! AXISYMMETRIC PROBLEM ! PIEZOELECTRIC DISK ! Static problem ! Invert background from black to white /RGB,INDEX,100,100,100,0 /RGB,INDEX,0,0,0,15 ! Title of the problem /TITLE, PIEZOELECTRIC DISC ! Parameters for geometrical sizes (in SI system) H=0.002 ! thickness of the disk R=10*H ! radius of the disk ! Additional geometrical parameters R1=R/4 ! radius of the inner electrode surface R23=R/4 ! size along the radius of the electrode ring ! The value of applied electric potential VINP=1 ! Parameters of finite element mesh SM=1 ! scaling multiplier HDIV=8*SM ! Numbers of elements along the disk thickness ! (should be even number!) R1DIV=16*SM ! Numbers of elements along the radial direction from 0 to R1 R12DIV=32*SM ! Numbers of elements along the radial direction from R1 to R2 R23DIV=16*SM ! Numbers of elements along the radial direction from R2 to R ! Parameters for material constants of piezoceramics PZT-4 ! (all data in SI system) RO=7.5e3 ! density C11E=13.9e10 ! elastic moduli C12E=7.78e10 C13E=7.43e10 C33E=11.5e10 C66E=(C11E-C12E)/2. C44E=2.56e10 E31=-5.2 ! piezomoduli E33=15.1 E15=12.7 EPS11=730 ! dielectric permittivities,related to the permittivity of vacuum EPS33=635 /PREP7 ! Enter Preprocessor ! Data tables for material constants of piezoelectric material ! (for the case of axisymmetric problem and piezoceramics ! polarized along the axis) MP,DENS,1,RO TB,ANEL,1 TBDATA,1,C11E,C13E,C12E TBDATA,7,C33E,C13E TBDATA,12,C11E TBDATA,16,C44E TB,PIEZ,1 TBDATA,2,E31 TBDATA,5,E33 TBDATA,8,E31 TBDATA,10,E15 MP,PERX,1,EPS11 MP,PERY,1,EPS33 ! 2D quadrilateral finite element with 8 nodes for coupled analysis ET,1,PLANE223,1001,,1 ! KEYOPT(1)=1001 - degrees of freedom UX,UY,VOLT (piezoelectric FE) ! KEYOPT(3)=1 - axisymmetric problem R2=R-R23 ! Auxiliary geometrical size ! Define keypoints K,1,0,-H/2 ! Keypoint 1 with coordinates x=0, y=-H/2 K,2,R1,-H/2 K,3,R2,-H/2 K,4,R,-H/2 K,5,R,H/2 K,6,R2,H/2 K,7,R1,H/2 K,8,0,H/2 ! Define straight lines L,1,2 ! Line that connects keypoints 1 and 2 (will have number 1) L,2,3 $ L,3,4 ! Lines 2 and 3 !sign $ separates the commands written in one command line L,4,5 $ L,5,6 $ L,6,7 $ L,7,8 $ L,8,1 $ L,6,3 ! Lines 4 and 9 ! Define areas by keypoints ! Keypoints must be input in a clockwise or counterclockwise order ! around the area A,1,2,3,6,7,8 ! Area 1 A,3,4,5,6 ! Area 2 ! Define local coordinate system number 11, rotated at 180 degrees ! regarding z-axis LOCAL,11,0,,,,180 ! (Change System) CSYS,0 ! Change active coordinate system to Cartesian (default number 0) ! Define element coordinate system 11 for area 2 ! (to set the direction of polarization) ASEL,S,AREA,,2 ! Select area 2 ! AATT - Associate element attributes with selected unmeshed areas AATT,1,,1,11 ! 11 - element coordinate system number for the selected area ! Optional commands ASEL,S,AREA,,1 AATT,1,,1 ASEL,ALL ! select all areas ! Divide lines for mapped finite element mesh ! Important: total number of divisions for opposite lines of the area ! must be the same! ! Select all vertical lines (lines L8, L9, L4) LSEL,S,LINE,,8,9 LSEL,A,LINE,,4 ! Set the same number of divisions for all selected lines ! LESIZE - Set the number of divisions for unmeshed lines LESIZE,ALL,,,HDIV ! HDIV is the number of divisions LSEL,S,LOC,X,0,R1 ! Select lines with coordinates 0<=X<=R1 ! (lines L1 and L7) LESIZE,ALL,,,R1DIV ! Set the number of divisions R1DIV ! for all selected lines LSEL,S,LOC,X,R1,R2 ! Select lines with coordinates R1<=X<=R2 ! (lines L2 and L6) LESIZE,ALL,,,R12DIV ! Set the number of divisions R2DIV ! for all selected lines LSEL,S,LOC,X,R2,R ! Select lines with coordinates R2<=X<=R ! (lines L3 and L5) LESIZE,ALL,,,R23DIV ! Set the number of divisions R23DIV ! for all selected lines LSEL,ALL ! Select all lines ! Prepare area 1 for mapped meshing LCCAT,1,2 ! Concatenate lines L1 and L2 into one line (line L10) LCCAT,7,6 ! Concatenate lines L6 and L7 into one line (line L11) MSHKEY,1 ! Set mesh key ! (0 - free mesh, 1 - mapped mesh) MSHAPE,0,2 ! Set finite element shapes ! 1st argument is a key indicating the element shape to be used ! (0 - quadrilateral-shaped elements) ! 2nd argument is the dimension of the model to be meshed (2D - area mesh) AMESH,ALL ! Mesh all areas FINISH ! Exit the preprocessor /SOLU ! Enter the solver ANTYPE,STAT ! Select the analysis type: static analysis ! Define the electrodes ! Select the nodes for the first electrode ! (with coordinates 0<=X<=R1, Y=-H/2) NSEL,S,LOC,Y,-H/2 NSEL,R,LOC,X,0,R1 ! For all selected nodes define a set of coupled degrees of freedom VOLT ! (group number 1) CP,1,VOLT,ALL ! Define the parameter N_VOLT1 - minimal node number from group 1 ! Node N_VOLT1 will be the reference node for group 1 *GET,N_VOLT1,NODE,,NUM,MIN ! Select the nodes for the second electrode ! (with coordinates 0<=X<=R1, Y=H/2) NSEL,S,LOC,Y,H/2 NSEL,R,LOC,X,0,R1 ! For all selected nodes define a set of coupled degrees of freedom VOLT ! (group number 2) CP,2,VOLT,ALL ! Define the parameter N_VOLT2 - minimal node number from group 2 ! Node with number N_VOLT2 will be the reference node for group 2 *GET,N_VOLT2,NODE,,NUM,MIN ! Select the nodes for the third electrode ! (with coordinates R2<=X<=R, Y=-H/2) NSEL,S,LOC,Y,-H/2 NSEL,R,LOC,X,R2,R ! For all selected nodes define a set of coupled degrees of freedom VOLT ! (group number 3) CP,3,VOLT,ALL ! Define the parameter N_VOLT3 - minimal node number from group 3 ! Node with number N_VOLT3 will be the reference node for group 3 *GET,N_VOLT3,NODE,,NUM,MIN ! Select the nodes for the fourth electrode ! (with coordinates R2<=X<=R, Y=H/2) NSEL,S,LOC,Y,H/2 NSEL,R,LOC,X,R2,R ! For all selected nodes define a set of coupled degrees of freedom VOLT ! (group number 4) CP,4,VOLT,ALL ! Define the parameter N_VOLT4 - minimal node number from group 4 ! Node with number N_VOLT4 will be the reference node for group 4 *GET,N_VOLT4,NODE,,NUM,MIN NSEL,ALL ! Select all nodes ! Set the values of electric potential at the electrodes D,N_VOLT1,VOLT,-VINP D,N_VOLT2,VOLT,VINP D,N_VOLT3,VOLT,-VINP D,N_VOLT4,VOLT,VINP ! Conditions of symmetry with respect to OY-axis (axis along line 8) DL,8,,SYMM ! Constraint of the middle point along the Y-axis ! Select node with coordinates X=R, Y=0 NSEL,S,LOC,Y,0 NSEL,R,LOC,X,R D,ALL,UY,0 ! Define DOF constraint UY=0 for all selected nodes NSEL,ALL ! Select all nodes SOLVE ! Solve the system of finite element equations FINISH ! Exit the solver ! Enter the postprocessor /POST1 ! Commands for graphical output /SHOW,WIN32C ! Specify device for graphical output /TRIAD,OFF ! Do not show the global coordinate triad /PLOPTS,INFO,2 ! Use Auto-legend format /PLOPTS,LEG2,OFF /PLOPTS,LOGO,OFF ! Do not show ANSYS logo /PLOPTS,FRAME,OFF ! Do not show frame /PLOPTS,DATE,OFF ! Do not show date ! Plot displacements UY PLNSOL,U,Y