User:Eml5526.s11.team01.roark/Mtg29

[[media: Fe1.s11.mtg29.djvu| Mtg 29]]: Fri, 4 Mar 11 [[media: Fe1.s11.mtg29.djvu| Page 29-1]] Ex: $$\displaystyle n=4,{{y}_{1}}=1,{{y}_{2}}=2,{{y}_{3}}=3,{{y}_{4}}=4$$
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$$\displaystyle {{L}_{\underbrace{1}_{j},\underbrace{4}_{n}}}\left( y \right)=\frac{\left( y-{{y}_{2}} \right)\left( y-{{y}_{3}} \right)\left( y-{{y}_{4}} \right)}{\left( {{y}_{1}}-{{y}_{2}} \right)\left( {{y}_{1}}-{{y}_{3}} \right)\left( {{y}_{1}}-{{y}_{4}} \right)}=\frac{\left( y-2 \right)\left( y-3 \right)\left( y-4 \right)}{\left( 1-2 \right)\left( 1-3 \right)\left( 1-4 \right)}$$
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Ex: 2-D LIBF
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$$\displaystyle {{N}_{I}}\left( x,y \right)={{L}_{i,m}}\left( x \right)\cdot {{L}_{j,n}}\left( y \right)\,\,\,,\,\,\,I=i+\left( j-1 \right)m$$
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A different perspective:



Important prop of LIBF: c.f. FB, p.80, (4.7) 1-D:
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$$\displaystyle {{L}_{i,m}}\left( {{x}_{j}} \right)={{\delta }_{ij}}$$ 2-D:
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$$\displaystyle {{N}_{I}}\left( {{\mathbf x}_{J}} \right)={{\delta }_{IJ}}$$ (3-D) $$\displaystyle {{x}_{J}}=\left( x_{J}^{1},x_{J}^{2} \right)=\left( {{x}_{J}},{{y}_{j}} \right)$$
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HW5.3:

Similar to HW 5.1, but using LIBF with uniform discretization (equidistant nodes. m=4.6.8,… End HW 5.3
 * 1) Explain how LIBF are used as a CBS
 * 2) Plot all LIBF used.
 * 3) Use matlab quad, WA,… to int.
 * 4) Plot $$\displaystyle u_{m}^{h}$$ vs $$\displaystyle u$$, $$\displaystyle u_{m}^{h}\left( 0.5 \right)-u\left( 0.5 \right)$$vs. m

HW 5.4:

Similar to HW 5.2, but using LIBF with uniform discretization (equidistant nodes. m=4.6.8,…

Same tasks as in HW 5.3

End HW 5.4

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HW5.5:

Continuation of HW 4.7 on Calculix End HW 5.5
 * 1) For the disk problem, extract: Node info: node numbers and coordinates, and Element info: element numbers and element nodes.
 * 2) Generate 3 meshes of same disk with triangular elements (increase number of elements)
 * 3) Install ccx, run examples, write report for “dummies” (explain commands, screenshots, …)