PyAnsys Math overview

PyAnsys Math provides the ability to access and manipulate large sparse matrices and solve a variety of eigenproblems in a similar manner to the popular numpy and scipy libraries.

PyMAPDL and PyAnsys Math

This example demonstrates how to take advantage of the ansys-math-core package with PyMAPDL.

It illustrates how to send an MAPDL Math matrix from MAPDL to Python and then send it back to be solved. While this example runs the mm.eigs() method on mass and stiffness matrices generated from MAPDL, you could instead use mass and stiffness matrices generated from an external FEM tool or even modify the mass and stiffness matrices within Python.

First, solve the first 10 modes of a 1 x 1 x 1 steel meter cube in MAPDL.

import re
from ansys.mapdl.core import launch_mapdl

mapdl = launch_mapdl()

# setup the full file
mapdl.prep7()
mapdl.block(0, 1, 0, 1, 0, 1)
mapdl.et(1, 186)
mapdl.esize(0.5)
mapdl.vmesh("all")

# Define a material (nominal steel in SI)
mapdl.mp("EX", 1, 210e9)  # Elastic moduli in Pa (kg/(m*s**2))
mapdl.mp("DENS", 1, 7800)  # Density in kg/m3
mapdl.mp("NUXY", 1, 0.3)  # Poisson's Ratio

# solve first 10 non-trivial modes
out = mapdl.modal_analysis(nmode=10, freqb=1)

# store the first 10 natural frequencies
mapdl.post1()
resp = mapdl.set("LIST")
w_n = np.array(re.findall(r"\s\d*\.\d\s", resp), np.float32)
print(w_n)

You now have solved for the first 10 modes of the cube:

[1475.1 1475.1 2018.8 2018.8 2018.8 2024.8 2024.8 2024.8 2242.2 2274.8]

Next, load the mass and stiffness matrices that are stored by default in the <jobname>.full file. First, create an instance of the MapdlMath class as mm:

from ansys.math.core.math import AnsMath

# Importing and connecting PyAnsys Math to PyMAPDL
mm = AnsMath(mapdl)

# load by default from file.full
k = mm.stiff()
m = mm.mass()

# convert to numpy
k_py = k.asarray()
m_py = m.asarray()
mapdl.clear()
print(k_py)

After running the mapdl.clear() method, these matrices are stored solely within Python.

(0, 0)      37019230769.223404
(0, 1)      10283119658.117708
(0, 2)      10283119658.117706
:   :
(240, 241)  11217948717.943113
(241, 241)  50854700854.68495
(242, 242)  95726495726.47179

To call PyAnsys Math directly from PyMAPDL, you can run this command:

# Launching PyAnsys Math directly with PyMAPDL
mm = mapdl.math

The final step is to send these matrices back to MAPDL to be solved. While you have cleared MAPDL, you could have shut down MAPDL or even transferred the matrices to a different MAPDL session to be solved:

my_stiff = mm.matrix(k_py, triu=True)
my_mass = mm.matrix(m_py, triu=True)

# solve for the first 10 modes above 1 Hz
nmode = 10
mapdl_vec = mm.eigs(nmode, my_stiff, my_mass, fmin=1)
eigval = mapdl_vec.asarray()
print(eigval)

As expected, the natural frequencies obtained from the mm.eigs() method is identical to the result from the mapdl.solve() method within MAPDL.

[1475.1333421  1475.1333426  2018.83737064 2018.83737109 2018.83737237
 2024.78684466 2024.78684561 2024.7868466  2242.21532585 2274.82997741]

If you want to obtain the eigenvectors as well as the eigenvalues, initialize a matrix eigvec and send that to the mm.eigs() method:

>>> nmode = 10
>>> eigvec = mm.zeros(my_stiff.nrow, nmode)  # for eigenvectors
>>> val = mm.eigs(nmode, my_stiff, my_mass, fmin=1)

The AnsMath matrix eigvec now contains the eigenvectors for the solution.

PyAnsys Math reference

For more information, see the PyAnsys Math API reference.