User:Eml5526.s11.team01.roark/Mtg15

[[media: Fe1.s11.mtg15.djvu| Mtg 15]]: Wed, 2 Feb 11 [[media: Fe1.s11.mtg15.djvu| Page 15-1]] Summary HW 3.5:

FB, p.37, Problem 2.2

End HW 3.5

HW 3.6:

FB, p.38, Problem 2.4

End HW 3.6

Montesquieu!

Weak Form: (WF)

[[media: Fe1.s11.mtg14.djvu| p. 14-3]] continued. Pros:

A) $$\displaystyle \mathbf K$$ Symmetric

B) $$\displaystyle {{u}^{h}}$$ only needed to be once different. Weaker requirement, less conditions

C) $$\displaystyle {{u}^{h}}$$ only need to satisfy essential boundary condition (more flexibility) (natural boundary condition absorbed into WF)

D) applicable to problems with complex geometry

G1DM1.0 D3 [[media: Fe1.s11.mtg9.djvu| (p. 9-1)]]
 * {| style="width:100%" border="0"


 * style="width:92%; padding:10px; border:2px solid #0000FF " |
 * style="width:92%; padding:10px; border:2px solid #0000FF " |

$$\displaystyle \Omega =\left] \alpha ,\beta \right[$$

Essential boundary condition $$\displaystyle {{\Gamma }_{g}}=\left\{ \beta \right\},g$$
 * {| style="width:100%" border="0"

$$\displaystyle u(x=\beta )=g$$ Natural boundary condition $$\displaystyle {{\Gamma }_{h}}=\left\{ \alpha \right\},h$$
 *  (1)
 * }
 * }


 * {| style="width:100%" border="0"

$$\displaystyle n\left( \alpha \right){{a}_{2}}\left( \alpha  \right)\frac{\partial u\left( \alpha  \right)}{\partial x}=-{{a}_{2}}\frac{\partial u\left( \alpha  \right)}{\partial x}=h$$
 *  (2)
 * }
 * }


 * }

[[media: Fe1.s11.mtg15.djvu| Page 15-2]]

WRF: [[media: Fe1.s11.mtg6.djvu|(4) p. 6-4]]

Mass \\ (inertia) \end{smallmatrix}}$$
 * 1) $$\displaystyle \int_{\Omega }^ – {w\mathbf P(u)}dx=\overbrace{K}^{Stiffness}+\overbrace{F}^{Force}-\underbrace{M}_{\begin{smallmatrix}
 * 1) $$\displaystyle K:=\int_{\alpha }^{\beta }{\underbrace{w}_{f}}\frac{\partial }{\partial x}\left( {{a}_{2}}\frac{\partial u}{\partial x} \right)dx=\underbrace{\int_ – ^ – }_{\left[ fg \right]_{\alpha }^{\beta }}-\int_ – ^ – {{f}'g}$$

$$\displaystyle =\underbrace{\left[ w{{a}_{2}}\frac{\partial u}{\partial x} \right]_{x=\alpha }^{x=\beta }}_{\begin{smallmatrix} Bound.\,term \\ =K1 \end{smallmatrix}}=\underbrace{\int_{\alpha }^{\beta }{\frac{\partial w}{\partial x}{{a}_{2}}\frac{\partial u}{\partial x}}dx}_{\begin{smallmatrix} \operatorname{int}.\,term\,\,\Rightarrow \,sym! \\ =K2 \end{smallmatrix}}\,$$