@@ -1293,7 +1293,7 @@ The constraint are applied after the full system has been assembled.
12931293
12941294
12951295Spring Elements
1296- ~~~~~~~~~~~
1296+ ~~~~~~~~~~~~~~~
12971297
12981298Do not confuse the spring member with the springs defined as
12991299a boundary condition in land-based systems. The spring element
@@ -1302,16 +1302,16 @@ is assumed symmetric (k_ij = k_ji).
13021302
13031303.. math ::
13041304
1305- \b egin{aligned}
1306- K=
1307- \b egin{bmatrix}
1308- k_{11} & k_{12} & k_{13} & k_{14} & k_{15} & k_{16} \\
1309- k_{21} & k_{22} & k_{23} & k_{24} & k_{25} & k_{26} \\
1310- k_{31} & k_{32} & k_{33} & k_{34} & k_{35} & k_{36} \\
1311- k_{41} & k_{42} & k_{43} & k_{44} & k_{45} & k_{46} \\
1312- k_{51} & k_{52} & k_{53} & k_{54} & k_{55} & k_{56} \\
1313- k_{61} & k_{62} & k_{63} & k_{64} & k_{65} & k_{66} \\
1314- \e nd{bmatrix}
1305+ \begin {aligned}
1306+ K=
1307+ \begin {bmatrix}
1308+ k_{11 } & k_{12 } & k_{13 } & k_{14 } & k_{15 } & k_{16 } \\
1309+ k_{21 } & k_{22 } & k_{23 } & k_{24 } & k_{25 } & k_{26 } \\
1310+ k_{31 } & k_{32 } & k_{33 } & k_{34 } & k_{35 } & k_{36 } \\
1311+ k_{41 } & k_{42 } & k_{43 } & k_{44 } & k_{45 } & k_{46 } \\
1312+ k_{51 } & k_{52 } & k_{53 } & k_{54 } & k_{55 } & k_{56 } \\
1313+ k_{61 } & k_{62 } & k_{63 } & k_{64 } & k_{65 } & k_{66 } \\
1314+ \end {bmatrix} \end {aligned }
13151315
13161316 The spring element does not have a mass associated. However, if desired, a lumped mass can be
13171317defined at the joints.
@@ -1320,12 +1320,12 @@ Since each joint has 6 DOFs (3 translations and 3 rotations), mathematically, th
13201320spring element has a 12 by 12 dimension.
13211321.. math ::
13221322
1323- \b egin{aligned}
1324- K_e=
1325- \b egin{bmatrix}
1326- k_{6x6} & -k_{6x6} \\
1327- -k_{6x6} & k_{6x6} \\
1328- \e nd{bmatrix}
1323+ \begin {aligned}
1324+ K_e=
1325+ \begin {bmatrix}
1326+ k_{6 x6 } & -k_{6 x6 } \\
1327+ -k_{6 x6 } & k_{6 x6 } \\
1328+ \end {bmatrix} \end {aligned }
13291329
13301330 The spring element must be defined between two coincident joints and the orientation has to be
13311331provided by means of the direction cosine. This allows the assembly of the spring element in the
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