Question

For a 3D truss element, transformation matrix L between local and global co-ordinates is given by ___

(a) \( \begin{bmatrix}l &0&0 \\ 0&m&0\\0&0&n\end{bmatrix}\)

(b) \( \begin{bmatrix}l &m&n \end{bmatrix}\)

(c) \( \begin{bmatrix}l&0&n \\ 0&m&0 \end{bmatrix}\)

(d) \( \begin{bmatrix}l&m&n&0&0&0\\ 0&0&0&l&m&n\end{bmatrix}\)

This question was addressed to me during an interview for a job.

I'm obligated to ask this question of Three Dimensional Trusses topic in portion Trusses of Finite Element Method

Answer 1

Right option is (d) \( \begin{bmatrix}l&m&n&0&0&0\\ 0&0&0&l&m&n\end{bmatrix}\)

The explanation: A transformation matrix is a special matrix that can describe 2D and 3D transformations. Transformations are frequently used in linear algebra and computer graphics. Since transformations can be easily represented, combined and computed.