Un problema di contatto

Si tratta di una lastra con una fessura (vedi fig.1). Nella parte superiore è applicata una pressione. Se si indica con l l'altezza della fessura, si vuole tenere conto del contatto che si realizza tra le due superfici non appena il bordo superiore tocca quello inferiore.
Fig. 1 Il modello utilizzato
Elementi gap Si è fatto uso di elementi gap ("Compression Only") dotati di rigidezza assiali molto elevata e vincolati solo tramite vincoli multipunto. Per far si che tali bielle non intervengano a fessura aperta, è stato assegnato un DT=-1. La relazione che lega la variazione di temperatura con l'ampiezza della fessura è: l = a DT L dove L indica la lunghezza delle aste (1000 in questo modello, ma si tratta di una misura che può essere variata mantenendo verificata la relazione di cui sopra). Così facendo il gap resta teso a fessura aperta (vedi constraint). Vincoli L'analisi è piana. I plate sono vincolati in X e Y alla base. Le bielle sono vincolate tramite constraint del tipo: dX(A)=dX(C) dY(A)=dY(B) Listato
===============================================================================
 STRAND6.15 | DATA LISTING - STRUCTURE INPUT
===============================================================================

FILENAME :
C:\STRAND61\MODELLI\CONTATTO

HEADING :
STRAND6.1

PROJECT :


CREATED BY :
STEFANO SECCHI

REVISION :
1.0

DATE CREATED :
12  /  10  /  1995

DATE MODIFIED :
12  /  10  /  1995



  NODE TOTAL =    114
  NODE           X                       Y                       Z
     1          0.000000000000          0.000000000000          0.000000000000
     2        100.000000000000          0.000000000000          0.000000000000
     3          0.000000000000        100.000000000000          0.000000000000
     4        100.000000000000        100.000000000000          0.000000000000
     5        200.000000000000          0.000000000000          0.000000000000
     6        200.000000000000        100.000000000000          0.000000000000
     7        300.000000000000          0.000000000000          0.000000000000
     8        300.000000000000        100.000000000000          0.000000000000
     9        400.000000000000          0.000000000000          0.000000000000
    10        400.000000000000        100.000000000000          0.000000000000
    11        500.000000000000          0.000000000000          0.000000000000
    12        500.000000000000        100.000000000000          0.000000000000
    13        600.000000000000          0.000000000000          0.000000000000
    14        600.000000000000        100.000000000000          0.000000000000
    15        700.000000000000          0.000000000000          0.000000000000
    16        700.000000000000        100.000000000000          0.000000000000
    17        800.000000000000          0.000000000000          0.000000000000
    18        800.000000000000        100.000000000000          0.000000000000
    19        900.000000000000          0.000000000000          0.000000000000
    20        900.000000000000        100.000000000000          0.000000000000
    21       1000.000000000000          0.000000000000          0.000000000000
    22       1000.000000000000        100.000000000000          0.000000000000
    23       1100.000000000000          0.000000000000          0.000000000000
    24       1100.000000000000        100.000000000000          0.000000000000
    25          0.000000000000        200.000000000000          0.000000000000
    26        100.000000000000        200.000000000000          0.000000000000
    27        200.000000000000        200.000000000000          0.000000000000
    28        300.000000000000        200.000000000000          0.000000000000
    29        400.000000000000        200.000000000000          0.000000000000
    30        500.000000000000        200.000000000000          0.000000000000
    31        600.000000000000        200.000000000000          0.000000000000
    32        700.000000000000        200.000000000000          0.000000000000
    33        800.000000000000        200.000000000000          0.000000000000
    34        900.000000000000        200.000000000000          0.000000000000
    35       1000.000000000000        200.000000000000          0.000000000000
    36       1100.000000000000        200.000000000000          0.000000000000
    37          0.000000000000        300.000000000000          0.000000000000
    38        100.000000000000        300.000000000000          0.000000000000
    39        200.000000000000        300.000000000000          0.000000000000
    40        300.000000000000        300.000000000000          0.000000000000
    41        400.000000000000        300.000000000000          0.000000000000
    42        500.000000000000        300.000000000000          0.000000000000
    43        600.000000000000        300.000000000000          0.000000000000
    44        700.000000000000        300.000000000000          0.000000000000
    45        800.000000000000        300.000000000000          0.000000000000
    46        900.000000000000        300.000000000000          0.000000000000
    47       1000.000000000000        300.000000000000          0.000000000000
    48       1100.000000000000        300.000000000000          0.000000000000
    49          0.000000000000        400.000000000000          0.000000000000
    50        100.000000000000        400.000000000000          0.000000000000
    51        200.000000000000        400.000000000000          0.000000000000
    52        300.000000000000        400.000000000000          0.000000000000
    53        400.000000000000        400.000000000000          0.000000000000
    54        500.000000000000        400.000000000000          0.000000000000
    55        600.000000000000        400.000000000000          0.000000000000
    56        700.000000000000        400.000000000000          0.000000000000
    57        800.000000000000        400.000000000000          0.000000000000
    58        900.000000000000        400.000000000000          0.000000000000
    59       1000.000000000000        400.000000000000          0.000000000000
    60       1100.000000000000        400.000000000000          0.000000000000
    61          0.000000000000        500.000000000000          0.000000000000
    62        100.000000000000        500.000000000000          0.000000000000
    63        200.000000000000        500.000000000000          0.000000000000
    64        300.000000000000        500.000000000000          0.000000000000
    65        400.000000000000        500.000000000000          0.000000000000
    66        500.000000000000        500.000000000000          0.000000000000
    67        600.000000000000        500.000000000000          0.000000000000
    68        700.000000000000        500.000000000000          0.000000000000
    69        800.000000000000        500.000000000000          0.000000000000
    70        900.000000000000        500.000000000000          0.000000000000
    71       1000.000000000000        500.000000000000          0.000000000000
    72       1100.000000000000        500.000000000000          0.000000000000
    73          0.000000000000        600.000000000000          0.000000000000
    74        100.000000000000        600.000000000000          0.000000000000
    75        200.000000000000        600.000000000000          0.000000000000
    76        300.000000000000        600.000000000000          0.000000000000
    77        400.000000000000        600.000000000000          0.000000000000
    78        500.000000000000        600.000000000000          0.000000000000
    79        600.000000000000        600.000000000000          0.000000000000
    80        700.000000000000        600.000000000000          0.000000000000
    81        800.000000000000        600.000000000000          0.000000000000
    82        900.000000000000        600.000000000000          0.000000000000
    83       1000.000000000000        600.000000000000          0.000000000000
    84       1100.000000000000        600.000000000000          0.000000000000
    85          0.000000000000        650.000000000000          0.000000000000
    86        100.000000000000        650.000000000000          0.000000000000
    87        200.000000000000        650.000000000000          0.000000000000
    88        300.000000000000        650.000000000000          0.000000000000
    89        400.000000000000        650.000000000000          0.000000000000
    90        500.000000000000        650.000000000000          0.000000000000
    91        600.000000000000        650.000000000000          0.000000000000
    92        700.000000000000        650.000000000000          0.000000000000
    93        800.000000000000        650.000000000000          0.000000000000
    94        900.000000000000        650.000000000000          0.000000000000
    95       1000.000000000000        650.000000000000          0.000000000000
    96       1100.000000000000        650.000000000000          0.000000000000
    97          0.000000000000        700.000000000000          0.000000000000
    98        100.000000000000        700.000000000000          0.000000000000
    99        200.000000000000        700.000000000000          0.000000000000
   100        300.000000000000        700.000000000000          0.000000000000
   101        400.000000000000        700.000000000000          0.000000000000
   102        500.000000000000        700.000000000000          0.000000000000
   103        600.000000000000        700.000000000000          0.000000000000
   104        700.000000000000        700.000000000000          0.000000000000
   105        800.000000000000        700.000000000000          0.000000000000
   106        900.000000000000        700.000000000000          0.000000000000
   107       1000.000000000000        700.000000000000          0.000000000000
   108       1100.000000000000        700.000000000000          0.000000000000
   109        300.000000000000       -350.000000000000          0.000000000000
   110        400.000000000000       -350.000000000000          0.000000000000
   111        500.000000000000       -350.000000000000          0.000000000000
   112        600.000000000000       -350.000000000000          0.000000000000
   113        700.000000000000       -350.000000000000          0.000000000000
   114        800.000000000000       -350.000000000000          0.000000000000

FREEDOM CONDITIONS FOR NODES : (0 -> FREE ; 1 -> FIXED)
DEFAULT  :     0    0    1    1    1    0
   NODE       DX   DY   DZ   RX   RY   RZ
     1         1    1    1    1    1    1
     2         1    1    1    1    1    1
     5         1    1    1    1    1    1
     7         1    1    1    1    1    1
     9         1    1    1    1    1    1
    11         1    1    1    1    1    1
    13         1    1    1    1    1    1
    15         1    1    1    1    1    1
    17         1    1    1    1    1    1
    19         1    1    1    1    1    1
    21         1    1    1    1    1    1
    23         1    1    1    1    1    1


REFERENCE TEMPERATURE =   0.0000E+00
TEMPERATURE DATA (NODAL)
   NODE       TEMPERATURE
    88        -1.0000E+00
    89        -1.0000E+00
    90        -1.0000E+00
    91        -1.0000E+00
    92        -1.0000E+00
    93        -1.0000E+00
   109        -1.0000E+00
   110        -1.0000E+00
   111        -1.0000E+00
   112        -1.0000E+00
   113        -1.0000E+00
   114        -1.0000E+00


CONSTRAINT EQUATIONS TOTAL =     12
 Eq.No.  DOF  N(i)         A     DOF  N(j)       B     DOF  N(k)       C
     1   DX(  109) = +   1.00000*DX(   88)                       +   0.00000
     2   DY(  109) = +   1.00000*DY(   76)                       +   0.00000
     3   DX(  110) = +   1.00000*DX(   89)                       +   0.00000
     4   DY(  110) = +   1.00000*DY(   77)                       +   0.00000
     5   DX(  111) = +   1.00000*DX(   90)                       +   0.00000
     6   DY(  111) = +   1.00000*DY(   78)                       +   0.00000
     7   DX(  112) = +   1.00000*DX(   91)                       +   0.00000
     8   DY(  112) = +   1.00000*DY(   79)                       +   0.00000
     9   DX(  113) = +   1.00000*DX(   92)                       +   0.00000
    10   DY(  113) = +   1.00000*DY(   80)                       +   0.00000
    11   DX(  114) = +   1.00000*DX(   93)                       +   0.00000
    12   DY(  114) = +   1.00000*DY(   81)                       +   0.00000

  BEAM TOTAL =      6
  BEAM     N1     N2    Nref   Prop   EndRel
     1     88    109      0      1    1  1  1  1  1  1
     2     89    110      0      1    1  1  1  1  1  1
     3     90    111      0      1    1  1  1  1  1  1
     4     91    112      0      1    1  1  1  1  1  1
     5     92    113      0      1    1  1  1  1  1  1
     6     93    114      0      1    1  1  1  1  1  1


 PLATE TOTAL =     81
 PLATE     N1    N2    N3    N4    N5    N6    N7    N8   Prop    Type
     1      1     2     4     3     0     0     0     0     1    QUAD4
     2      2     5     6     4     0     0     0     0     1    QUAD4
     3      5     7     8     6     0     0     0     0     1    QUAD4
     4      7     9    10     8     0     0     0     0     1    QUAD4
     5      9    11    12    10     0     0     0     0     1    QUAD4
     6     11    13    14    12     0     0     0     0     1    QUAD4
     7     13    15    16    14     0     0     0     0     1    QUAD4
     8     15    17    18    16     0     0     0     0     1    QUAD4
     9     17    19    20    18     0     0     0     0     1    QUAD4
    10     19    21    22    20     0     0     0     0     1    QUAD4
    11     21    23    24    22     0     0     0     0     1    QUAD4
    12      3     4    26    25     0     0     0     0     1    QUAD4
    13      4     6    27    26     0     0     0     0     1    QUAD4
    14      6     8    28    27     0     0     0     0     1    QUAD4
    15      8    10    29    28     0     0     0     0     1    QUAD4
    16     10    12    30    29     0     0     0     0     1    QUAD4
    17     12    14    31    30     0     0     0     0     1    QUAD4
    18     14    16    32    31     0     0     0     0     1    QUAD4
    19     16    18    33    32     0     0     0     0     1    QUAD4
    20     18    20    34    33     0     0     0     0     1    QUAD4
    21     20    22    35    34     0     0     0     0     1    QUAD4
    22     22    24    36    35     0     0     0     0     1    QUAD4
    23     25    26    38    37     0     0     0     0     1    QUAD4
    24     26    27    39    38     0     0     0     0     1    QUAD4
    25     27    28    40    39     0     0     0     0     1    QUAD4
    26     28    29    41    40     0     0     0     0     1    QUAD4
    27     29    30    42    41     0     0     0     0     1    QUAD4
    28     30    31    43    42     0     0     0     0     1    QUAD4
    29     31    32    44    43     0     0     0     0     1    QUAD4
    30     32    33    45    44     0     0     0     0     1    QUAD4
    31     33    34    46    45     0     0     0     0     1    QUAD4
    32     34    35    47    46     0     0     0     0     1    QUAD4
    33     35    36    48    47     0     0     0     0     1    QUAD4
    34     37    38    50    49     0     0     0     0     1    QUAD4
    35     38    39    51    50     0     0     0     0     1    QUAD4
    36     39    40    52    51     0     0     0     0     1    QUAD4
    37     40    41    53    52     0     0     0     0     1    QUAD4
    38     41    42    54    53     0     0     0     0     1    QUAD4
    39     42    43    55    54     0     0     0     0     1    QUAD4
    40     43    44    56    55     0     0     0     0     1    QUAD4
    41     44    45    57    56     0     0     0     0     1    QUAD4
    42     45    46    58    57     0     0     0     0     1    QUAD4
    43     46    47    59    58     0     0     0     0     1    QUAD4
    44     47    48    60    59     0     0     0     0     1    QUAD4
    45     49    50    62    61     0     0     0     0     1    QUAD4
    46     50    51    63    62     0     0     0     0     1    QUAD4
    47     51    52    64    63     0     0     0     0     1    QUAD4
    48     52    53    65    64     0     0     0     0     1    QUAD4
    49     53    54    66    65     0     0     0     0     1    QUAD4
    50     54    55    67    66     0     0     0     0     1    QUAD4
    51     55    56    68    67     0     0     0     0     1    QUAD4
    52     56    57    69    68     0     0     0     0     1    QUAD4
    53     57    58    70    69     0     0     0     0     1    QUAD4
    54     58    59    71    70     0     0     0     0     1    QUAD4
    55     59    60    72    71     0     0     0     0     1    QUAD4
    56     61    62    74    73     0     0     0     0     1    QUAD4
    57     62    63    75    74     0     0     0     0     1    QUAD4
    58     63    64    76    75     0     0     0     0     1    QUAD4
    59     64    65    77    76     0     0     0     0     1    QUAD4
    60     65    66    78    77     0     0     0     0     1    QUAD4
    61     66    67    79    78     0     0     0     0     1    QUAD4
    62     67    68    80    79     0     0     0     0     1    QUAD4
    63     68    69    81    80     0     0     0     0     1    QUAD4
    64     69    70    82    81     0     0     0     0     1    QUAD4
    65     70    71    83    82     0     0     0     0     1    QUAD4
    66     71    72    84    83     0     0     0     0     1    QUAD4
    67     85    86    98    97     0     0     0     0     1    QUAD4
    68     86    87    99    98     0     0     0     0     1    QUAD4
    69     87    88   100    99     0     0     0     0     1    QUAD4
    70     88    89   101   100     0     0     0     0     1    QUAD4
    71     89    90   102   101     0     0     0     0     1    QUAD4
    72     90    91   103   102     0     0     0     0     1    QUAD4
    73     91    92   104   103     0     0     0     0     1    QUAD4
    74     92    93   105   104     0     0     0     0     1    QUAD4
    75     93    94   106   105     0     0     0     0     1    QUAD4
    76     94    95   107   106     0     0     0     0     1    QUAD4
    77     95    96   108   107     0     0     0     0     1    QUAD4
    78     73    74    86    85     0     0     0     0     1    QUAD4
    79     74    75    87    86     0     0     0     0     1    QUAD4
    80     82    83    95    94     0     0     0     0     1    QUAD4
    81     83    84    96    95     0     0     0     0     1    QUAD4

 EDGE STRESS TOTAL =     81 LOAD CASE =   1
 PLATE      S1          S2          S3          S4
            T1          T2          T3          T4
    69    0.0000E+00  0.0000E+00 -2.0000E+03  0.0000E+00
          0.0000E+00  0.0000E+00  0.0000E+00  0.0000E+00
    70    0.0000E+00  0.0000E+00 -2.0000E+03  0.0000E+00
          0.0000E+00  0.0000E+00  0.0000E+00  0.0000E+00
    71    0.0000E+00  0.0000E+00 -2.0000E+03  0.0000E+00
          0.0000E+00  0.0000E+00  0.0000E+00  0.0000E+00
    72    0.0000E+00  0.0000E+00 -2.0000E+03  0.0000E+00
          0.0000E+00  0.0000E+00  0.0000E+00  0.0000E+00
    73    0.0000E+00  0.0000E+00 -2.0000E+03  0.0000E+00
          0.0000E+00  0.0000E+00  0.0000E+00  0.0000E+00
    74    0.0000E+00  0.0000E+00 -2.0000E+03  0.0000E+00
          0.0000E+00  0.0000E+00  0.0000E+00  0.0000E+00
    75    0.0000E+00  0.0000E+00 -2.0000E+03  0.0000E+00
          0.0000E+00  0.0000E+00  0.0000E+00  0.0000E+00

 BEAM PROPERTIES TOTAL =   2 TYPE =   1 Section
 Standard: Circular (OD= 3.568E+01 ID= 0.000E+00)
 Beam Type: Comp. Only CutoffType: ElastPlast    Max.Comp.= 1.000E+11

           E =   1.0000E+08           A =   1.0000E+03
           J =   0.0000E+00           G =   0.0000E+00

         I11 =   0.0000E+00         I22 =   0.0000E+00
    Shear:L1 =   0.0000E+00    Shear:L2 =   0.0000E+00
  NodLine:L1 =   0.0000E+00  NodLine:L2 =   0.0000E+00
       UDL:1 =   0.0000E+00       UDL:2 =   0.0000E+00
        TG:1 =   0.0000E+00        TG:2 =   0.0000E+00

       Alpha =   5.0000E-02        SA11 =   0.0000E+00
     Density =   0.0000E+00        SA22 =   0.0000E+00

 Temperature Table =      0

 BEAM PROPERTIES TOTAL =   2 TYPE =   2
 Beam Type:  Normal Beam

           E =   0.0000E+00           A =   0.0000E+00
           J =   0.0000E+00           G =   0.0000E+00

         I11 =   0.0000E+00         I22 =   0.0000E+00
    Shear:L1 =   0.0000E+00    Shear:L2 =   0.0000E+00
  NodLine:L1 =   0.0000E+00  NodLine:L2 =   0.0000E+00
       UDL:1 =   0.0000E+00       UDL:2 =   0.0000E+00
        TG:1 =   0.0000E+00        TG:2 =   0.0000E+00

       Alpha =   0.0000E+00        SA11 =   0.0000E+00
     Density =   0.0000E+00        SA22 =   0.0000E+00

 Temperature Table =      0


 PLATE PROPERTIES TOTAL =   1 TYPE =   1
 ISOTROPIC     Element : LinearQuad, PlateShell, Von Mises

             E =   3.0000E+05
 Poisson Ratio =   4.0000E-01
         Alpha =   0.0000E+00
    Layers No. =   0

 Memb.Thick =   1.0000E+01 Bend.Thick =   1.0000E+01
   Pressure =   0.0000E+00    Density =   0.0000E+00

   Stress:1 =   0.0000E+00   Stress:2 =   0.0000E+00
   Stress:3 =   0.0000E+00   Stress:4 =   0.0000E+00
   Shear :1 =   0.0000E+00   Shear :2 =   0.0000E+00
   Shear :3 =   0.0000E+00   Shear :4 =   0.0000E+00

 Temperature Table =      0
 Stress-Strain Table =      0
Risultati: E' stato utilizzato il solutore "Linear Static". Nella condizione di carico 1 devono essere inclusi anche gli effetti termici. Di seguito sono riportate una sequenza di immagini corrispondenti ad un carico crescente.
Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6