Category: Study

import sympy
from sympy import Symbol, Matrix, *
t = Symbol('t') #t should be \tau, please keep in mind
T = Matrix(([0, t, 0], [t, 0, 0], [0, 0, 0]))
R = Matrix(([a, -a, 0],[a, a, 0], [0, 0, 1]))
T1

\begin{bmatrix} 1.0t & 0 & 0\\ 0 & -1.0t & 0 \\ 0 & 0 & 0 \\ \end{bmatrix}

E = Symbol('E')
v = Symbol('v') # v should be \upsilon

V = 1.0/E * Matrix(([1, -v, -v],[-v, 1, -v],[-v, -v, 1]))
V

\begin{bmatrix} \frac{1}{E} & -\frac{\upsilon}{E} & -\frac{\upsilon}{E} \\ -\frac{\upsilon}{E} & \frac{1}{E} & -\frac{\upsilon}{E} \\ -\frac{\upsilon}{E} & -\frac{\upsilon}{E} & \frac{1}{E} \\ \end{bmatrix}

E1 = V * T1
V * T1 * Matrix([1, 1, 0]) #This was written on the Lecture 11-Extend

The complete function should be:
(\varepsilon_\zeta, \varepsilon_\eta, \varepsilon_z) ^T = \frac{1}{E} \cdot V \cdot (\tau, -\tau, 0) ^T
where V is the matrix before.

The result is the following vector:
\begin{pmatrix} \varepsilon_\zeta \\ \varepsilon_\eta \\ \varepsilon_z\\ \end{pmatrix} = \begin{pmatrix} \frac{\upsilon \tau + \tau}{E} \\ -\frac{\upsilon \tau + \tau}{E} \\ 0 \\ \end{pmatrix}