+PROG AQUA urs:1
HEAD AIR-BRIQ - Deformation with constant volume leads to no stresses
NORM EC1
MAT 1 E 0.0006 MUE 0.499999 G 0.0002 K 100 GAM 0
END
END
 without temperatur increase: p*v=constant
     p0 = 1 bar = 100 kN/m2
     delta-V = 1 % Volume decrease
     delta-p = 1 % von 100 = 1 kN/m2 increased pressure
 d.h. Compression-modulus K = delta-sigma/delta-eps-V
                          K = 1/0.01 = 100 kN/m2
 Poisson-Ratio should be 0.5
 due to the fact that 0.5 is according to numerical reasons not possible:
 mue=0.499999  (= 0.5-1E-6)
 leads to:
                   E
         K  =  ---------
                3(1-2mue)
 E = K*(3*(1-2mue)) = 0.0006 KN/m2
                   E
         G  =   --------
                 2(1+m)

 G = E/3            = 0.0002 KN/m2

Transformation in the materials law:


         E     Youngs-modulus
         Es    Subgrade modulus (horizontally constrained)
         K     Compression-modulus/Bulk-modulus
         G     Shear-modulus
         m     Poisson-ratio

                   E                      E
         K  =  ---------        G  =   --------
                3(1-2m)                 2(1+m)

                 9·K·G                  3K - 2G
         E  =  ----------       m  =   ----------
                 3K + G                 6K + 2G

                    1 - m
         Es  =  E -----------
                  (1+m)(1-2m)

                 3·K·E                  3·K·(1-2m)
         G  =  ---------        G  =   ------------
                9·K - E                   2·(1+m)

+PROG GENF urs:2
HEAD AIR-BRIQ - Deformation with constant volume leads to no stresses
SYST SPAC FIXS mm
NODE NO X Y
  11 0 0 ; 12 0 4 ; 13 4 0 ; 14 4 4
TRAN FROM TO INC DZ DNO
      11  14    1  4 100
BRIC NO N1 N2 N3 N4  N5  N6  N7  N8  MNO
     21 11 12 14 13 111 112 114 113   1
  SPRI NO        NA      CP   CT DZ
    (11  14 1)  (11 1)  1E6  1E6  1      $ All Nodes supported by very stiff springs
   (111 114 1) (111 1)  1E6  1E6  1
END

+PROG ASE urs:3
HEAD
PAGE UNIO 7                                       $vvvvv  v 3=3 Nachkommastellen
$1092 MAT_STRESS       71  2  71  2  71  1  71  2  75  2  71  2  71  2  72  3 271  2 271  2 271  1 271  2 275  2 \
$                     271  2 271  2 271  1 271  2 275  2 271  1 271  2 275  2                                    \
$                      74  2  74  2  74  1  74  2  75  2  74  2  74  2  74  1
LC 1 TITL   '1 Percent deflection in z'
  LOAD NNO          PZ
     11,12,13,14  0.04*1E6
END
END
leads to -0.001 MN/m2 Compression or -0.999 kN/m2    OK
  or support conditions:
  Node 111 with -4.0 kN on 4m2  =   -1 kN/m2   OK

+PROG ASE urs:4
HEAD
PAGE UNIO 7
LC 2 TITL   'Volume-constant deformation'
  LOAD 11,12,13,14     PZ 0.4*1E6
  LOAD 13,14,113,114   PX 0.4*1E6
LC 3 TITL   'Volume-constant shear-deformation'
  LOAD 12,14,112,114   PX 0.4*1E6
END
END

leads to 0.00 MN/m2 compression
  3  Volume-constant shear-deformation
  Element     sig-x     sig-y     sig-z    tau-xy    tau-xz    tau-yz
       Nr   [kN/m2]   [kN/m2]   [kN/m2]   [kN/m2]   [kN/m2]   [kN/m2]
       21     0.000     0.000     0.000     0.000     0.000     0.000
and no support reactions:
  Node 111 with 0 kN

JB 22.08.2002

+sys animator $(name) /L1 /f /a3
$ Batch-Animator for input description see: animator.htm Version 11.01