PHOTON USE p gr ou z 1 con thex z 1 fil;.001 gr ou z 1 x 1 3 y 6 m gr ou z 1 x 8 m y 6 m msg Linear thermal expansion coefficient pause con cl;red con stif z 1 fil;.001 gr ou z 1 x 1 3 y 6 m gr ou z 1 x 8 m y 6 m msg Stiffnes ( Young's module ) contours pause con cl;red vec z 1 sh msg Velocity and displacement vectors pause vec cl;red con u1 z 1 fil;.001 gr ou z 1 x 1 3 y 6 m gr ou z 1 x 8 m y 6 m msg X-component displacement contours pause con cl;red con v1 z 1 fil;.001 gr ou z 1 x 1 3 y 6 m gr ou z 1 x 8 m y 6 m msg Y-component displacement contours pause con cl;red con dil z 1 fil;.001 gr ou z 1 x 1 3 y 6 m gr ou z 1 x 8 m y 6 m msg Dilatation contours pause con cl;red con epsx z 1 fil;.001 gr ou z 1 x 1 3 y 6 m gr ou z 1 x 8 m y 6 m msg X-strain contours pause con cl;red con epsy z 1 fil;.001 gr ou z 1 x 1 3 y 6 m gr ou z 1 x 8 m y 6 m msg Y-strain contours pause con cl;red con epst z 1 fil;.001 gr ou z 1 x 1 3 y 6 m gr ou z 1 x 8 m y 6 m msg Thermal strain contours pause con cl;red con strx z 1 fil;.001 gr ou z 1 x 1 3 y 6 m gr ou z 1 x 8 m y 6 m msg X-normal stress contours pause con cl;red con stry z 1 fil;.001 gr ou z 1 x 1 3 y 6 m gr ou z 1 x 8 m y 6 m msg Y-normal stress contours pause con cl;red con taxy z 1 fil;.001 gr ou z 1 x 1 3 y 6 m gr ou z 1 x 8 m y 6 m msg Shear stress contours pause msg Press E to end enduse >>>>>>>>>>>>>>>>>>>>>> Comment begins >>>>>>>>>>>>>>>>>>>> DISPLAY This case, deals with the calculations of the displacements and stresses in uniformly heated block composed the materials of different mechanical properties. It is used here as an example of extensive processing the calculation results with the aim to get the distribution of normal and shear stresses by the numerical differentiation of displacement field. The outcome is the stress fields which may be viewed by PHOTON. The use file for the latter is also supplied. ENDDIS The PLANT statements placed in Q1, below the headings "OUTPUT INFORMATION", mainly use the indicial operations. Besides, PLANT is used to initialise some fields and to introduce the displacement boundary conditions. PLANT information : * Data input groups used: 11, 13, 19 * Ground groups planted : 11, 13, 19-6 * Headings used : INIT??, SORC??, SCO6?? * Functions used : None * Commands used : None <<<<<<<<<<<<<<<<<<<<<<< Comment ends <<<<<<<<<<<<<<<<<<<<< ** LOAD(Z458) from the USER Input Library ***** To load case 458, type load(Z458) **** GROUP 1. Run title and other preliminaries TEXT(2D Stress in solid, XY plane CASE STUDY: Thermal stresses in composite solid block REAL(LENGTH,WIDTH,ALFA,TISO,STRNY,STRNX,STIFFN,STRSX,STRSY) REAL(NORTEM,SOUTEM,HEATSOR,POISSN) BOOLEAN(ISOTHER,TEMLIN,TEMSOR) TISO=100.0 LENGTH=1.0;WIDTH =1.0 STIFFN=2.e11 STRSY =-1.e8;STRSX=0.0 ALFA =1.e-05 ; RG(1)=ALFA STRNY =STRSY ; RG(2)=STRNY STRNX =STRSX ; RG(3)=STRNX POISSN=0.3333 ; RG(4)=POISSN NX =10 ; NY =10 ISOTHER=t;TEMLIN=f;TEMSOR=f GROUP 3. X-direction grid specification GRDPWR(X,NX,LENGTH,1.0) GROUP 4. Y-direction grid specification GRDPWR(Y,NY,WIDTH,1.0) GROUP 7. Variables stored, solved & named SOLVE(P1,U1,V1,TEM) Provide the storage for thermal expansion coefficient ,THEX, stiffnes, STIF, and Poisson ratio to be initialised for the presence of different materials STORE(THEX,STIF,POIS) STORE(CON1,CON2,CON3,CON4) GROUP 8. Terms (in differential equations) & devices TERMS(U1,Y,N,Y,Y,Y,Y) TERMS(V1,Y,N,Y,Y,Y,Y) terms(tem,n,n,y,p,p,p) GROUP 9. Properties of the medium (or media) ENUL=1. GROUP 11. Initialization of variable or porosity fields IF(ISOTHER) THEN iniadd=f PATCH(STELP,INIVAL,1,NX,1,NY,1,1,1,1) INIT (STELP,POIS,0.0,POISSN) PATCH(STELT,INIVAL,1,NX,1,NY,1,1,1,1) INIT (STELT,THEX,0.0,ALFA) PATCH(STELS,INIVAL,1,NX,1,NY,1,1,1,1) INIT (STELS,STIF,0.0,STIFFN) fiinit(tem)=TISO # PATCH(ALMT1,INIVAL,1,3,NY/2+1,NY,1,1,1,1) INIT (ALMT1,THEX,0.0,10.*ALFA) INIT (ALMT1,STIF,0.0,0.1*STIFFN) PATCH(ALMT2,INIVAL,8,NX,NY/2+1,NY,1,1,1,1) INIT (ALMT2,THEX,0.0,10.*ALFA) INIT (ALMT2,STIF,0.0,0.1*STIFFN) ENDIF GROUP 13. Boundary conditions and special sources ** Linear temperature field IF(TEMLIN) THEN PATCH(TEMPN,NWALL,1,NX,NY,NY,1,1,1,1) COVAL(TEMPN,TEM,1.0,0.0) PATCH(TEMPS,SWALL,1,NX,1,1,1,1,1,1) COVAL(TEMPS,TEM,1.0,1.0) ENDIF ** Source generated temperature field IF(TEMSOR) THEN PATCH(TEMPN,NWALL,1,NX,NY,NY,1,1,1,1) COVAL(TEMPN,TEM,1.0,0.0) PATCH(TEMSOR,VOLUME,1,NX,1,NY,1,1,1,1) COVAL(TEMSOR,TEM,FIXFLU,2.0) ENDIF PLANTBEGIN PATCH(STELC,INIVAL,1,NX,1,NY,1,1,1,1)VAL=(1.-RG(4))/((1.+RG(4))*(1-2.*RG(4))) INIT (STELC,CON1,0.0,GRND) VAL=RG(4)/((1.+RG(4))*(1-2.*RG(4))) INIT (STELC,CON2,0.0,GRND) VAL=1./(1.-2.*RG(4)) INIT (STELC,CON3,0.0,GRND) VAL=1./(2.*(1+RG(4))) INIT (STELC,CON4,0.0,GRND) Stress - in -Solid BC ---------------- WEST ---------------------------- ** Zero displacement at the west boundary PATCH(WESZD,WWALL,1,1,1,NY,1,1,1,1) COVAL(WESZD,U1,1.,0.0) ---------------- EAST ---------------------------- ** Normal stress at the east solid boundary PATCH(EASZN,EAST,NX-1,NX-1,1,NY,1,1,1,1) VAL=U1[-1,,]+0.333*(P1+4.*(THEX*TEM+RG(3)/STIF))*DXU2D COVAL(EASZN,U1,FIXVAL,GRND) ** Zero shear stress at the east boundary PATCH(EASZS,EAST,NX,NX,1,NY-1,1,1,1,1) VAL=-(U1[-1,+1,]-U1[-1,,])/DYG2D COVAL(EASZS,V1,FIXFLU,GRND) ** Dilatation at the east solid boundary PATCH(FXDEAS,EAST,NX,NX,2,NY-1,1,1,1,1) VAL=2.*(THEX*TEM-RG(3)/STIF)-1.5*(V1-V1[,-1,])/DYV2D COVAL(FXDEAS,P1,FIXVAL, grnd) PATCH(FXDEAC,EAST,NX,NX,1,1,1,1,1,1) VAL=2.*(THEX*TEM-RG(3)/STIF)-$ 1.5*(V1[,+1,]-V1)/DYV2D[,+1,] COVAL(FXDEAC,P1,FIXVAL, grnd) ---------------- NORTH ---------------------------- ** Normal stress at the free north boundary PATCH(NORZN,CELL,1,NX,NY-1,NY-1,1,1,1,1) VAL=V1[,-1,]+0.333*(P1+4.*(THEX*TEM+RG(2)/STIF))*DYV2D COVAL(NORZN,V1,FIXVAL,grnd) ** Zero shear stress at the free north boundary PATCH(NORZS,NORTH,1,NX-1,NY,NY,1,1,1,1) VAL=-(V1[+1,-1,]-V1[,-1,])/DXG2D COVAL(NORZS,U1,FIXFLU,GRND) ** Dilatation at the free north boundary PATCH(FDNW,NORTH,1,1,NY,NY,1,1,1,1) VAL=2.*(THEX*TEM-RG(2)/STIF)-$ 1.5*(U1[+1,,]-U1)/DXU2D[+1,,] COVAL(FDNW,P1,FIXVAL, grnd) PATCH(FDNOR,NORTH,2,NX-1,NY,NY,1,1,1,1) VAL=2.*(THEX*TEM-RG(2)/STIF)-1.5*(U1-U1[-1,,])/DXU2D COVAL(FDNOR,P1,FIXVAL, grnd) PATCH(FDNEC,NORTH,NX,NX,NY,NY,1,1,1,1) VAL=2.*(THEX*TEM-RG(2)/STIF)-$ 1.5*(U1[-1,,]-U1[-2,,])/DXU2D[-1,,] COVAL(FDNEC,P1,FIXVAL, grnd) ---------------- SOUTH ---------------------------- ** Zero displacement at the south symmetry PATCH(SOUZD,SWALL,1,NX,1,1,1,1,1,1) COVAL(SOUZD,V1,1.,0.0) ================================================== ** Volumetric mass source for dilatation PATCH(DILAT,VOLUME,1,nx,1,ny,1,1,1,1) VAL=-P1/CON3+THEX*TEM/CON4 COVAL(DILAT,P1,FIXFLU,GRND) =================================================== OUTPUT INFORMATION ** Dilatation STORE(DIL) DIL=-P1/CON3+THEX*TEM/CON4 ** Stress and strain calculations STORE(STRX,STRY,TAXY) STORE(EPSX,EPSY,EPST) * Thermal strains EPST=THEX*TEM REGION(1,NX,1,NY,1,1) * Normal strains EPSX=(U1-WEST(U1))/DXU2D REGION(2,NX-1,1,NY,1,1) EPSX=(U1[+1,,]-U1)/DXU2D[+1,,] REGION(1,1,1,NY,1,1) EPSX=(U1[-1,,]-U1[-2,,])/DXU2D[-1,,] REGION(NX,NX,1,NY,1,1) EPSY=(V1-SOUTH(V1))/DYV2D REGION(1,NX,2,NY-1,1,1) EPSY=(V1[,+1,]-V1)/DYV2D[,+1,] REGION(1,NX,1,1,1,1) EPSY=(V1[,-1,]-V1[,-2,])/DYV2D[,-1,] REGION(1,NX,NY,NY,1,1) * Normal stresses STRX=STIF*(CON1*EPSX+CON2*EPSY-CON3*EPST) REGION(1,NX,1,NY,1,1) STRY=STIF*(CON1*EPSY+CON2*EPSX-CON3*EPST) REGION(1,NX,1,NY,1,1) * Shear stresses STORE(DDYU,DDXV) == ddy.u == DDYU=0.25*((U1-U1[,-1,])/DYG2D[,-1,]+ $ (U1[,+1,]-U1)/DYG2D+(U1[-1,,]-$ U1[-1,-1,])/DYG2D[,-1,]+$ (U1[-1,+1,]-U1[-1,,])/DYG2D) REGION(2,NX-1,2,NY-1,1,1) DDYU=0.5*((U1-U1[,-1,])/DYG2D[,-1,]+$ (U1[,+1,]-U1)/DYG2D) REGION(1,1,2,NY-1,1,1) DDYU=(U1[,+1,]-U1)/DYG2D REGION(1,1,1,1,1,1) DDYU=(U1-U1[,-1,])/DYG2D[,-1,] REGION(1,1,NY,NY,1,1) DDYU=0.5*((U1[-1,,]-U1[-1,-1,])/DYG2D[,-1,]+$ (U1[-1,+1,]-U1[-1,,])/DYG2D) REGION(NX,NX,2,NY-1,1,1) DDYU=(U1[-1,+1,]-U1[-1,,])/DYG2D REGION(NX,NX,1,1,1,1) DDYU=(U1[-1,,]-U1[-1,-1,])/DYG2D[,-1,] REGION(NX,NX,NY,NY,1,1) DDYU=0.5*((U1-U1[,-1,])/DYG2D[,-1,]+$ (U1[-1,,]-U1[-1,-1,])/DYG2D[,-1,]) REGION(2,NX-1,NY,NY,1,1) DDYU=0.5*((U1[,+1,]-U1)/DYG2D+$ (U1[-1,+1,]-U1[-1,,])/DYG2D) REGION(2,NX-1,1,1,1,1) == ddx.v == DDXV=0.25*((V1[+1,-1,]-V1[,-1,] )/DXG2D+$ (V1[+1,,]-V1)/DXG2D+(V1[,-1,]-$ V1[-1,-1,])/DXG2D[-1,,]+$ (V1-V1[-1,,])/DXG2D[-1,,]) REGION(2,NX-1,2,NY-1,1,1) DDXV=(V1[+1,,] -V1)/DXG2D REGION(1,1,1,1,1,1) DDXV=0.5*((V1[+1,-1,]-V1[,-1,])/DXG2D+$ (V1[+1,,]-V1)/DXG2D) REGION(1,1,2,NY-1,1,1) DDXV=(V1[+1,-1,]-V1[,-1,] )/DXG2D REGION(1,1,NY,NY,1,1) DDXV=(V1-V1[-1,,])/DXG2D[-1,,] REGION(NX,NX,1,1,1,1) DDXV=0.5*((V1[,-1,]-V1[-1,-1,])/DXG2D[-1,,]+$ (V1-V1[-1,,])/DXG2D[-1,,]) REGION(NX,NX,2,NY-1,1,1) DDXV=(V1[,-1,] -V1[-1,-1,])/DXG2D[-1,,] REGION(NX,NX,NY,NY,1,1) DDXV=0.5*((V1[+1,,]-V1)/DXG2D+$ (V1-V1[-1,,])/DXG2D[-1,,]) REGION(2,NX-1,1,1,1,1) DDXV=0.5*((V1[+1,-1,]-V1[,-1,])/DXG2D+$ (V1[,-1,]-V1[-1,-1,])/DXG2D[-1,,]) REGION(2,NX-1,NY,NY,1,1) TAXY=STIF*CON4*(DDYU+DDXV) REGION(1,NX,1,NY,1,1) PLANTEND RELAX(P1,LINRLX,0.005) RELAX(U1,FALSDT,0.0005) RELAX(V1,FALSDT,0.0005) NAMSAT=MOSG GROUP 15. Termination of sweeps LSWEEP=3000 selref=f RESREF(P1)=1.E-8 RESREF(U1)=1.E-8;RESREF(V1)=1.E-8 tstswp=-1 GROUP 22. Spot-value print-out IYMON=NY-1 GROUP 23. Field print-out and plot control NXPRIN=1;NYPRIN=1 dmpstk=t DISTIL=T EX(P1)=4.671E-03; EX(U1)=3.079E-03; EX(V1)=6.590E-04 EX(DDXV)=2.347E-03; EX(DDYU)=3.255E-03; EX(EPST)=3.700E-03 EX(EPSY)=3.955E-03; EX(EPSX)=6.382E-03; EX(TAXY)=1.362E+08 EX(STRY)=3.664E+08; EX(STRX)=1.830E+08; EX(DIL)=8.618E-03 EX(CON4)=3.750E-01; EX(CON3)=2.999E+00; EX(CON2)=7.498E-01 EX(CON1)=1.500E+00; EX(POIS)=3.333E-01; EX(STIF)=1.460E+11 EX(THEX)=3.700E-05; EX(TEM)=1.000E+02 LIBREF=611 STOP