Skip to content

Commit

Permalink
Docs: Formatting error preventing rendering on RTD (PR #1889)
Browse files Browse the repository at this point in the history
  • Loading branch information
andrew-platt committed Nov 29, 2023
1 parent f620731 commit 92c8754
Show file tree
Hide file tree
Showing 2 changed files with 19 additions and 18 deletions.
2 changes: 1 addition & 1 deletion docs/source/user/subdyn/input_files.rst
Original file line number Diff line number Diff line change
Expand Up @@ -529,7 +529,7 @@ An example of rigid link properties table is given below
3 7000.0
Spring Properties
~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~
Members that are specified as spring elements (**MType=5**),
have their properties defined in the spring element properties table.
The table lists for each spring property: the property ID (**PropSetID**) and the
Expand Down
35 changes: 18 additions & 17 deletions docs/source/user/subdyn/theory.rst
Original file line number Diff line number Diff line change
Expand Up @@ -1293,7 +1293,7 @@ The constraint are applied after the full system has been assembled.


Spring Elements
~~~~~~~~~~~
~~~~~~~~~~~~~~~

Do not confuse the spring member with the springs defined as
a boundary condition in land-based systems. The spring element
Expand All @@ -1302,30 +1302,31 @@ is assumed symmetric (k_ij = k_ji).

.. math::
\begin{aligned}
K=
\begin{bmatrix}
k_{11} & k_{12} & k_{13} & k_{14} & k_{15} & k_{16} \\
k_{21} & k_{22} & k_{23} & k_{24} & k_{25} & k_{26} \\
k_{31} & k_{32} & k_{33} & k_{34} & k_{35} & k_{36} \\
k_{41} & k_{42} & k_{43} & k_{44} & k_{45} & k_{46} \\
k_{51} & k_{52} & k_{53} & k_{54} & k_{55} & k_{56} \\
k_{61} & k_{62} & k_{63} & k_{64} & k_{65} & k_{66} \\
\end{bmatrix}
\begin{aligned}
K=
\begin{bmatrix}
k_{11} & k_{12} & k_{13} & k_{14} & k_{15} & k_{16} \\
k_{21} & k_{22} & k_{23} & k_{24} & k_{25} & k_{26} \\
k_{31} & k_{32} & k_{33} & k_{34} & k_{35} & k_{36} \\
k_{41} & k_{42} & k_{43} & k_{44} & k_{45} & k_{46} \\
k_{51} & k_{52} & k_{53} & k_{54} & k_{55} & k_{56} \\
k_{61} & k_{62} & k_{63} & k_{64} & k_{65} & k_{66} \\
\end{bmatrix}\end{aligned}
The spring element does not have a mass associated. However, if desired, a lumped mass can be
defined at the joints.

Since each joint has 6 DOFs (3 translations and 3 rotations), mathematically, the
spring element has a 12 by 12 dimension.

.. math::
\begin{aligned}
K_e=
\begin{bmatrix}
k_{6x6} & -k_{6x6} \\
-k_{6x6} & k_{6x6} \\
\end{bmatrix}
\begin{aligned}
K_e=
\begin{bmatrix}
k_{6x6} & -k_{6x6} \\
-k_{6x6} & k_{6x6} \\
\end{bmatrix}\end{aligned}
The spring element must be defined between two coincident joints and the orientation has to be
provided by means of the direction cosine. This allows the assembly of the spring element in the
Expand Down

0 comments on commit 92c8754

Please sign in to comment.