User:Eml5526.s11.team01.roark/Mtg33

[[media: Fe1.s11.mtg33.djvu| Mtg 33]]: Mon, 21 Mar 11 [[media: Fe1.s11.mtg33.djvu| Page 33-1]]
 * comments on HW 4.8
 * Stigler’s law of misnomy: “Gaussian”(normal) distr -> de Moivre
 * Algorithm: al-Kharizmi
 * Calculix tutorial by Ty Beede, Mechanical hacks blog

HW 6.3:

Reproduce all steps in tutorial by Beede.

End HW 6.3

2D&3D cont’d: [[media: Fe1.s11.mtg32.djvu| p. 32-4]]

$$\displaystyle d\omega =d{{x}_{1}}d{{x}_{2}}d{{x}_{3}}=dxdydz$$

$$\displaystyle div \mathbf q=\frac{\partial {{q}_{i}}}{\partial {{x}_{i}}}=\frac{\partial {{q}_{1}}}{\partial {{x}_{1}}}+\frac{\partial {{q}_{2}}}{\partial {{x}_{2}}}+\frac{\partial {{q}_{3}}}{\partial {{x}_{3}}}$$

Where i stands for sum on the repeated index [[media: Fe1.s11.mtg33.djvu| Page 33-2]]
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$$\displaystyle =\frac{\partial {{q}_{x}}}{\partial x}+\frac{\partial {{q}_{y}}}{\partial x}+\frac{\partial {{q}_{z}}}{\partial x}$$
 *  (1)
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$$\displaystyle \mathbf q={{q}_{i}}{{\mathbf e}_{i}}~,~\left\{ {{\mathbf e}_{i}} \right\}$$basis vectors Sum on i.
 *  (2)
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Fourier’s law:


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$$\displaystyle \mathbf q=-\mathbf K\cdot gradu$$ Isotropic Material => $$\displaystyle \mathbf K=K\mathbf I$$ where $$\displaystyle \mathbf I$$ is the identity matrix, $$\displaystyle \mathbf q=-K\,gradu$$
 *  (3)
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[[media: Fe1.s11.mtg32.djvu|(7) p. 32-4]]:


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$$\displaystyle +\underbrace{div\left( K\cdot gradu \right)}_{\frac{\partial }{\partial {{x}_{i}}}\left( {{K}_{ij}}\frac{\partial u}{\partial {{x}_{j}}} \right)}+f=\rho c\frac{\partial u}{\partial t}$$
 *  (4)
 * }
 * }
 * }

With sum on i,j