV2 ALLS MSHAPE,0 ESIZE,0.5 VMESH,ALL EMUNIT,EPZRO,1 MP,EX,1,1E-6 MP,PRXY,1,0 MP,PERX,1,PER MP,DENS,1,0 ET,2,14,,,0 ! SPRING ELEMENT, UX, UY, UZ DOFS ET,3,21,,,2 ! MASS ELEMENT, UX, UY, UZ DOFS ! GENERATE LUMPED ELEMENTS, SPRINGS AND MASSES *GET,NMAX,NODE,0,NUM,MAX CSYS,2 ! SPHERICAL CS NROTATE,ALL NSEL,S,LOC,X,B *GET,NMAXS,NODE,0,COUNT,MAX R,2,K/NMAXS ! NODAL STIFFNESS R,3,M/NMAXS ! NODAL MASS _J=0 *DO,_I,1,NMAXS N1=NDNEXT(_J) _J=N1 N2=N1+NMAX N,N2,B+1,NY(N1),NZ(N1) TYPE,2 REAL,2 E,N2,N1 TYPE,3 REAL,3 E,N1 *ENDDO NSEL,ALL NSEL,S,LOC,X,B+1 D,ALL,UX,0 NSEL,S,LOC,X,A D,ALL,VOLT,0.0 D,ALL,UX ALLS NSEL,S,LOC,X,B CP,1,VOLT,ALL CP,2,UX,ALL NLOAD=NDNEXT(0) ALLS D,ALL,UY,0 D,ALL,UZ,0 CSYS,0 /SHOW,PNG /VIEW,1,1,1,1 ESEL,S,TYPE,,1 EPLOT ESEL,ALL EPLOT /SHOW,CLOSE FINISH CDWRITE,db,vm312,cdb *ELSE CDREAD,db,vm312,cdb *ENDIF /COM, /COM, ********************************************** /COM, *** NONLINEAR STATIC ANALYSIS *** /COM, ********************************************** /COM, /SOLU D,NLOAD,VOLT,VDC ALLSE ANTYPE,STATIC RESCONTROL,DEFINE,ALL,ALL OUTRES,ALL,ALL NLGEOM,ON NSUB,NS,20*NS,NS AUTOTS,ON SOLVE FINISH /POST26 NSOL,3,NLOAD,VOLT,,VOLT NSOL,4,NLOAD,U,X,'UX VS VOLT' PRVAR,3,4 /SHOW,PNG XVAR,3 /AXLAB,X,VOLTAGE /AXLAB,Y,DISPLACEMENT /XRANGE,0,400 /YRANGE,0,-(B-A)/2 PLVAR,4 /SHOW,CLOSE VGET,VEC1,3 VGET,VEC2,4 *GET,NS,ACTIVE,0,SET,NSET RATIO=0 *DO,I,1,NS,1 U=-VEC2(I) V=((B-U)/A-1)*SQRT(K*U/(2*PI*PER)) ! EQUATION (10) RATIO=RATIO+V/VEC1(I) *ENDDO RATIO=RATIO/NS FINISH PARSAV SAVE /COM, /COM, ********************************************** /COM, *** LP STATIC ANALYSIS *** /COM, *** (VOLTAGE LOAD) *** /COM, ********************************************** /COM, RESUME /SOLU ANTYP,STATIC,RESTART,1,NS2,PERTURB PERTURB,STATIC SOLVE,ELFORM PARRES D,NLOAD,VOLT,VLP SOLVE FINISH PARRES /POST1 RSYS,2 FILE,,rst SET,1,NS2 U=-UX(NLOAD) *GET,V,NODE,NLOAD,VOLT *GET,Q,NODE,NLOAD,RF,CHRG C=-Q/V F=K*U FILE,,rstp SET,LAST DU=-UX(NLOAD) FINISH PARSAV /COM, /COM, ********************************************** /COM, *** LP STATIC ANALYSIS *** /COM, *** (DISPLACEMENT LOAD) *** /COM, ********************************************** /COM, /SOLU ANTYP,STATIC,RESTART,1,NS2,PERTURB PERTURB,STATIC SOLVE,ELFORM PARRES DDELE,NLOAD,VOLT D,NLOAD,UX,-ULP SOLVE FINISH PARRES /POST1 FILE,,rstp SET,LAST *GET,DV,NODE,NLOAD,VOLT FINISH PARSAV /COM, /COM, ********************************************** /COM, *** LP MODAL ANALYSIS *** /COM, *** (RESONANCE) *** /COM, ********************************************** /COM, /SOLU ANTYP,STATIC,RESTART,1,NS2,PERTURB PERTURB,MODAL SOLVE,ELFORM PARRES D,NLOAD,VOLT,0 MODOPT,LANB,1 SOLVE FINI PARRES /POST1 SET,LAST *GET,FRQ1,MODE,1,FREQ FINISH PARSAV /COM, /COM, ********************************************** /COM, *** LP MODAL ANALYSIS *** /COM, *** (ANTI-RESONANCE) *** /COM, ********************************************** /COM, /SOLU ANTYP,STATIC,RESTART,1,NS2,PERTURB PERTURB,MODAL SOLVE,ELFORM PARRES DDELE,NLOAD,VOLT MODOPT,LANB,1 SOLVE FINI PARRES /POST1 SET,LAST *GET,FRQ2,MODE,1,FREQ FINISH PARSAV /COM, /COM, ****************************************** /COM, *** LP HARMONIC ANALYSIS *** /COM, *** (ACTUATOR MODE) *** /COM, ****************************************** /COM, /SOLU ANTYP,STATIC,RESTART,1,NS2,PERTURB PERTURB,HARM SOLVE,ELFORM PARRES D,NLOAD,VOLT,VLP HARFRQ,FRQ NSUB,1 SOLVE FINISH PARRES /POST1 RSYS,2 FILE,,rstp SET,LAST UHR=-UX(NLOAD) FINISH PARSAV /COM, /COM, ****************************************** /COM, *** LP HARMONIC ANALYSIS *** /COM, *** (SENSOR MODE) *** /COM, ****************************************** /COM, /SOLU ANTYP,STATIC,RESTART,1,NS2,PERTURB PERTURB,HARM SOLVE,ELFORM PARRES DDELE,NLOAD,VOLT F,NLOAD,FX,-FLP HARFRQ,FRQ NSUB,1 SOLVE FINISH PARRES /POST1 RSYS,2 FILE,,rstp SET,LAST VHR=VOLT(NLOAD) FINISH ! ANALYTICAL SOLUTION C_TAR=4*PI*PER/(1/A-1/(B-U)) ! EQUATION (6) F_TAR=2*PI*PER*V**2/((B-U)/A-1)**2 ! EQUATION (8) KR=K-2*F_TAR/(B-A-U) ! EQUATION (18) DU_TAR=(2*F_TAR*VLP/V)/KR ! EQUATION (17) DV_TAR=-V*A/(B-U)*ULP/(B-A-U) ! EQUATION (20) FRQ1_TAR=1/(2*PI)*SQRT(KR/M) ! EQUATION (23) KA=K-2*F_TAR/(B-U) ! EQUATION (26) FRQ2_TAR=1/(2*PI)*SQRT(KA/M) ! EQUATION (27) W=2*PI*FRQ UHR_TAR=1/(-W**2*M+KR)*2*F_TAR*VLP/V ! EQUATION (28) VHR_TAR=-V*A/((B-U)*(B-A-U))*FLP/(-W**2*M+KA) ! EQUATION (32) PARSAV /OUT,vm312,vrt /COM, /COM, ---------------------------- VM312 RESULTS COMPARISON ---------------------- /COM, /COM, | TARGET | MECHANICAL APDL | RATIO /COM, | | | /COM, NONLINEAR STATIC ANALYSIS TILL PULL-IN VOLTAGE: /COM, | | | *VWRITE,RATIO (2X,'DISP-VOLT CURVE',5X,'|',14X,'|',19X,'|',2X,F9.6) *VWRITE,C_TAR,C,C/C_TAR (2X,'CAPACITANCE AT V_DC',1X,'|',1X,E12.6,1X,'|',3X,E12.6,4X,'|',2X,F9.6) *VWRITE, (2X,'ELECTROSTATIC FORCE',1X,'|',14X,'|',19X,'|') *VWRITE,F_TAR,F,F/F_TAR (2X,'AT V_DC',13X,'|',3X,F8.5,3X,'|',5X,F8.5,6X,'|',2X,F9.6) /COM, | | | /COM, LINEAR PERTURBATION STATIC ANALYSIS, VOLTAGE LOAD: /COM, | | | *VWRITE,DU_TAR,DU,DU/DU_TAR (2X,'DISPLACEMENT',8X,'|',2X,F10.7,2X,'|',3X,F10.7,6X,'|',2X,F9.6) /COM, | | | /COM, LINEAR PERTURBATION STATIC ANALYSIS, DISPLACEMENT LOAD: /COM, | | | *VWRITE,DV_TAR,DV,DV/DV_TAR (2X,'VOLTAGE',13X,'|',3X,F8.5,3X,'|',5X,F8.5,6X,'|',2X,F9.6) /COM, | | | /COM, LINEAR PERTURBATION MODAL ANALYSIS, RESONANCE: /COM, | | | *VWRITE,FRQ1_TAR,FRQ1,FRQ1/FRQ1_TAR (2X,'FREQUENCY',11X,'|',2X,F9.3,3X,'|',4X,F9.3,6X,'|',2X,F9.6) /COM, | | | /COM, LINEAR PERTURBATION MODAL ANALYSIS, ANTIRESONANCE: /COM, | | | *VWRITE,FRQ2_TAR,FRQ2,FRQ2/FRQ2_TAR (2X,'FREQUENCY',11X,'|',2X,F9.3,3X,'|',4X,F9.3,6X,'|',2X,F9.6) /COM, | | | /COM, LINEAR PERTURBATION HARMONIC ANALYSIS, ACTUATOR MODE: /COM, | | | *VWRITE,UHR_TAR,UHR,UHR/UHR_TAR (2X,'DISPLACEMENT',8X,'|',2X,F10.7,2X,'|',3X,F10.7,6X,'|',2X,F9.6) /COM, | | | /COM, LINEAR PERTURBATION HARMONIC ANALYSIS, SENSOR MODE: /COM, | | | *VWRITE,VHR_TAR,VHR,VHR/VHR_TAR (2X,'VOLTAGE',13X,'|',2X,F9.5,3X,'|',4X,F9.5,6X,'|',2X,F9.6) /COM, /OUT *LIST,vm312,vrt /OUT,vm312_scratch,,,APPEND FINI