@@ -20,17 +20,21 @@ the response across the frequency range:
2020* Solves the reduced system
2121* Expands the results back to compute the harmonic response
2222
23- MAPDL provides the following ways to implement a harmonic analysis using
24- the Krylov method:
23+ Mechanical APDL provides the following ways to implement a harmonic analysis
24+ using the Krylov method:
2525
26- #. Mechanical APDL commands.
27- #. APDL macros as described in "Frequency-Sweep Harmonic Analysis via the
28- Krylov Method" in the * Structural Analysis Guide *.
29- #. PyMAPDL. You can use the Python programming language to expose the Krylov
30- features as described in this section.
26+ #. Mechanical APDL commands
27+ #. APDL macros as described in
28+ ` Frequency-Sweep Harmonic Analysis via the Krylov Method
29+ <https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/v222/en/ans_str/str_Krysweep.html> `_
30+ in the ** Structural Analysis ** guide for Mechanical APDL
3131
32- Assumptions
33- -----------
32+ PyMAPDL also provides a way to implement a harmonic analysis using the Kylov method.
33+ Subsequent sections describe how to use the Krylov method in PyMAPDL.
34+
35+
36+ **Assumptions **
37+ ---------------
3438The following assumptions are made when using the Kylov PyMAPDL method
3539to obtain the solution:
3640
@@ -45,23 +49,23 @@ to obtain the solution:
4549 method.
4650
4751
48- Krylov method implementation in PyMADL
49- ======================================
50- The PyMAPDL implementation of the Kylov method gives you customization
52+ Krylov method implementation in PyMAPDL
53+ =======================================
54+ The PyMAPDL implementation of the Krylov method gives you customization
5155and flexibility because you can access subspace vectors and reduced
5256solutions using the Python programming language for user-defined routines.
5357
54- If you do not require customization, you can use the APDL commands to
55- solve a harmonic analysis with the Krylov method.
58+ If you do not require customization, you can use the Mechanical APDL
59+ commands to solve a harmonic analysis with the Krylov method. For more
60+ information, including the theory behind this method, see
61+ `Frequency-Sweep Harmonic Analysis via the Krylov Method
62+ <https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/v222/en/ans_str/str_Krysweep.html> `_
63+ in the **Structural Analysis ** guide for Mechanical APDL.
5664
57- More information on the theory of Krylov method can be found in the
58- `Structural Analysis Guide
59- <https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/v222/en/ans_str/Hlp_G_STR4_4.html> `_.
60- The procedure described here implements an analysis identical to that
61- defined by the macros. Details on the theory and equations describing
62- the Krylov method can be found in the works of Puri [1 ]_ and Eser [2 ]_.
65+ For additional theory information and equations for
66+ the Krylov method, see the works of Puri [1 ]_ and Eser [2 ]_.
6367
64- The exposure in PyMAPDL follows the same theory as the APDL macro and
68+ The exposure in PyMAPDL follows the same theory as the Mechanical APDL macros and
6569has the following methods:
6670
6771* :func: `KrylovSolver.gensubspace() <ansys.mapdl.core.krylov.KrylovSolver.gensubspace> `:
@@ -75,8 +79,13 @@ has the following methods:
7579
7680Usage
7781=====
82+ This section shows how to implement an analysis identical to that
83+ defined by the Mechanical APDL macros.
7884
79- Generate the full file (``.full ``) for the Krylov method using Mechanical APDL:
85+ Generate the FULL file and FEA model
86+ ------------------------------------
87+ Generate the FULL file for the Krylov method and the FEA model
88+ using Mechanical APDL:
8089
8190.. code :: py
8291
@@ -107,8 +116,8 @@ Create an instance of the Krylov class
107116
108117
109118:func: `gensubspace <ansys.mapdl.core.krylov.KrylovSolver.gensubspace> `
110- method, to create the Krylov subspace:
111- Build a subspace of size / dimension 10 and at a frequency of 500 Hz.
119+ method to create the Krylov subspace and build a subspace of
120+ size/ dimension 10 at a frequency of 500 Hz:
112121
113122.. code :: py
114123
@@ -118,9 +127,8 @@ Return the Krylov subspace
118127--------------------------
119128
120129Call the :func: `solve <ansys.mapdl.core.krylov.KrylovSolver.solve> ` method to
121- reduce the system of equations, and then solve at each frequency.
122- The following code solves from 0 Hz
123- to 1000 Hz with 100 intervals in between, with stepped loading.
130+ reduce the system of equations and solve at each frequency. This code
131+ solves from 0 Hz to 1000 Hz with 100 intervals in between, with stepped loading:
124132
125133.. code :: py
126134
@@ -131,23 +139,24 @@ Return the reduced solution over the frequency range
131139----------------------------------------------------
132140
133141Call the :func: `expand <ansys.mapdl.core.krylov.KrylovSolver.expand> ` method
134- to expand the reduced solution back to FE space. Output the expanded
135- solution and calculate the residual.
142+ to expand the reduced solution back to the FE space, output the expanded
143+ solution, and calculate the residual:
136144
137145.. code :: py
138146
139147 >> > result = mk.expand(residual_computation = True , " L-inf" compute_solution_vectors = True , True )
140148
141- It returns a :class: `numpy array<numpy.ndarray> ` ( if the kwarg ``out_key ``
142- is set to ``True ``) solution vectors mapped to user order.
149+ The preceding code returns a :class: `numpy array<numpy.ndarray> ` if the kwarg ``out_key ``
150+ is set to ``True ``. Solution vectors are mapped to user order.
143151
144- .. note :: The ``ndarray`` returned by the method ``expand`` contains
152+ .. note :: The :class:`numpy array<numpy.ndarray>` returned by the
153+ `:func: `expand <ansys.mapdl.core.krylov.KrylovSolver.expand> ` method contains
145154 the node number along with the dof solution for each of the calculated
146155 frequencies.
147156
148157Get the dof solution at a specific frequency
149158--------------------------------------------
150- This code shows how you can get the nodal solution at a specific frequency
159+ This code shows how to get the nodal solution at a specific frequency
151160or step:
152161
153162.. code :: py
@@ -164,17 +173,18 @@ Examples of using the Krylov method in PyMAPDL are available in :ref:`krylov_exa
164173Requirements
165174============
166175
167- To use the Krylov method in PyMAPDL, Ansys MAPDL version 2022 R2 or later must be used.
176+ To use the Krylov method in PyMAPDL, Mechanical APDL version 2022 R2 or later
177+ must be used.
168178
169179.. warning :: This feature does not support Distributed Ansys.
170- However, you can still run MAPDL Math commands without specifying the `` -smp ``
171- flag when launching MAPDL .
180+ However, you can still run Mechanical APDL Math commands without
181+ specifying the `` -smp `` flag when launching Mechanical APDL .
172182
173183Reference
174184=========
175185For more information on the Krylov method, see `Frequency-Sweep Harmonic Analysis via the Krylov Method
176186<https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/v222/en/ans_str/str_Krysweep.html> `_
177- in the **Structural Analysis ** guide for Mechanical APDL.
187+ in the **Structural Analysis ** guide for Mechanical APDL and these resources:
178188
179189.. [1 ] Puri, S. R. (2009). Krylov Subspace Based Direct Projection Techniques for Low Frequency,
180190 Fully Coupled, Structural Acoustic Analysis and Optimization. PhD Thesis. Oxford Brookes University,
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