User:Arthurv~enwiki/coordinates

NASTRAN provides coordinates

$$ \left[ \begin{matrix} F_x \\ F_y \\ F_z \end{matrix} \right]_{6120} = \left[\begin{matrix} & &  \\ & \textrm{R}_{6120}&  \\ & &  \end{matrix}\right] \left[\begin{matrix} & &  \\ & \textrm{R}_{bolt}^{T}&  \\ & &  \end{matrix}\right] \left[ \begin{matrix} F_x \\ F_y \\ F_z \end{matrix} \right]_{bolt} $$

because $$ \left[ \begin{matrix} F_x \\ F_y \\ F_z \end{matrix} \right]_{bolt} = \left[\begin{matrix} & &  \\ & \textrm{R}_{bolt}&  \\ & &  \end{matrix}\right] \left[ \begin{matrix} F_x \\ F_y \\ F_z \end{matrix} \right]_{global} $$

$$ \left[ \begin{matrix} F_x \\ F_y \\ F_z \end{matrix} \right]_{6120} = \left[\begin{matrix} & &  \\ & \textrm{R}_{6120}&  \\ & &  \end{matrix}\right] \left[ \begin{matrix} F_x \\ F_y \\ F_z \end{matrix} \right]_{global} $$

$$ \mathbf{R}^{-1} = \mathbf{R}^T $$

$$ N_{y_i} = N_{y_{i-1}} + \frac{F_y}{5D}$$

$$ N_{x_i} = N_{x_{i-1}} + \frac{F_y}{5D}$$

$$ N_x = E\varepsilon t $$

$$ \therefore N_{x_2} = N_{x_1} \times \frac{E_2}{E_1} \times \frac{t_2}{t_1} $$

$$ K = \frac{E\pi d^2}{4 \sum t} = \frac{E\pi d^2}{4 (t_{ss}+t_{spar}+t_{backup})} $$

$$ \therefore t_{ss} = \frac{E\pi d^2}{4 K} - t_{spar} - t_{backup} $$

$$ K = \frac{E\pi d^2}{4 \sum t} = \frac{E\pi d^2}{4 (t_{ss}+t_{spar}+t_{backup(new)})} $$