Axisymmetric stress analysis in Python

Overview

I improved the 2D stress analysis program and made an axisymmetric stress analysis program. Axisymmetric stress analysis is often used as a simple method for stress analysis around the casing of hydroelectric power plants and barrel concrete. The simple method means that analysis by a three-dimensional solid model is now being performed with the improvement of computer performance and the development of analysis methods, so it is positioned as a simple method compared to that.

program

The program is shown by a link to Gist.

Axisymmetric FEM analysis program (py_fem_asnt.py)

Input data format

npoin  nele  nsec  npfix  nlod #Basic amount
E  po  alpha  gamma  gkz     #Material property
..... (1~nsec) .....
node1  node2  node3  node4  isec     #element-Nodal relationship, material property number
..... (1~nele) .....
z  r  deltaT                         #Nodal coordinates, nodal temperature changes
..... (1~npoin) .....
node  koz  kor  rdisz  rdisr         #Displacement constraint conditions
..... (1~npfix) .....
node  fz  fr                         #External force
..... (1~nlod) .....

npoin, nele, nsec	Number of nodes, number of elements, number of material characteristics
npfix, nlod	Number of constrained nodes, number of loaded nodes
E, po, alpha	Elastic modulus, Poisson's ratio, coefficient of linear expansion
gamma, gkz	Unit volume weight, z-direction acceleration (ratio of g)
z, r, delta T	Node z coordinate, node r coordinate, node temperature change
node, koz, kor	Constrain node number, z and r direction Constrained (constraint: 1, freedom: 0)
rdisz, rdisr	z and r displacement (enter 0 even if unconstrained)
node, fz, fr	Load node number, z-direction load, r-direction load

Output data format

npoin  nele  nsec npfix  nlod
   10     4     1     7     0
  sec               E              po           alpha           gamma             gkz
    1   2.0000000e+06   3.0000000e-01   1.0000000e-05   0.0000000e+00   0.0000000e+00
 node               z               r              fz              fr          deltaT   koz   kor
    1   0.0000000e+00   0.0000000e+00   0.0000000e+00   0.0000000e+00  -1.0000000e+01     1     1
    2   1.0000000e+00   0.0000000e+00   0.0000000e+00   0.0000000e+00  -1.0000000e+01     0     1
    3   2.0000000e+00   0.0000000e+00   0.0000000e+00   0.0000000e+00  -1.0000000e+01     0     1
    4   3.0000000e+00   0.0000000e+00   0.0000000e+00   0.0000000e+00  -1.0000000e+01     0     1
    5   4.0000000e+00   0.0000000e+00   0.0000000e+00   0.0000000e+00  -1.0000000e+01     1     1
    6   0.0000000e+00   1.0000000e+00   0.0000000e+00   0.0000000e+00  -1.0000000e+01     1     0
    7   1.0000000e+00   1.0000000e+00   0.0000000e+00   0.0000000e+00  -1.0000000e+01     0     0
    8   2.0000000e+00   1.0000000e+00   0.0000000e+00   0.0000000e+00  -1.0000000e+01     0     0
    9   3.0000000e+00   1.0000000e+00   0.0000000e+00   0.0000000e+00  -1.0000000e+01     0     0
   10   4.0000000e+00   1.0000000e+00   0.0000000e+00   0.0000000e+00  -1.0000000e+01     1     0
 node   kox   koy          rdis_z          rdis_r
    1     1     1   0.0000000e+00   0.0000000e+00
    2     0     1   0.0000000e+00   0.0000000e+00
    3     0     1   0.0000000e+00   0.0000000e+00
    4     0     1   0.0000000e+00   0.0000000e+00
    5     1     1   0.0000000e+00   0.0000000e+00
    6     1     0   0.0000000e+00   0.0000000e+00
   10     1     0   0.0000000e+00   0.0000000e+00
 elem     i     j     k     l   sec
    1     1     2     7     6     1
    2     2     3     8     7     1
    3     3     4     9     8     1
    4     4     5    10     9     1
 node           dis-z           dis-r
    1   0.0000000e+00   0.0000000e+00
    2  -1.5079475e-21   0.0000000e+00
    3  -6.6349691e-21   0.0000000e+00
    4   1.6651950e-20   0.0000000e+00
    5   0.0000000e+00   0.0000000e+00
    6   0.0000000e+00  -1.3000000e-04
    7  -4.9830486e-21  -1.3000000e-04
    8   2.0274556e-20  -1.3000000e-04
    9   1.2150518e-20  -1.3000000e-04
   10   0.0000000e+00  -1.3000000e-04
 elem           sig_z           sig_r           sig_t          tau_zr              p1              p2             ang
    1   2.0000000e+02   5.6843419e-14   6.3948846e-14  -1.1672750e-15   2.0000000e+02   5.6843419e-14   5.6843419e-14
    2   2.0000000e+02  -2.1316282e-14   1.7763568e-15  -3.8487337e-15   2.0000000e+02  -2.8421709e-14  -2.8421709e-14
    3   2.0000000e+02  -1.0658141e-14  -8.8817842e-15   1.9212820e-14   2.0000000e+02   0.0000000e+00   0.0000000e+00
    4   2.0000000e+02   8.1712415e-14   9.2370556e-14   1.0166131e-14   2.0000000e+02   8.5265128e-14   8.5265128e-14
n=20  time=0.008 sec

node, dis-z, dis-r	Node number, z-direction displacement, r-direction displacement
elme, sig_z, sig_r, sig_t, tau_zr	Element number, z-direction direct stress, r-direction direct stress, rotational direction direct stress, shear stress
p1, p2, ang	Direction of first principal stress, second principal stress, first principal stress in z-r plane
n, time	total degrees of freedom, calculation time

that's all