diff --git a/docs/source/user/subdyn/input_files.rst b/docs/source/user/subdyn/input_files.rst index 745767713d..1db0e858c1 100644 --- a/docs/source/user/subdyn/input_files.rst +++ b/docs/source/user/subdyn/input_files.rst @@ -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 diff --git a/docs/source/user/subdyn/theory.rst b/docs/source/user/subdyn/theory.rst index edb6762327..d93c169b1a 100644 --- a/docs/source/user/subdyn/theory.rst +++ b/docs/source/user/subdyn/theory.rst @@ -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 @@ -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