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A static load is applied to the center of an ellipsoidal dome. Shell elements are used. Nodes at the base of the dome are constrained, and included in a NODFOR output database. Adaptivity is used to automatically refine the mesh in areas of high curvature.

Introduction

LS-DYNA Implicit Workshop

Problem #10: Adaptive Ellipsoidal Dome

Objectives
* Learn to activate mesh adaptivity in an implicit simulation.
* Learn how to minimize hourglass problems.

Problem Description
A static load is applied to the center of an ellipsoidal dome.
Shell elements are used. Nodes at the base of the dome are
constrained, and included in a NODFOR output database. Adaptivity
is used to automatically refine the mesh in areas of high curvature.

Input Filename: aellipse.k

Procedure
Copy the input file to your local directory. Using an editor, view the input file and
answer the following questions:

1. How frequently will the mesh be evaluated for refinement?

2. How many times can each element be subdivided?

3. How do you indicate which parts will be adapted?

4. Which element formulation is used?

5. How is load applied?

Execute the simulation, and view the results with the postprocessor.

6. How many time steps and cycles were used? steps cycles

7. Applied load: Center displacement:

8. Does the adaptive mesh improve the hourglassing problem

Switch to pressure driven load application, and repeat the simulation. Postprocess the
results. Using the NODFOR database, verify that the load is applied correctly as the
mesh is refined.

9. How many time steps and cycles were used? steps cycles

10. Does the pressure load improve nonlinear convergence?

11. Applied loadr: Center displacement:

Experiment with shell element formulation #16.

12. Does shell type #16 improve hourglassing?

13. Does shell type #16 improve convergence behavior (number of steps/cycles)?

Keywords

*CONTROL_ADAPTIVE
*CONTROL_HOURGLASS
*CONTROL_IMPLICIT_AUTO
*CONTROL_IMPLICIT_DYNAMICS
*CONTROL_IMPLICIT_GENERAL
*CONTROL_IMPLICIT_SOLUTION
*CONTROL_IMPLICIT_SOLVER
*CONTROL_TERMINATION
*DATABASE_BINARY_D3PLOT
*DATABASE_EXTENT_BINARY
*DATABASE_GLSTAT
*DATABASE_NODAL_FORCE_GROUP
*DATABASE_NODFOR
$*DEFINE_CURVE
*DEFINE_CURVE
*END
*KEYWORD
*LOAD_NODE_POINT
$*LOAD_SEGMENT
*MAT_elastic
*PART
*SECTION_SHELL
*SET_NODE_LIST
*TITLE

Reduced Input

  *KEYWORD
  *TITLE
  PINCHED ELLIPSE
  $
  $ A. Tabiei, March 99
  $ units; mm, s, ton, N
  $
  *CONTROL_TERMINATION
      1.0000
  $
  *CONTROL_ADAPTIVE
  $  adpfreq    adptol    adpopt    maxlvl    tbirth    tdeath     lcadp    ioflag
        0.10     5.000         2         3       0.0       0.0         0         0
  $  adpsize    adpass    ireflg    adpene
   0.0000000         1         0       1.0
  $
  $========1=========2=========3=========4=========5=========6=========7=========8
  $
  *CONTROL_IMPLICIT_GENERAL
  $   imflag       dt0      iefs   nstepsb      igso
           1      0.01         0         0         0
  $
  *CONTROL_IMPLICIT_SOLUTION
  $  nlsolvr    ilimit    maxref     dctol     ectol     rctol     lstol
           0         0         0       0.0       0.0         0         0
  $    dnorm   divflag   inistif   nlprint
           0         0         0         0
  $
  *CONTROL_IMPLICIT_SOLVER
  $   lsolvr   prntflg    negeig
           0         0         0
  $
  *CONTROL_IMPLICIT_AUTO
  $    iauto    iteopt    itewin     dtmin     dtmax
           1         0         0       0.0       0.0
  $
  *CONTROL_IMPLICIT_DYNAMICS
  $    imass     gamma      beta
           0       0.0       0.0
  $
  $========1=========2=========3=========4=========5=========6=========7=========8
  $
  *DATABASE_EXTENT_BINARY
  $    neiph     neips    maxint    strflg    sigflg    epsflg    rltflg    engflg
                                         1         1                                  
  $   cmpflg    ieverp    beamip
                     
  *DATABASE_BINARY_D3PLOT
      0.01
  *DATABASE_GLSTAT
      0.01
  *DATABASE_NODFOR
      0.01
  *DATABASE_NODAL_FORCE_GROUP
         2
  *SET_NODE_LIST
         2
           1         7        13        19        25        31        37        48
          54        60        66        72        78        84        91        97
         103       109       115       121       127       206       212       218
         224       230       236       242
  $
  $---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
  $
  *CONTROL_HOURGLASS
           4
  $
  *MAT_elastic
  $      MID        RO         E        PR    
           1 7.890E-09 2.100E+05 3.000E-01
  $
  *SECTION_SHELL
  $      SID    ELFORM
           1         2
   3.000E-00 3.000E-00 3.000E-00 3.000E-00
  $
  *PART
  SHELL
  $      PID       SID       MID                                  ADPOPT
           1         1         1                                       0
  $
  $---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
  $
  *LOAD_NODE_POINT
  $      NID       DOF      LCID        SF
         164         3         1      -1.0
  $
  *DEFINE_CURVE
           1
  0.00000000000000E+00 00.000000000000E+00
  1.00000000000000E+00 500000.00000000E+00
  $
  $---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
  $
  $*LOAD_SEGMENT
  $$     LCID        SF                  N1        N2        N3        N4
  $         2      -1.0                 154       155       164       163
  $         2      -1.0                 155       156       165       164
  $         2      -1.0                 163       164       173       172
  $         2      -1.0                 164       165       174       173
  $
  $*DEFINE_CURVE
  $         2
  $0.00000000000000E+00 00.000000000000E+00
  $1.00000000000000E+00 7500.0000000000E+00
  $
  $---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
  *NODE
         1 22.627417       -16.97056299999 0.0                   7       7            
         2 22.332757       -16.749568      3.8763777      
         3 21.462          -16.09649999999 7.615231       
         4 20.065733999999 -15.0493        11.096923      
         5 18.217324       -13.662993      14.235898      
         6 16.0            -12.0           16.970562999999
         7 27.446269999999 -12.339774      0.0                   7       7           
         8 26.906521999999 -12.067746      4.8105589      
         9 25.311105       -11.481794      9.1543237      
        10 22.863424999999 -10.624359      13.003226      
        11 19.716536999999 -9.5432552      16.317444999999
        12 16.0            -8.290928299999 19.059394      
        13 30.783318999999 -6.5549861      0.0                   7       7           
        14 30.006588       -6.3723023      5.3778628      
        15 27.897109       -6.0202527      10.099093      
        16 24.740081       -5.5252473      14.183842      
        17 20.726296       -4.9196061      17.611333999999
        18 16.0            -4.2342801      20.348731      
        19 32.0            0.0             0.0                   7       7         
        20 31.126259       0.0             5.5700325      
        21 28.826521       0.0             10.420188      
        22 25.412948       0.0             14.585178      
        23 21.088252       0.0             18.051265      
        24 16.0            0.0             20.78461       
        25 30.783199       6.5553032       0.0                   7       7           
        26 30.006492999999 6.3725534       5.3778627      
        27 27.897037999999 6.0204347       10.099093999999
        28 24.740034       5.525362        14.183843      
        29 20.726272999999 4.9196591       17.611333999999
        30 16.0            4.2342801       20.348731      
        31 27.447541999999 12.338182       0.0                   7       7           
        32 26.907578999999 12.066411       4.8105821      
        33 25.311917999999 11.480756       9.1543614      
        34 22.863966       10.623673       13.003251      
        35 19.716805       9.5429215       16.317457      
        36 16.0            8.2909282999999 19.059394      
        37 22.627417       16.970562999999 0.0                   7       7            
        38 22.332757       16.749568       3.8763777      
        39 21.462          16.096499999999 7.615231       
        40 20.065733999999 15.0493         11.096923      
        41 18.217324       13.662993       14.235898      
        42 16.0            12.0            16.970562999999
        43 -16.0           -12.0           16.970562999999
        44 -18.218449      -13.66383699999 14.234035      
        45 -20.065732      -15.049299      11.096848      
        46 -21.462235      -16.09667599999 7.6152887      
        47 -22.332974      -16.749731      3.8764176      
        48 -22.627417      -16.97056299999 0.0                   7       7            
        49 -16.0           -8.290928299999 19.059394      
        50 -19.723448      -9.5445661      16.311979      
        51 -22.86926899999 -10.625037      12.996888999999
        52 -25.31559599999 -11.482084      9.1469713      
        53 -26.908767      -12.067244      4.804753       
        54 -27.44754199999 -12.338182      0.0                   7       7            
        55 -16.0           -4.2342801      20.348731      
        56 -20.737171      -4.9208503      17.603784      
        57 -24.74971199999 -5.5265164      14.173892      
        58 -27.90404399999 -6.0215693      10.087524      
        59 -30.009139      -6.3732333      5.368744       
        60 -30.783199      -6.5553032      0.0                   7       7            
        61 -16.0           0.0             20.78461       
        62 -21.100687      0.0             18.043088999999
        63 -25.42426199999 0.0             14.574083      
        64 -28.834848      0.0             10.407221      
        65 -31.129503      0.0             5.5598258      
        66 -32.0           0.0             0.0                   7       7            
        67 -16.0           4.2342801       20.348731      
        68 -20.73719399999 4.9207969       17.603784      
        69 -24.749759      5.5264012       14.173892      
        70 -27.904115      6.0213868       10.087522999999
        71 -30.00923399999 6.3729818       5.3687441      
        72 -30.78331899999 6.5549861       0.0                   7       7            
        73 -16.0           8.2909282999999 19.059394      
        74 -19.723178      9.5449018999999 16.311966      
        75 -22.86872599999 10.625724999999 12.996864      
        76 -25.314781      11.483124       9.1469337999999
        77 -26.907708      12.06858        4.80473        
        78 -27.44626999999 12.339774       0.0                   7       7            
        79 -16.0           12.0            16.970562999999
        80 -18.218449      13.663836999999 14.234035      
        81 -20.065732      15.049299       11.096848      
        82 -21.462235      16.096675999999 7.6152887      
        83 -22.332974      16.749731       3.8764176      
        84 -22.627417      16.970562999999 0.0                   7       7            
        91 -17.48928       -20.098392      0.0                   7       7            
        92 -17.26152199999 -19.650828      4.7161829      
        93 -16.542732      -18.416694      9.1044219      
        94 -15.403636      -16.59363799999 12.93003       
        95 -13.932169      -14.398075      16.109351      
        96 -12.209959      -12.0           18.659607      
        97 -11.88277199999 -22.28395899999 0.0                   7       7            
        98 -11.726379      -21.686772      5.3231273      
        99 -11.217618      -20.039218      10.180745999999
       100 -10.418631      -17.66228299999 14.247301      
       101 -9.4029368      -14.898503      17.444227      
       102 -8.2337168      -12.0           19.847377      
       103 -6.0041111      -23.57376199999 0.0                   7       7            
       104 -5.9212821      -22.889416      5.6879244      
       105 -5.6568419      -20.99456       10.827211999999
       106 -5.2464861      -18.28748699999 15.036111999999
       107 -4.7312145      -15.188826      18.240293999999
       108 -4.1437314      -12.0           20.551518      
       109 0.0             -24.0           0.0                   7       7            
       110 0.0             -23.286255      5.8095019      
       111 0.0             -21.30883199999 11.042358      
       112 0.0             -18.49231299999 15.298182      
       113 0.0             -15.283376      18.504550999999
       114 0.0             -12.0           20.784751      
       115 6.0041111       -23.57376199999 0.0                   7       7            
       116 5.9212863       -22.889278      5.6884796      
       117 5.6569458       -20.994126      10.828023      
       118 5.2467251       -18.286845      15.036846      
       119 4.7301217       -15.187905      18.241220999999
       120 4.1437648       -12.0           20.551594999999
       121 11.882771999999 -22.28395899999 0.0            
       122 11.726438       -21.686547      5.3239722      
       123 11.217784999999 -20.038532      10.181991999999
       124 10.41892        -17.66126699999 14.248442      
       125 9.4018628       -14.896951      17.445878      
       126 8.2337532       -12.0           19.847474999999
       127 17.48928        -20.098392      0.0                   7       7            
       128 17.261614       -19.650618      4.7168692      
       129 16.542929       -18.41608799999 9.1054476      
       130 15.403937       -16.592737      12.930984      
       131 13.931139       -14.39643       16.111322      
       132 12.20998        -12.0           18.659656999999
       143 12.209709999999 -8.276903799999 20.582445      
       144 8.2335151999999 -8.2726636      21.66635       
       145 4.1437061       -8.2721876      22.313956      
       146 0.0             -8.2723656      22.529268999999
       147 -4.1436886      -8.2722233      22.313943999999
       148 -8.2335029      -8.2727105      21.666335      
       149 -12.209705      -8.2769288      20.582436999999
       152 12.209707999999 -4.2329685      21.776734999999
       153 8.2335121       -4.2360558      22.801832      
       154 4.1437017       -4.2392893      23.417304999999
       155 0.0             -4.2405908      23.622392      
       156 -4.143693       -4.2393245      23.417299      
       157 -8.233506       -4.2361022      22.801825      
       158 -12.209706      -4.2329933      21.776731      
       161 12.209707       0.0             22.184324      
       162 8.233509        0.0             23.191976      
       163 4.1436974       0.0             23.797936      
       164 0.0             0.0             24.0           
       165 -4.1436974      0.0             23.797936      
       166 -8.233509       0.0             23.191976      
       167 -12.209707      0.0             22.184324      
       170 12.209706       4.2329932       21.776731      
       171 8.2335059       4.2361022       22.801825      
       172 4.143693        4.2393245       23.417299      
       173 0.0             4.2405908       23.622392      
       174 -4.1437017      4.2392893       23.417304999999
       175 -8.233511999999 4.2360558       22.801832      
       176 -12.20970799999 4.2329684       21.776734999999
       179 12.209704       8.2769288       20.582436999999
       180 8.2335027       8.2727105       21.666335      
       181 4.1436886       8.2722233       22.313943999999
       182 0.0             8.2723656       22.529268999999
       183 -4.1437061      8.2721876       22.313956      
       184 -8.233515       8.2726636       21.66635       
       185 -12.209709      8.2769037999999 20.582445      
       188 12.209959       12.0            18.659607      
       189 8.2337168       12.0            19.847377      
       190 4.1437314       12.0            20.551518      
       191 0.0             12.0            20.784751      
       192 -4.1437648      12.0            20.551594999999
       193 -8.2337532      12.0            19.847474999999
       194 -12.20998       12.0            18.659656999999
       202 -13.932105      14.398275999999 16.109202      
       203 -15.403756      16.593589       12.930012      
       204 -16.54281699999 18.416656       9.1044137      
       205 -17.26155199999 19.650814       4.7161801      
       206 -17.48928       20.098392       0.0                   7       7            
       208 -9.4027747      14.898944999999 17.443898999999
       209 -10.418839      17.662222       14.247291      
       210 -11.21776599999 20.039172       10.180744      
       211 -11.726431      21.686757       5.3231261      
       212 -11.88277199999 22.283958999999 0.0                   7       7            
       214 -4.7309327      15.189534999999 18.239744999999
       215 -5.246739       18.287448       15.03611       
       216 -5.6570229      20.994532       10.827214      
       217 -5.9213468      22.889408       5.6879202      
       218 -6.0041111      23.573761999999 0.0                   7       7            
       220 0.0             15.284345       18.503751      
       221 0.0             18.492312999999 15.298182      
       222 0.0             21.308831999999 11.042358      
       223 0.0             23.286258       5.8094905      
       224 0.0             24.0            0.0                   7       7            
       226 4.730731        15.189071999999 18.240159999999
       227 5.2464714       18.286884       15.036848      
       228 5.6567643       20.994154999999 10.828021      
       229 5.9212221       22.889291       5.6884616      
       230 6.0041111       23.573761999999 0.0                   7       7            
       232 9.4026744       14.898198       17.444566999999
       233 10.418711       17.661328       14.248452      
       234 11.217637       20.038578       10.181994      
       235 11.726387       21.686567       5.3239526      
       236 11.882771999999 22.283958999999 0.0                   7       7            
       238 13.932152       14.397596999999 16.109787      
       239 15.403816       16.592786       12.931003      
       240 16.542845       18.416126999999 9.1054556      
       241 17.261586       19.650635       4.7168534      
       242 17.48928        20.098392       0.0                   7       7
  $---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
  *ELEMENT_SHELL
         1       1       1       2       8       7
         2       1       2       3       9       8
         3       1       3       4      10       9
         4       1       4       5      11      10
         5       1       5       6      12      11
         6       1       7       8      14      13
         7       1       8       9      15      14
         8       1       9      10      16      15
         9       1      10      11      17      16
        10       1      11      12      18      17
        11       1      13      14      20      19
        12       1      14      15      21      20
        13       1      15      16      22      21
        14       1      16      17      23      22
        15       1      17      18      24      23
        16       1      19      20      26      25
        17       1      20      21      27      26
        18       1      21      22      28      27
        19       1      22      23      29      28
        20       1      23      24      30      29
        21       1      25      26      32      31
        22       1      26      27      33      32
        23       1      27      28      34      33
        24       1      28      29      35      34
        25       1      29      30      36      35
        26       1      31      32      38      37
        27       1      32      33      39      38
        28       1      33      34      40      39
        29       1      34      35      41      40
        30       1      35      36      42      41
        31       1      43      44      50      49
        32       1      44      45      51      50
        33       1      45      46      52      51
        34       1      46      47      53      52
        35       1      47      48      54      53
        36       1      49      50      56      55
        37       1      50      51      57      56
        38       1      51      52      58      57
        39       1      52      53      59      58
        40       1      53      54      60      59
        41       1      55      56      62      61
        42       1      56      57      63      62
        43       1      57      58      64      63
        44       1      58      59      65      64
        45       1      59      60      66      65
        46       1      61      62      68      67
        47       1      62      63      69      68
        48       1      63      64      70      69
        49       1      64      65      71      70
        50       1      65      66      72      71
        51       1      67      68      74      73
        52       1      68      69      75      74
        53       1      69      70      76      75
        54       1      70      71      77      76
        55       1      71      72      78      77
        56       1      73      74      80      79
        57       1      74      75      81      80
        58       1      75      76      82      81
        59       1      76      77      83      82
        60       1      77      78      84      83
        61       1      48      47      92      91
        62       1      47      46      93      92
        63       1      46      45      94      93
        64       1      45      44      95      94
        65       1      44      43      96      95
        66       1      91      92      98      97
        67       1      92      93      99      98
        68       1      93      94     100      99
        69       1      94      95     101     100
        70       1      95      96     102     101
        71       1      97      98     104     103
        72       1      98      99     105     104
        73       1      99     100     106     105
        74       1     100     101     107     106
        75       1     101     102     108     107
        76       1     103     104     110     109
        77       1     104     105     111     110
        78       1     105     106     112     111
        79       1     106     107     113     112
        80       1     107     108     114     113
        81       1     109     110     116     115
        82       1     110     111     117     116
        83       1     111     112     118     117
        84       1     112     113     119     118
        85       1     113     114     120     119
        86       1     115     116     122     121
        87       1     116     117     123     122
        88       1     117     118     124     123
        89       1     118     119     125     124
        90       1     119     120     126     125
        91       1     121     122     128     127
        92       1     122     123     129     128
        93       1     123     124     130     129
        94       1     124     125     131     130
        95       1     125     126     132     131
        96       1     127     128       2       1
        97       1     128     129       3       2
        98       1     129     130       4       3
        99       1     130     131       5       4
       100       1     131     132       6       5
       101       1       6     132     143      12
       102       1     132     126     144     143
       103       1     126     120     145     144
       104       1     120     114     146     145
       105       1     114     108     147     146
       106       1     108     102     148     147
       107       1     102      96     149     148
       108       1      96      43      49     149
       109       1      12     143     152      18
       110       1     143     144     153     152
       111       1     144     145     154     153
       112       1     145     146     155     154
       113       1     146     147     156     155
       114       1     147     148     157     156
       115       1     148     149     158     157
       116       1     149      49      55     158
       117       1      18     152     161      24
       118       1     152     153     162     161
       119       1     153     154     163     162
       120       1     154     155     164     163
       121       1     155     156     165     164
       122       1     156     157     166     165
       123       1     157     158     167     166
       124       1     158      55      61     167
       125       1      24     161     170      30
       126       1     161     162     171     170
       127       1     162     163     172     171
       128       1     163     164     173     172
       129       1     164     165     174     173
       130       1     165     166     175     174
       131       1     166     167     176     175
       132       1     167      61      67     176
       133       1      30     170     179      36
       134       1     170     171     180     179
       135       1     171     172     181     180
       136       1     172     173     182     181
       137       1     173     174     183     182
       138       1     174     175     184     183
       139       1     175     176     185     184
       140       1     176      67      73     185
       141       1      36     179     188      42
       142       1     179     180     189     188
       143       1     180     181     190     189
       144       1     181     182     191     190
       145       1     182     183     192     191
       146       1     183     184     193     192
       147       1     184     185     194     193
       148       1     185      73      79     194
       149       1      79      80     202     194
       150       1      80      81     203     202
       151       1      81      82     204     203
       152       1      82      83     205     204
       153       1      83      84     206     205
       154       1     194     202     208     193
       155       1     202     203     209     208
       156       1     203     204     210     209
       157       1     204     205     211     210
       158       1     205     206     212     211
       159       1     193     208     214     192
       160       1     208     209     215     214
       161       1     209     210     216     215
       162       1     210     211     217     216
       163       1     211     212     218     217
       164       1     192     214     220     191
       165       1     214     215     221     220
       166       1     215     216     222     221
       167       1     216     217     223     222
       168       1     217     218     224     223
       169       1     191     220     226     190
       170       1     220     221     227     226
       171       1     221     222     228     227
       172       1     222     223     229     228
       173       1     223     224     230     229
       174       1     190     226     232     189
       175       1     226     227     233     232
       176       1     227     228     234     233
       177       1     228     229     235     234
       178       1     229     230     236     235
       179       1     189     232     238     188
       180       1     232     233     239     238
       181       1     233     234     240     239
       182       1     234     235     241     240
       183       1     235     236     242     241
       184       1     188     238      41      42
       185       1     238     239      40      41
       186       1     239     240      39      40
       187       1     240     241      38      39
       188       1     241     242      37      38
  *END

Figures

image01.gif

image02.gif

Animated Result

Result

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