FEA R3: Static analysis of a 2D curved beam structure

Initial setup

! White canvas
/RGB/RGB, Kywrd, PRED, PGRN, PBLU, N1, N2, NINC, NCNTR Specifies the RGB color values for indices and contours.,INDEX,100,100,100,0
/RGB/RGB, Kywrd, PRED, PGRN, PBLU, N1, N2, NINC, NCNTR Specifies the RGB color values for indices and contours.,INDEX,0,0,0,15
! Units: [N],[Nmm],[N/mm^2=MPa],[N/mm]

Constant parameters

A=40
B=60
P0=10
F1=5000
M0=1500E3
ELAST=210E3
NU=0.3

SETUP: element types, materials, sections

KEYWKEYW, Keyword, KEY Sets a keyword used by the GUI for context filtering (GUI).,PR_STRUC,1! Preferences / Structural
/PREP7/PREP7 Enters the model creation preprocessor.
ETET, ITYPE, Ename, KOP1, KOP2, KOP3, KOP4, KOP5, KOP6, INOPR Defines a local element type from the element library.,1,BEAM188

! Order of interpolation 0 - linear, 2 - quadratic, 3 - cubic
KEYOPTKEYOPT, ITYPE, KNUM, VALUE Sets element key options.,1,3,0
! Define the I-section (I80)
SECTYPESECTYPE, SECID, Type, Subtype, Name, REFINEKEY Associates section type information with a section ID number.,1,BEAM,I
SECOFFSETSECOFFSET, Location, OFFSET1, OFFSET2, CG-Y, CG-Z, SH-Y, SH-Z Defines the section offset for cross sections.,CENT
SECDATASECDATA, VAL1, VAL2, VAL3, VAL4, VAL5, VAL6, VAL7, VAL8, VAL9, VAL10, VAL11, VAL12 Describes the geometry of a section.,42,42,80,5.9,5.9,3.9
! Define the solid rectangle section
SECTYPESECTYPE, SECID, Type, Subtype, Name, REFINEKEY Associates section type information with a section ID number.,2,BEAM,RECT
SECOFFSETSECOFFSET, Location, OFFSET1, OFFSET2, CG-Y, CG-Z, SH-Y, SH-Z Defines the section offset for cross sections.,CENT
SECDATASECDATA, VAL1, VAL2, VAL3, VAL4, VAL5, VAL6, VAL7, VAL8, VAL9, VAL10, VAL11, VAL12 Describes the geometry of a section.,BB = 60,AA = 40
MPTEMPMPTEMP, SLOC, T1, T2, T3, T4, T5, T6 Defines a temperature table for material properties.,1,0
MPDATAMPDATA, Lab, MAT, SLOC, C1, C2, C3, C4, C5, C6 Defines property data to be associated with the temperature table.,EX,1,,ELASTELAST = 210E3
MPDATAMPDATA, Lab, MAT, SLOC, C1, C2, C3, C4, C5, C6 Defines property data to be associated with the temperature table.,PRXY,1,,NUNU = 0.3

Modelling

KK, NPT, X, Y, Z Defines a keypoint.,1,-1000,0
KK, NPT, X, Y, Z Defines a keypoint.,2,0,0
KK, NPT, X, Y, Z Defines a keypoint.,3,0,1000
KK, NPT, X, Y, Z Defines a keypoint.,4,1000,1000
KK, NPT, X, Y, Z Defines a keypoint.,5,1000,0
KK, NPT, X, Y, Z Defines a keypoint.,6,1000,1500
KK, NPT, X, Y, Z Defines a keypoint.,7,1400,1500
KK, NPT, X, Y, Z Defines a keypoint.,8,2000,1500
LL, P1, P2, NDIV, SPACE, XV1, YV1, ZV1, XV2, YV2, ZV2 Defines a line between two keypoints.,3,4
LL, P1, P2, NDIV, SPACE, XV1, YV1, ZV1, XV2, YV2, ZV2 Defines a line between two keypoints.,5,4
LL, P1, P2, NDIV, SPACE, XV1, YV1, ZV1, XV2, YV2, ZV2 Defines a line between two keypoints.,4,6
LL, P1, P2, NDIV, SPACE, XV1, YV1, ZV1, XV2, YV2, ZV2 Defines a line between two keypoints.,6,7
LL, P1, P2, NDIV, SPACE, XV1, YV1, ZV1, XV2, YV2, ZV2 Defines a line between two keypoints.,7,8
LARCLARC, P1, P2, PC, RAD Defines a circular arc.,1,3,2,1000 ! Create the arc

Meshing

! Set the number of elements on the lines
LESIZELESIZE, NL1, SIZE, ANGSIZ, NDIV, SPACE, KFORC, LAYER1, LAYER2, KYNDIV Specifies the divisions and spacing ratio on unmeshed lines.,1,,,10
LESIZELESIZE, NL1, SIZE, ANGSIZ, NDIV, SPACE, KFORC, LAYER1, LAYER2, KYNDIV Specifies the divisions and spacing ratio on unmeshed lines.,2,,,10
LESIZELESIZE, NL1, SIZE, ANGSIZ, NDIV, SPACE, KFORC, LAYER1, LAYER2, KYNDIV Specifies the divisions and spacing ratio on unmeshed lines.,3,,,6
LESIZELESIZE, NL1, SIZE, ANGSIZ, NDIV, SPACE, KFORC, LAYER1, LAYER2, KYNDIV Specifies the divisions and spacing ratio on unmeshed lines.,4,,,6
LESIZELESIZE, NL1, SIZE, ANGSIZ, NDIV, SPACE, KFORC, LAYER1, LAYER2, KYNDIV Specifies the divisions and spacing ratio on unmeshed lines.,5,,,6
LESIZELESIZE, NL1, SIZE, ANGSIZ, NDIV, SPACE, KFORC, LAYER1, LAYER2, KYNDIV Specifies the divisions and spacing ratio on unmeshed lines.,6,,,12
! Mesh the beams with I-section
SECNUMSECNUM, SECID Sets the element section attribute pointer.,1
LMESHLMESH, NL1, NL2, NINC Generates nodes and line elements along lines.,2,5
! Mesh the beams with rectangle section
SECNUMSECNUM, SECID Sets the element section attribute pointer.,2
LMESHLMESH, NL1, NL2, NINC Generates nodes and line elements along lines.,1
LMESHLMESH, NL1, NL2, NINC Generates nodes and line elements along lines.,6

Constraints and Loads

! Define the kinematic constraints
DKDK, KPOI, Lab, VALUE, VALUE2, KEXPND, Lab2, Lab3, Lab4, Lab5, Lab6 Defines DOF constraints at keypoints.,1,UY,0
DKDK, KPOI, Lab, VALUE, VALUE2, KEXPND, Lab2, Lab3, Lab4, Lab5, Lab6 Defines DOF constraints at keypoints.,5,UY,0
DKDK, KPOI, Lab, VALUE, VALUE2, KEXPND, Lab2, Lab3, Lab4, Lab5, Lab6 Defines DOF constraints at keypoints.,5,UX,0
DKDK, KPOI, Lab, VALUE, VALUE2, KEXPND, Lab2, Lab3, Lab4, Lab5, Lab6 Defines DOF constraints at keypoints.,8,ALL,0
! Plane model, constrain UZ of all nodes
DD, Node, Lab, VALUE, VALUE2, NEND, NINC, Lab2, Lab3, Lab4, Lab5, Lab6 Defines degree-of-freedom constraints at nodes.,ALL,UZ,0
! Constant load on curved beam
LSELLSEL, Type, Item, Comp, VMIN, VMAX, VINC, KSWP Selects a subset of lines.,S,,,6
ESLLESLL, Type Selects those elements associated with the selected lines.,S
SFBEAMSFBEAM, Elem, LKEY, Lab, VALI, VALJ, VAL2I, VAL2J, IOFFST, JOFFST, LENRAT Specifies surface loads on beam and pipe elements.,ALL,2,PRES,P0P0 = 10 ! [kN/m]
ALLSELALLSEL, LabT, Entity Selects all entities with a single command.,ALL
! Ramped load on line 1
! Select carefully the first and last element numbers!
ENUM1ST=29
ENUMLAST=38
*DO*DO, Par, IVAL, FVAL, INC Defines the beginning of a do-loop.,ENUM,ENUM1STENUM1ST = 29,ENUMLASTENUMLAST = 38
! Define the ramped load on the ENUMth element
  SFBEAMSFBEAM, Elem, LKEY, Lab, VALI, VALJ, VAL2I, VAL2J, IOFFST, JOFFST, LENRAT Specifies surface loads on beam and pipe elements.,ENUM,2,PRES, P0*(1 - (ENUM - ENUM1ST)/(ENUMLAST - ENUM1ST + 1)), P0*(1 - (ENUM - ENUM1ST + 1)/(ENUMLAST - ENUM1ST + 1))
*ENDDO*ENDDO Ends a do-loop and starts the looping action.
! Bending moment
FKFK, KPOI, Lab, VALUE, VALUE2 Defines force loads at keypoints.,6,MZ,-M0M0 = 1500E3
! Force
FKFK, KPOI, Lab, VALUE, VALUE2 Defines force loads at keypoints.,7,FY,-F1F1 = 5000
FINISHFINISH Exits normally from a processor.

Solution: solve the finite element equation K.U = F

/SOL/SOLU Enters the solution processor.
SOLVESOLVE, Action Starts a solution.

Postprocessing

/POST1/POST1 Enters the database results postprocessor.

! Define the element tables
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,FXI,SMISC,1
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,FXJ,SMISC,14
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,MZI,SMISC,3
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,MZJ,SMISC,16
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,SFYI,SMISC,6
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,SFYJ,SMISC,19
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,EXI,SMISC,7
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,EXJ,SMISC,20
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,EPELBYTI,SMISC,42
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,EPELBYTJ,SMISC,47
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,EPELBYBI,SMISC,43
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,EPELBYBJ,SMISC,48
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,SDIRI,SMISC,31
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,SDIRJ,SMISC,36
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,SBYTI,SMISC,32
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,SBYTJ,SMISC,37
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,SBYBI,SMISC,33
ETABLEETABLE, Lab, Item, Comp, Option Fills a table of element values for further processing.,SBYBJ,SMISC,38
! Plot the element tables on the structure
PLLSPLLS, LabI, LabJ, Fact, KUND, ViewUP Displays element table items as contoured areas along elements.,FXI,FXJ,1,0,0 ! Click here to view image
PLLSPLLS, LabI, LabJ, Fact, KUND, ViewUP Displays element table items as contoured areas along elements.,MZI,MZJ,1,0,0 ! Click here to view image
PLLSPLLS, LabI, LabJ, Fact, KUND, ViewUP Displays element table items as contoured areas along elements.,SFYI,SFYJ,1,0,0 ! Click here to view image
PLLSPLLS, LabI, LabJ, Fact, KUND, ViewUP Displays element table items as contoured areas along elements.,SFYI,SFYJ,1,0,0 ! Click here to view image
PLLSPLLS, LabI, LabJ, Fact, KUND, ViewUP Displays element table items as contoured areas along elements.,EXI,EXJ,1,0,0 ! Click here to view image
PLLSPLLS, LabI, LabJ, Fact, KUND, ViewUP Displays element table items as contoured areas along elements.,EPELBYTI,EPELBYTJ,1,0,0 ! Click here to view image
PLLSPLLS, LabI, LabJ, Fact, KUND, ViewUP Displays element table items as contoured areas along elements.,EPELBYBI,EPELBYBJ,1,0,0 ! Click here to view image
PLLSPLLS, LabI, LabJ, Fact, KUND, ViewUP Displays element table items as contoured areas along elements.,SDIRI,SDIRJ,1,0,0 ! Click here to view image
PLLSPLLS, LabI, LabJ, Fact, KUND, ViewUP Displays element table items as contoured areas along elements.,SBYTI,SBYTJ,1,0,0 ! Click here to view image
PLLSPLLS, LabI, LabJ, Fact, KUND, ViewUP Displays element table items as contoured areas along elements.,SBYBI,SBYBJ,1,0,0 ! Click here to view image