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com:nastranfrom [2018/02/16 14:26] phil [Thick Shell] |
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| - | ====== NAS Command Transformations ====== | ||
| - | The transformation equations for the [[com:NASVEC]] and [[com:NASCCV]] commands. | ||
| - | |||
| - | ===== Stress Transformation Equations ===== | ||
| - | |||
| - | #;; | ||
| - | \(\quad \alpha = \text{Angle between global X and local X}\)\\ | ||
| - | \(\quad t = \text{Shell thickness}\)\\ | ||
| - | \(\quad E = \text{Shell material's Young's modulus}\)\\ | ||
| - | \(\quad \nu = \text{Shell material's Poisson ratio}\)\\ | ||
| - | #;; | ||
| - | ==== Thin Shell ==== | ||
| - | #;; | ||
| - | \( \quad S_{x_G} = S_{x_L}*cos^2(\alpha)+2*S_{xy_L}*sin(\alpha)*cos(\alpha)+S_{y_L}sin^2(\alpha) \) | ||
| - | \( \quad S_{y_G} = S_{x_L}*sin^2(\alpha)-2*S_{xy_L}*sin(\alpha)*cos(\alpha)+S_{y_L}cos^2(\alpha) \) | ||
| - | \( \quad S_{xy_G} = S_{xy_L}*(cos^2(\alpha)-sin^2(\alpha))-(S_{y_L}+S_{x_L})*sin(\alpha)*cos(\alpha) \) | ||
| - | \( \quad M_{x_G} = M_{x_L}*cos^2(\alpha)+2*M_{xy_L}*sin(\alpha)*cos(\alpha)+M_{y_L}sin^2(\alpha) \) | ||
| - | \( \quad M_{y_G} = M_{x_L}*sin^2(\alpha)-2*M_{xy_L}*sin(\alpha)*cos(\alpha)+M_{y_L}cos^2(\alpha) \) | ||
| - | \( \quad M_{xy_G} = M_{xy_L}*(cos^2(\alpha)-sin^2(\alpha))-(M_{y_L}+M_{x_L})*sin(\alpha)*cos(\alpha) \) | ||
| - | #;; | ||
| - | ==== Thick Shell ==== | ||
| - | \( \quad N_{x_G} = N_{x_L}*cos^2(\alpha)+2*N_{xy_L}*sin(\alpha)*cos(\alpha)+N_{y_L}sin^2(\alpha) \) | ||
| - | \( \quad N_{y_G} = N_{x_L}*sin^2(\alpha)-2*N_{xy_L}*sin(\alpha)*cos(\alpha)+N_{y_L}cos^2(\alpha) \) | ||
| - | \( \quad N_{xy_G} = N_{xy_L}*(cos^2(\alpha)-sin^2(\alpha))-(N_{y_L}+N_{x_L})*sin(\alpha)*cos(\alpha) \) | ||
| - | \( \quad M_{x_G} = M_{x_L}*cos^2(\alpha)+2*M_{xy_L}*sin(\alpha)*cos(\alpha)+M_{y_L}sin^2(\alpha) \) | ||
| - | \( \quad M_{y_G} = M_{x_L}*sin^2(\alpha)-2*M_{xy_L}*sin(\alpha)*cos(\alpha)+M_{y_L}cos^2(\alpha) \) | ||
| - | \( \quad M_{xy_G} = M_{xy_L}*(cos^2(\alpha)-sin^2(\alpha))-(M_{y_L}+M_{x_L})*sin(\alpha)*cos(\alpha) \) | ||
| - | \( \quad Q_{x_G} = Q_{x_L}*cos(\alpha)+Q_{y_L}*sin(\alpha) \) | ||
| - | \( \quad Q_{y_G} = -Q_{x_L}*sin(\alpha)+Q_{y_L}*cos(\alpha) \) | ||
| - | ===== Strain Equations ===== | ||
| - | $$ \varepsilon_x = \frac{\gamma_x}{E}-\nu \frac{\gamma_y}{E} \qquad \varepsilon_y = \frac{\gamma_y}{E}-\nu \frac{\gamma_x}{E} \qquad \varepsilon_{xy} = \frac{\gamma_{xy}}{E}*2(1+\nu) $$ | ||
| - | $$\varepsilon_{1,2} = \frac{\varepsilon_x+\varepsilon_y}{2} \pm \frac{\sqrt{(\varepsilon_x-\varepsilon_y)^2+\varepsilon_{xy}}}{2}$$ | ||
| - | ==== Thin Shell ==== | ||
| - | $$ \gamma_x=S_{x_G} \pm \frac{6*M_{x_G}}{t^2} \qquad \gamma_y=S_{y_G} \pm \frac{6*M_{y_G}}{t^2} \qquad \gamma_{xy}=S_{xy_G} \pm \frac{6*M_{xy_G}}{t^2}$$ | ||
| - | |||
| - | ==== Thick Shell ==== | ||
| - | $$ \gamma_x=\frac{N_{x_G}}{t} \pm \frac{6*M_{x_G}}{t^2} \qquad \gamma_y=\frac{N_{y_G}}{t} \pm \frac{6*M_{y_G}}{t^2} \qquad \gamma_{xy}=\frac{N_{xy_G}}{t} \pm \frac{6*M_{xy_G}}{t^2}$$ | ||
com/nastranfrom.1518809170.txt.gz ยท Last modified: 2018/02/16 14:26 by phil
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