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Finite Element Analysis in Structural Mechanics

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en:example:nlin:3:1

Table of Contents

Hexahedra, BEAM56G2

Problem

Mesh

element type nodes
1 56 1 2 3 4 5 6 7 8 21 22 23 24 25 26 27 28 29 30 31 32
2 56 5 6 7 8 9 10 11 12 29 30 31 32 33 34 35 36 37 38 39 40
3 56 9 10 11 12 13 14 15 16 37 38 39 40 41 42 43 44 45 46 47 48
4 56 13 45 15 16 17 18 19 20 45 46 47 48 49 50 51 52 53 54 55 56 

Boundary conditions

$u=v=w=0$ at node 24
$u=w=0$ at node 22
$v=w=0$ at node 56
$w=0$ at node 54

Solution

For the loading given we replace the end force with the equivalent surface tractions in the usual fashion, i.e., $$q_x=\frac{F_x}{0.01\times0.02}=\left\{\begin{align}-16.40 \\ -16.45 \\ -17.45 \\ -17.50\end{align}\right.\text{ MPa}.$$

beam56g2.bat
rmd3 beam56g2.i1
rpd3 beam56g2.i2
srh3 beam56g2.i3
fefs beam56g2.i4
hpp3 beam56g2.iP
hpls beam56g2.iL
str3 beam56g2.i5

Input

beam56g2.i1
;  NELEM NNOD ITED
IP   4    56   56
;  CRIT SCALE
RP 1.01   1
XY N 1:20 X 4*0 4*0.25 4*0.5 4*0.75 4*1
          Y 5*(0 0.02 0.02 0)
          Z 5*(0 0 0.01 0.01)
EL E 1:4 N =A 1:8 =A =B 21:32 =B
           =4A =8B =8A =16B =12A =24B
EN
EN
beam56g2.i2
;  KREST
IP   1
         ; E    α ν   ρ
MP 1 T 1 V 2e11 0 0.3 0
SV 1 T 9 V -1.640e7 0 0 ; undercritical force
SV 2 T 9 V -1.645e7 0 0 ; critical force
SV 3 T 9 V -1.745e7 0 0 ; critical force for ITE=56
SV 4 T 9 V -1.750e7 0 0 ; postcritical force
NV 1 T 6 V 0 0 0.5      ; perturbation 1 N

AS 1 /M 1
  /B 0 N 24 /B 0 C 1 3 N 22     ; left end
  /B 0 C 2 3 N 56 /B 0 C 3 N 54 ; right end

AS 2
  /S 1 E 4 S6 /N 1 N 38 40

AS 3
  /S 2 E 4 S6 /N 1 N 38 40

AS 4
  /S 3 E 4 S6 /N 1 N 38 40

AS 5
  /S 4 E 4 S6 /N 1 N 38 40

EN
EN
beam56g2.i3
;  KREST
IP   1
EN
EN
beam56g2.i4
;  KREST
IP   1
EN
EN
beam56g2.iP
;  KREST NLC NCYC KMOD KCRP KLARG ...
IP   1    4    0    0    0    1   4*0
;  load case sequence
   2 3 4 5
EN
EN
beam56g2.iL
;  KMET KOUT NSUBI NITER NINT KTPR
IP   0    1    0    100    0    0
;  UTOL RTOL XTOL PENAL
RP   0    0    0     0
EN
EN
beam56g2.i5
;  KLC 0 KOUT ILC  ...  KPROB KGRAF
IP  1  0   0   0   6*0    2     2
EN
EN

Output

beam56g2.o5
;  KLC 0 KOUT ILC  ...  KPROB KGRAF                                             
IP  1  0   0   0   6*0    2     2                                               
EN                                                                              
EN                                                                              
                                                      1TH LOAD CASE

                                                    DISPLACEMENTS
           NODE             U                V                W             ALPHA            BETA             GAMMA
                           [m]              [m]              [m]           [rad]            [rad]            [rad]

              1       0.1598971E-04   -0.5773814E-07   -0.1058244E-06
              2       0.1598971E-04    0.5722053E-06   -0.1058236E-06
              3      -0.1602676E-04    0.4547416E-06    0.8614451E-07
              4      -0.1602676E-04    0.5972560E-07    0.8614532E-07
              5      -0.1042854E-04   -0.8649459E-07    0.6793311E-03
              6      -0.1042840E-04    0.5991823E-06    0.6793311E-03
              7      -0.3269092E-04    0.4062700E-06    0.6795513E-03
              8      -0.3269106E-04    0.1064184E-06    0.6795513E-03
              9      -0.4224436E-04   -0.1236951E-06    0.9581265E-03
             10      -0.4224410E-04    0.6313217E-06    0.9581265E-03
             11      -0.4224497E-04    0.3670032E-06    0.9583706E-03
             12      -0.4224523E-04    0.1406240E-06    0.9583706E-03
             13      -0.7409379E-04   -0.9155781E-07    0.6793704E-03
             14      -0.7409345E-04    0.5916154E-06    0.6793704E-03
             15      -0.5183236E-04    0.3989055E-06    0.6795911E-03
             16      -0.5183270E-04    0.1011517E-06    0.6795911E-03
             17      -0.1004058E-03   -0.5942634E-07   -0.1068613E-06
             18      -0.1004054E-03    0.5505422E-06   -0.1068611E-06
             19      -0.6838429E-04    0.4318301E-06    0.8735668E-07
             20      -0.6838467E-04    0.5928451E-07    0.8735694E-07
             21       0.1584070E-04    0.2572340E-06   -0.1421085E-06
             22       0.0000000E+00    0.5144670E-06    0.0000000E+00
             23      -0.1617403E-04    0.2572340E-06    0.4557930E-07
             24       0.0000000E+00    0.0000000E+00    0.0000000E+00
             25       0.2714981E-05   -0.4218146E-07    0.3700878E-03
             26       0.2715052E-05    0.5562028E-06    0.3700878E-03
             27      -0.2447603E-04    0.4416253E-06    0.3703007E-03
             28      -0.2447610E-04    0.7239650E-07    0.3703007E-03
             29      -0.1038807E-04    0.2563443E-06    0.6792351E-03
             30      -0.2156468E-04    0.5029211E-06    0.6794653E-03
             31      -0.3265162E-04    0.2563446E-06    0.6794544E-03
             32      -0.2156483E-04    0.9766805E-08    0.6794653E-03
             33      -0.2640213E-04   -0.1263759E-06    0.8883020E-03
             34      -0.2640193E-04    0.6369086E-06    0.8883020E-03
             35      -0.3756006E-04    0.3677181E-06    0.8885422E-03
             36      -0.3756026E-04    0.1428154E-06    0.8885422E-03
             37      -0.4225488E-04    0.2538136E-06    0.9579736E-03
             38      -0.4224319E-04    0.4989836E-06    0.9582867E-03
             39      -0.4225575E-04    0.2538139E-06    0.9582186E-03
             40      -0.4224345E-04    0.8643151E-08    0.9582867E-03
             41      -0.5810386E-04   -0.1289000E-06    0.8883227E-03
             42      -0.5810356E-04    0.6329927E-06    0.8883227E-03
             43      -0.4694702E-04    0.3638841E-06    0.8885630E-03
             44      -0.4694732E-04    0.1402088E-06    0.8885630E-03
             45      -0.7409133E-04    0.2500290E-06    0.6792742E-03
             46      -0.6296324E-04    0.4953482E-06    0.6795049E-03
             47      -0.5182921E-04    0.2500288E-06    0.6794946E-03
             48      -0.6296358E-04    0.4709144E-08    0.6795049E-03
             49      -0.8719169E-04   -0.5595232E-07    0.3701286E-03
             50      -0.8719134E-04    0.5516314E-06    0.3701286E-03
             51      -0.5999868E-04    0.4365508E-06    0.3703378E-03
             52      -0.5999903E-04    0.5912752E-07    0.3703378E-03
             53      -0.1004064E-03    0.2455580E-06   -0.1460520E-06
             54      -0.8439464E-04    0.4911152E-06    0.0000000E+00

                                                    DISPLACEMENTS
           NODE             U                V                W             ALPHA            BETA             GAMMA
                           [m]              [m]              [m]           [rad]            [rad]            [rad]

             55      -0.6838701E-04    0.2455574E-06    0.4847673E-07
             56      -0.8439501E-04    0.0000000E+00    0.0000000E+00

                                                    DISPLACEMENTS
           NODE             U                V                W             ALPHA            BETA             GAMMA
                           [m]              [m]              [m]           [rad]            [rad]            [rad]

              1       0.1598969E-04   -0.5773479E-07   -0.1061962E-06
              2       0.1598969E-04    0.5737725E-06   -0.1061954E-06
              3      -0.1602685E-04    0.4563094E-06    0.8651665E-07
              4      -0.1602685E-04    0.5972831E-07    0.8651746E-07
              5      -0.1049135E-04   -0.8646612E-07    0.6793332E-03
              6      -0.1049120E-04    0.6007179E-06    0.6793332E-03
              7      -0.3275385E-04    0.4078053E-06    0.6795541E-03
              8      -0.3275399E-04    0.1064473E-06    0.6795541E-03
              9      -0.4236965E-04   -0.1236737E-06    0.9581301E-03
             10      -0.4236939E-04    0.6328474E-06    0.9581301E-03
             11      -0.4237025E-04    0.3685274E-06    0.9583750E-03
             12      -0.4237052E-04    0.1406468E-06    0.9583750E-03
             13      -0.7428167E-04   -0.9154570E-07    0.6793724E-03
             14      -0.7428133E-04    0.5931277E-06    0.6793724E-03
             15      -0.5202011E-04    0.4004174E-06    0.6795939E-03
             16      -0.5202045E-04    0.1011642E-06    0.6795939E-03
             17      -0.1006561E-03   -0.5942622E-07   -0.1072366E-06
             18      -0.1006558E-03    0.5520414E-06   -0.1072364E-06
             19      -0.6863455E-04    0.4333300E-06    0.8773228E-07
             20      -0.6863492E-04    0.5928397E-07    0.8773254E-07
             21       0.1584023E-04    0.2580193E-06   -0.1424732E-06
             22       0.0000000E+00    0.5160375E-06    0.0000000E+00
             23      -0.1617457E-04    0.2580193E-06    0.4594554E-07
             24       0.0000000E+00    0.0000000E+00    0.0000000E+00
             25       0.2683548E-05   -0.4213357E-07    0.3700885E-03
             26       0.2683619E-05    0.5577238E-06    0.3700885E-03
             27      -0.2450756E-04    0.4431470E-06    0.3703021E-03
             28      -0.2450763E-04    0.7244365E-07    0.3703021E-03
             29      -0.1045076E-04    0.2571263E-06    0.6792371E-03
             30      -0.2162757E-04    0.5044571E-06    0.6794677E-03
             31      -0.3271443E-04    0.2571267E-06    0.6794572E-03
             32      -0.2162771E-04    0.9794872E-08    0.6794677E-03
             33      -0.2649618E-04   -0.1263498E-06    0.8883052E-03
             34      -0.2649597E-04    0.6384391E-06    0.8883052E-03
             35      -0.3765417E-04    0.3692470E-06    0.8885462E-03
             36      -0.3765437E-04    0.1428430E-06    0.8885462E-03
             37      -0.4238020E-04    0.2545871E-06    0.9579772E-03
             38      -0.4236847E-04    0.5005080E-06    0.9582907E-03
             39      -0.4238107E-04    0.2545874E-06    0.9582229E-03
             40      -0.4236874E-04    0.8665836E-08    0.9582907E-03
             41      -0.5826045E-04   -0.1288821E-06    0.8883259E-03
             42      -0.5826014E-04    0.6345110E-06    0.8883259E-03
             43      -0.4710354E-04    0.3654008E-06    0.8885669E-03
             44      -0.4710384E-04    0.1402282E-06    0.8885669E-03
             45      -0.7427920E-04    0.2507911E-06    0.6792763E-03
             46      -0.6315105E-04    0.4968605E-06    0.6795073E-03
             47      -0.5201695E-04    0.2507910E-06    0.6794974E-03
             48      -0.6315140E-04    0.4721181E-08    0.6795073E-03
             49      -0.8741080E-04   -0.5594617E-07    0.3701293E-03
             50      -0.8741044E-04    0.5531373E-06    0.3701293E-03
             51      -0.6021768E-04    0.4380574E-06    0.3703392E-03
             52      -0.6021804E-04    0.5913293E-07    0.3703392E-03
             53      -0.1006568E-03    0.2463076E-06   -0.1464271E-06
             54      -0.8464493E-04    0.4926146E-06    0.0000000E+00

                                                    DISPLACEMENTS
           NODE             U                V                W             ALPHA            BETA             GAMMA
                           [m]              [m]              [m]           [rad]            [rad]            [rad]

             55      -0.6863727E-04    0.2463071E-06    0.4885343E-07
             56      -0.8464530E-04    0.0000000E+00    0.0000000E+00

                                                    DISPLACEMENTS
           NODE             U                V                W             ALPHA            BETA             GAMMA
                           [m]              [m]              [m]           [rad]            [rad]            [rad]

              1       0.1388432E-03   -0.5141790E-06    0.1725226E-05
              2       0.1388432E-03    0.1009646E-05    0.1725227E-05
              3      -0.1388770E-03   -0.2079879E-07   -0.1900566E-05
              4      -0.1388770E-03    0.5162661E-06   -0.1900565E-05
              5       0.4253297E-05   -0.7985837E-06    0.5881713E-02
              6       0.4253448E-05    0.1292158E-05    0.5881713E-02
              7      -0.1878297E-03   -0.3819949E-06    0.5880074E-02
              8      -0.1878298E-03    0.8755764E-06    0.5880074E-02
              9      -0.1290965E-03   -0.1075110E-05    0.8286251E-02
             10      -0.1290962E-03    0.1563298E-05    0.8286251E-02
             11      -0.1291043E-03   -0.7171132E-06    0.8286429E-02
             12      -0.1291046E-03    0.1205308E-05    0.8286429E-02
             13      -0.2624800E-03   -0.8031428E-06    0.5882082E-02
             14      -0.2624796E-03    0.1283266E-05    0.5882082E-02
             15      -0.7040988E-04   -0.3890299E-06    0.5880444E-02
             16      -0.7041024E-04    0.8691506E-06    0.5880444E-02
             17      -0.3969917E-03   -0.5210689E-06    0.1725439E-05
             18      -0.3969913E-03    0.9916597E-06    0.1725440E-05
             19      -0.1192274E-03   -0.5031087E-07   -0.1899172E-05
             20      -0.1192278E-03    0.5208907E-06   -0.1899171E-05
             21       0.1386895E-03    0.2477341E-06    0.1384878E-05
             22       0.0000000E+00    0.4954671E-06    0.0000000E+00
             23      -0.1390158E-03    0.2477341E-06   -0.2245047E-05
             24       0.0000000E+00    0.0000000E+00    0.0000000E+00
             25       0.6539420E-04   -0.5261521E-06    0.3209242E-02
             26       0.6539428E-04    0.1021144E-05    0.3209242E-02
             27      -0.1699611E-03    0.1436984E-07    0.3206751E-02
             28      -0.1699612E-03    0.4806265E-06    0.3206751E-02
             29       0.4317137E-05    0.2467875E-06    0.5880877E-02
             30      -0.9179713E-04    0.4552293E-06    0.5881102E-02
             31      -0.1877747E-03    0.2467912E-06    0.5879237E-02
             32      -0.9179728E-04    0.3834827E-07    0.5881102E-02
             33      -0.6816276E-04   -0.1219752E-05    0.7684004E-02
             34      -0.6816254E-04    0.1711034E-05    0.7684004E-02
             35      -0.1644313E-03   -0.6112358E-06    0.7683844E-02
             36      -0.1644315E-03    0.1102526E-05    0.7683844E-02
             37      -0.1291077E-03    0.2440944E-06    0.8284938E-02
             38      -0.1290989E-03    0.4228035E-06    0.8286668E-02
             39      -0.1291158E-03    0.2440975E-06    0.8285117E-02
             40      -0.1290991E-03    0.6538753E-07    0.8286668E-02
             41      -0.1900484E-03   -0.1222108E-05    0.7684198E-02
             42      -0.1900481E-03    0.1706532E-05    0.7684198E-02
             43      -0.9379414E-04   -0.6149841E-06    0.7684037E-02
             44      -0.9379446E-04    0.1099410E-05    0.7684037E-02
             45      -0.2624981E-03    0.2400617E-06    0.5881247E-02
             46      -0.1664414E-03    0.4471519E-06    0.5881472E-02
             47      -0.7041961E-04    0.2400605E-06    0.5879608E-02
             48      -0.1664418E-03    0.3296992E-07    0.5881472E-02
             49      -0.3235851E-03   -0.5428779E-06    0.3209608E-02
             50      -0.3235847E-03    0.1018333E-05    0.3209608E-02
             51      -0.8821466E-04    0.6910032E-08    0.3207113E-02
             52      -0.8821504E-04    0.4685388E-06    0.3207113E-02
             53      -0.3969976E-03    0.2352954E-06    0.1377018E-05
             54      -0.2581064E-03    0.4705853E-06    0.0000000E+00

                                                    DISPLACEMENTS
           NODE             U                V                W             ALPHA            BETA             GAMMA
                           [m]              [m]              [m]           [rad]            [rad]            [rad]

             55      -0.1192482E-03    0.2352899E-06   -0.2246845E-05
             56      -0.2581068E-03    0.0000000E+00    0.0000000E+00

                                                    DISPLACEMENTS
           NODE             U                V                W             ALPHA            BETA             GAMMA
                           [m]              [m]              [m]           [rad]            [rad]            [rad]

              1       0.1577166E-03   -0.5850060E-06    0.2276667E-05
              2       0.1577166E-03    0.1066660E-05    0.2276668E-05
              3      -0.1577489E-03   -0.1054360E-06   -0.2476455E-05
              4      -0.1577489E-03    0.5870908E-06   -0.2476454E-05
              5      -0.3060678E-05   -0.9042824E-06    0.6679575E-02
              6      -0.3060536E-05    0.1383984E-05    0.6679574E-02
              7      -0.2211122E-03   -0.5177113E-06    0.6677387E-02
              8      -0.2211123E-03    0.9976591E-06    0.6677387E-02
              9      -0.1539379E-03   -0.1212935E-05    0.9409098E-02
             10      -0.1539376E-03    0.1687330E-05    0.9409097E-02
             11      -0.1539485E-03   -0.9013870E-06    0.9409251E-02
             12      -0.1539488E-03    0.1376053E-05    0.9409251E-02
             13      -0.3048491E-03   -0.9086885E-06    0.6680040E-02
             14      -0.3048488E-03    0.1375012E-05    0.6680039E-02
             15      -0.8681251E-04   -0.5246142E-06    0.6677853E-02
             16      -0.8681288E-04    0.9911694E-06    0.6677853E-02
             17      -0.4655582E-03   -0.5927188E-06    0.2277244E-05
             18      -0.4655578E-03    0.1049410E-05    0.2277244E-05
             19      -0.1500388E-03   -0.1358525E-06   -0.2475212E-05
             20      -0.1500392E-03    0.5925317E-06   -0.2475212E-05
             21       0.1575649E-03    0.2408275E-06    0.1888524E-05
             22       0.0000000E+00    0.4816542E-06    0.0000000E+00
             23      -0.1578838E-03    0.2408278E-06   -0.2868620E-05
             24       0.0000000E+00    0.0000000E+00    0.0000000E+00
             25       0.6934588E-04   -0.6069432E-06    0.3645227E-02
             26       0.6934595E-04    0.1088061E-05    0.3645226E-02
             27      -0.1979297E-03   -0.5724882E-07    0.3641937E-02
             28      -0.1979297E-03    0.5385233E-06    0.3641938E-02
             29      -0.2991163E-05    0.2398511E-06    0.6678624E-02
             30      -0.1120965E-03    0.4332672E-06    0.6678718E-02
             31      -0.2210527E-03    0.2399744E-06    0.6676436E-02
             32      -0.1120966E-03    0.4655718E-07    0.6678718E-02
             33      -0.8591404E-04   -0.1396511E-05    0.8725424E-02
             34      -0.8591383E-04    0.1873960E-05    0.8725424E-02
             35      -0.1952000E-03   -0.7621067E-06    0.8725142E-02
             36      -0.1952002E-03    0.1239828E-05    0.8725142E-02
             37      -0.1539491E-03    0.2371979E-06    0.9407607E-02
             38      -0.1539416E-03    0.3926529E-06    0.9409547E-02
             39      -0.1539600E-03    0.2373334E-06    0.9407762E-02
             40      -0.1539419E-03    0.8187739E-07    0.9409547E-02
             41      -0.2219803E-03   -0.1398808E-05    0.8725677E-02
             42      -0.2219800E-03    0.1869451E-05    0.8725677E-02
             43      -0.1127125E-03   -0.7657972E-06    0.8725395E-02
             44      -0.1127128E-03    0.1236704E-05    0.8725396E-02
             45      -0.3048728E-03    0.2331618E-06    0.6679090E-02
             46      -0.1958262E-03    0.4252154E-06    0.6679184E-02
             47      -0.8682662E-04    0.2332778E-06    0.6676903E-02
             48      -0.1958266E-03    0.4122366E-07    0.6679184E-02
             49      -0.3772230E-03   -0.6240152E-06    0.3645678E-02
             50      -0.3772226E-03    0.1085631E-05    0.3645678E-02
             51      -0.1099285E-03   -0.6502255E-07    0.3642384E-02
             52      -0.1099289E-03    0.5267795E-06    0.3642384E-02
             53      -0.4655665E-03    0.2283456E-06    0.1880218E-05
             54      -0.3077945E-03    0.4566851E-06    0.0000000E+00

                                                    DISPLACEMENTS
           NODE             U                V                W             ALPHA            BETA             GAMMA
                           [m]              [m]              [m]           [rad]            [rad]            [rad]

             55      -0.1500640E-03    0.2283397E-06   -0.2871365E-05
             56      -0.3077949E-03    0.0000000E+00    0.0000000E+00

                                * END OF STR3 *
 TOTAL CPU: 00:00:00
en/example/nlin/3/1.txt · Last modified: 2022-03-15 08:31 by Petr Pařík