Page 260 - Marine Structural Design
P. 260
236 Part II Ultimate Strength
12.4 Transformation Matrix
In this section, a new transformation matrix [T,] is described, which transfers element
displacements measured in the global coordinate system XYZ to element displacements
measured in the local coordinate xyz, at time t. The transformation matrix is evaluated as
[q ] = [.ATIT - df ] (12.59)
where [T, - da] is a matrix, which transfers the element displacements to the local coordinate
system at time f-df. [AT] is a matrix that transfers the element displacements measured in the
local coordinate system at the time f-df to the local coordinate system at time f.
Figure 12.2 Transformation Matrix
The transformation matrix [ATJ is composed of submatrices [tf] which transform the
displacement vectors. The submatrix [ff] is evaluated as:
[.I= E.l+[tbl (1 2.60)
where,
0
[tal=! cosa si:a]
-sina cosa
cos p cos B sin 6 sin p COS 6 (12.61)
-cospsinB case -sinpsino 1
- sin p 0 cos p
