TALK=f;RUN(1,1) DISPLAY Problem: Torsion of the long thin Beam (Plate). 1. Comparison - a analytical solution (Timoshenko, Paragraph 108) 2. Bottom of the beam is fixed (U1=V1=W1 = 0), Top - set tangential stress TauYZ for V1. ENDDIS ************************************************************ Group 1. Run Title and Number ************************************************************ TEXT(3D TORSION of thin Beam; s305) libref=305 title Declarations and settings REAL(LX,LY,LZ,POISSON,YOUNG) REAL(Momnt,TAUZ,GG,SHRYZ) LX=2.e-3 LZ=50.e-3 LY=10.e-3 YOUNG = 1/0.5E-11 ! Young's modulus POISSON=0.3 ! Poisson's ratio GG = YOUNG/(2.0*(1.0+POISSON)) ********************************* Momnt = 10.0 * LX TAUZ= 3*Momnt/LY/(LX**3)/GG TAUZ SHRYZ = 2*GG*TAUZ ******* plus SHRXZ (see Timoshenko, Paragraph 108 !) SHRYZ = 2*SHRYZ SHRYZ ********************************* INTEGER(NXBODY,NYBODY,NZBODY) ************************************************************ Group 2. Time dependence STEADY = T ************************************************************ Group 3. X-Direction Grid Spacing CARTES = T NXBODY = 6 GRDPWR(X,NXBODY,LX,1) ************************************************************ Group 4. Y-Direction Grid Spacing NYBODY = 8 GRDPWR(Y,NYBODY,LY,1) ************************************************************ Group 5. Z-Direction Grid Spacing NZBODY = 12 GRDPWR(Z,NZBODY,LZ,1) ************************************************************ Group 7. Variables: STOREd,SOLVEd,NAMEd ONEPHS = T SOLVE(P1,V1,U1,W1) SOLUTN(P1 ,Y,Y,Y,N,N,N) SOLUTN(U1 ,Y,Y,Y,N,N,Y) SOLUTN(V1 ,Y,Y,Y,N,N,Y) SOLUTN(W1 ,Y,Y,Y,N,N,Y) STORE(PRPS,DRH1,VISL) ! Necessary to save storage DRH1,VISL STORE(STRX,STRY,STRZ,STXY,STXZ,STYZ) STORE(EPSY,EPSX,EPSZ) STORE(U1T,V1T,U1/T,V1/T) ************************************************************ GROUP 8. ITERATION NUMBERS ETC RESFAC=1.e-7 RESREF(V1)=0.0 RESREF(U1)=0.0 ! to prevent premature exit LITER(V1) = 20 ! from solver LITER(U1) = 20 LITER(P1) = 20 RESREF(W1)=0.0 LITER(W1) = 20 ************************************************************ GROUP 9. PROPERTIES CSG10='Q1' ! materials with various POISSON ratios MATFLG=T;NMAT=1 160 7800.0 0.3 473.0 43.0 1.0e-5 0.5e-11 ************************************************************ GROUP 11. INITIAL VALUES fiinit(p1)=0.0 fiinit(u1)=0.0 fiinit(v1)=0.0 fiinit(w1)=0.0 FIINIT(PRPS)=160 ************************************************************ GROUP 13. BOUNDARY & SPECIAL SOURCES char(FormU,FormV) FormU=-:TAUZ:*ZG*(YG-0.5*:LY:) FormV=:TAUZ:*ZG*(XG-0.5*:LX:) PATCH(DOWNZ,LWALL,1,NX,1,NY,1,1,1,1) ! z=0 - fixed ALL COVAL(DOWNZ,W1,FIXVAL,0.0) PATCH(DOWN0X,CELL,1,NX-1,1,NY,1,1,1,1) (SOURCE of U1 at DOWN0X is COVAL(FIXVAL,:FormU:)) PATCH(DOWN0Y,CELL,1,NX,1,NY-1,1,1,1,1) (SOURCE of V1 at DOWN0Y is COVAL(FIXVAL,:FormV:)) PATCH(UP0Y,HIGH,1,NX,1,NY,NZ,NZ,1,1) ! UP - Moment of two force (SOURCE of V1 at UP0Y is COVAL(FIXFLU,:SHRYZ:*(XG-0.5*:LX:))) ************************************************************ GROUP 15. TERMINATE SWEEPS LSWEEP = 4500 ISG21=LSWEEP ************************************************************ GROUP 17. RELAXATION #CONPROM RELAX(P1 ,LINRLX, 1.000000E+00) spedat(rlxfac,rlxu1d,r,0.5) spedat(rlxfac,rlxv1d,r,0.5) spedat(rlxfac,rlxw1d,r,0.5) ************************************************************ GROUP 19. DATA TRANSMITTED TO GROUND STRA = T PARSOL = F ISG52 = 3 ! probe & res #maxmin ************************************************************ GROUP 23.FIELD PRINT-OUT & PLOT CONTROL TSTSWP = - 1 ! graphic-mode NYPRIN = 1 NXPRIN = 1 NZPRIN = 1 IXMON = NX-2 IYMON = 2 IZMON = NZ-2 #conprom inform7begin **** CALCULATE analytical solution *** (STORED VAR U1T IS :FormU:) (STORED VAR V1T IS :FormV:) (STORED VAR U1/T IS U1/(U1T+1.e-20)) (STORED VAR V1/T IS V1/(V1T+1.e-20)) inform7end restrt(all) STOP