Document Text Contents
Page 195
GENFDefinition of Finite Elements
5−23Version 10.20
$ SUBPROGRAM FOR NODE GENERATION IN A COORDINATE THIRD
$ NODE COORDINATES WITH NONLINEAR INCREMENT ROTATION
$ #1,#2,#3 = NODE NUMBER ON AXIS + INCREMENTS
LET#10 0,45/#4 $ Starting value + Increment phi−Y
LOOP #4+1
LET#20 0,45/#4 $ Starting value + Increment phi−Z
LOOP #4+1
LET#90 SQR(TAN(#10)**2+TAN(#20)**2)
LET#91 ATN(#90)
LET#92 COS(#91),0.0
LOOP #91−0.001 ; LET#93 SIN(#91)/#90 ; ENDLOOP −1
$ nodes
#1 #9*#92 #9*TAN(#20)*#93 #9*TAN(#10)*#93
LET#20 #20+#21
LET#1 #1+#3
ENDLOOP
LET#10 #10+#11
LET#1 #1−#3*(#4+1)+#2
ENDLOOP
$BLOCK END1
LET#1 101,10,1 $ Node number + Increments of the X−Sector
NODE NO X Y Z
$BLOCK SET1
LET#1 101+#4*101,−100,10 $ Node number + Increments of the Y−Sector
NODE NO Y Z X
$BLOCK SET1
LET#1 101+#4*110,1,−100 $ Node number + Increments of the Z−Sector
NODE NO Z X Y
$BLOCK SET1
END
The following values were selected for a comparison of the two mesh parti�
tionings:
Radius R = 10.0 m
Thickness t = 5 mm
E−Modulus E = 2.1E8 kN/m2
Poisson’s ratio µ = 0.2
Loading p = 10 kN/m2 radial
n� �� p�R�2��� 50�kN�m
�R� �� n
�E� t�
� �1��� �R� �� 0.381�mm
In the case of the mixed mesh, the results at the QUAD−corners are u = 0.380
mm, n−xx = 49.83 kN/m2 and n−yy = 49.83 kN/m2. At the triangle’s corner
Page 196
GENF Definition of Finite Elements
Version 10.205−24
though one obtains u = 0.843 mm, n−xx = 43.22 kN/m2 and n−yy = 65.55 kN/
m2.
The present mesh results in the following values:
Partition 4 Partition 8
Axes of coordinates (Node 101) 0.133 mm 0.363 mm
Bisecting line of the angle (Node 109) 1.280 mm 0.458 mm
Space diagonal (Node 189) 4.806 mm 0.388 mm
The stress resultants in the elements fluctuate in partition 8 from 45.30 up
to 54.41 kN/m; the value on the axis of coordinates is 49.86 kN/m.
Opposite to the mixed mesh, the QUAD−elements generated in such manner
are unfortunately not perfectly plane any more, a fact that was neglected
earlier and led to excellent results. Starting from version 93 ASE takes this
effect into consideration by means of eccentricities. The entire structure be�
comes more flexible this way and a clear bulge is obtained along the space di�
agonals in cases of coarse partitioning. The influence of the eccentricities
diminishes very fast by refining the mesh.
5.8. Examples in the Internet
Different statics examples are to be found in the Internet at www.sofis�
tik.com/bibliothek.htm
GENFDefinition of Finite Elements
5−23Version 10.20
$ SUBPROGRAM FOR NODE GENERATION IN A COORDINATE THIRD
$ NODE COORDINATES WITH NONLINEAR INCREMENT ROTATION
$ #1,#2,#3 = NODE NUMBER ON AXIS + INCREMENTS
LET#10 0,45/#4 $ Starting value + Increment phi−Y
LOOP #4+1
LET#20 0,45/#4 $ Starting value + Increment phi−Z
LOOP #4+1
LET#90 SQR(TAN(#10)**2+TAN(#20)**2)
LET#91 ATN(#90)
LET#92 COS(#91),0.0
LOOP #91−0.001 ; LET#93 SIN(#91)/#90 ; ENDLOOP −1
$ nodes
#1 #9*#92 #9*TAN(#20)*#93 #9*TAN(#10)*#93
LET#20 #20+#21
LET#1 #1+#3
ENDLOOP
LET#10 #10+#11
LET#1 #1−#3*(#4+1)+#2
ENDLOOP
$BLOCK END1
LET#1 101,10,1 $ Node number + Increments of the X−Sector
NODE NO X Y Z
$BLOCK SET1
LET#1 101+#4*101,−100,10 $ Node number + Increments of the Y−Sector
NODE NO Y Z X
$BLOCK SET1
LET#1 101+#4*110,1,−100 $ Node number + Increments of the Z−Sector
NODE NO Z X Y
$BLOCK SET1
END
The following values were selected for a comparison of the two mesh parti�
tionings:
Radius R = 10.0 m
Thickness t = 5 mm
E−Modulus E = 2.1E8 kN/m2
Poisson’s ratio µ = 0.2
Loading p = 10 kN/m2 radial
n� �� p�R�2��� 50�kN�m
�R� �� n
�E� t�
� �1��� �R� �� 0.381�mm
In the case of the mixed mesh, the results at the QUAD−corners are u = 0.380
mm, n−xx = 49.83 kN/m2 and n−yy = 49.83 kN/m2. At the triangle’s corner
Page 196
GENF Definition of Finite Elements
Version 10.205−24
though one obtains u = 0.843 mm, n−xx = 43.22 kN/m2 and n−yy = 65.55 kN/
m2.
The present mesh results in the following values:
Partition 4 Partition 8
Axes of coordinates (Node 101) 0.133 mm 0.363 mm
Bisecting line of the angle (Node 109) 1.280 mm 0.458 mm
Space diagonal (Node 189) 4.806 mm 0.388 mm
The stress resultants in the elements fluctuate in partition 8 from 45.30 up
to 54.41 kN/m; the value on the axis of coordinates is 49.86 kN/m.
Opposite to the mixed mesh, the QUAD−elements generated in such manner
are unfortunately not perfectly plane any more, a fact that was neglected
earlier and led to excellent results. Starting from version 93 ASE takes this
effect into consideration by means of eccentricities. The entire structure be�
comes more flexible this way and a clear bulge is obtained along the space di�
agonals in cases of coarse partitioning. The influence of the eccentricities
diminishes very fast by refining the mesh.
5.8. Examples in the Internet
Different statics examples are to be found in the Internet at www.sofis�
tik.com/bibliothek.htm
