Rasmus ÿstergaard forside 100%.indd - Solid Mechanics
Rasmus ÿstergaard forside 100%.indd - Solid Mechanics
Rasmus ÿstergaard forside 100%.indd - Solid Mechanics
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⎧<br />
⎪⎨<br />
⎪⎩<br />
a11<br />
a21<br />
a41<br />
a61<br />
a41<br />
0<br />
⎫ ⎧<br />
⎪⎬ ⎪⎨<br />
˙δ1 +<br />
⎪⎭ ⎪⎩<br />
a12<br />
a22<br />
a42<br />
a62<br />
a42<br />
0<br />
⎫<br />
⎪⎬<br />
⎪⎭<br />
⎧<br />
⎪⎨<br />
˙Δ1 +<br />
⎪⎩<br />
a14 + a12<br />
a24 + a22<br />
a44 + a42<br />
a64 + a62<br />
⎫ ⎧<br />
⎪⎬ ⎪⎨<br />
˙δ4 +<br />
⎪⎭ ⎪⎩<br />
a16<br />
a26<br />
a46<br />
a66<br />
⎫ ⎧<br />
⎪⎬ ⎪⎨<br />
˙δ6 =<br />
⎪⎭ ⎪⎩<br />
<br />
<br />
<br />
˙δ6 =0<br />
⎧ ⎫ ⎧ ⎫ ⎧ ⎫ ⎧ ⎫ ⎧<br />
a11 a12<br />
a14 ⎪⎨ ⎪⎬ ⎪⎨ ⎪⎬ ⎪⎨<br />
+ a12 ⎪⎬ ⎪⎨<br />
0 ⎪⎬ ⎪⎨<br />
a21 a22<br />
a24 + a22 0<br />
˙δ1 + ˙Δ1 +<br />
˙δ4 + ˙δ6 =<br />
a44 ⎪⎩ ⎪⎭ ⎪⎩ ⎪⎭ ⎪⎩<br />
+ a42 ⎪⎭ ⎪⎩<br />
0 ⎪⎭ ⎪⎩<br />
0<br />
1<br />
<br />
<br />
˙δ1<br />
˙δ0 :<br />
⎧ ⎫ ⎧ ⎫ ⎧ ⎫ ⎧ ⎫ ⎧<br />
⎪⎨<br />
1 ⎪⎬ ⎪⎨<br />
0 ⎪⎬ ⎪⎨<br />
0 ⎪⎬ ⎪⎨<br />
0 ⎪⎬ ⎪⎨<br />
a21 a22 a24 ˙δ1+ ˙Δ1+<br />
+ a22 ˙δ4+<br />
0 ˙δ6 =<br />
a41 a42 a44 ⎪⎩ ⎪⎭ ⎪⎩ ⎪⎭ ⎪⎩<br />
+ a42 ⎪⎭ ⎪⎩<br />
0 ⎪⎭ ⎪⎩<br />
0<br />
0<br />
0<br />
1<br />
x1<br />
⎧<br />
⎪⎨<br />
⎪⎩<br />
1<br />
a21<br />
a41<br />
0<br />
⎫ ⎧<br />
⎪⎬ ⎪⎨<br />
˙δ1+<br />
⎪⎭ ⎪⎩<br />
1<br />
0<br />
0<br />
0<br />
⎫<br />
⎪⎬<br />
(−<br />
⎪⎭<br />
˙ ⎧<br />
⎪⎨<br />
δ0)+<br />
⎪⎩<br />
<br />
0<br />
a24 + a22<br />
a44 + a42<br />
0<br />
<br />
<br />
<br />
˙Δ2,<br />
˙ <br />
δ5<br />
<br />
˙Δ1<br />
<br />
Δ0<br />
⎫ ⎧<br />
⎪⎬ ⎪⎨<br />
˙δ4+<br />
⎪⎭ ⎪⎩<br />
0<br />
0<br />
0<br />
1<br />
⎫<br />
⎪⎬<br />
⎧<br />
⎪⎨<br />
˙δ6 =<br />
⎪⎭ ⎪⎩<br />
c4<br />
0<br />
c1<br />
c2<br />
c4<br />
c6<br />
c1<br />
c2<br />
c4<br />
0<br />
⎫<br />
⎪⎬<br />
.<br />
⎪⎭<br />
⎫<br />
⎪⎬<br />
.<br />
⎪⎭<br />
⎫ ⎧ ⎫<br />
0 ⎪⎬ ⎪⎨<br />
1 ⎪⎬<br />
c2 0<br />
+ ˙δ0.<br />
⎪⎭ ⎪⎩<br />
0 ⎪⎭<br />
0<br />
0<br />
c2<br />
c4<br />
0<br />
⎫ ⎧<br />
⎪⎬ ⎪⎨<br />
−<br />
⎪⎭ ⎪⎩<br />
0<br />
a22<br />
a42<br />
0<br />
<br />
˙δ1, ˙ δ0, ˙ δ4, ˙ <br />
δ6.<br />
˙δ7<br />
˙δ1, ˙ δ0, ˙ Δ2, ˙ δ4, ˙ δ5, ˙ δ6, ˙ δ7.<br />
<br />
<br />
˙δ6<br />
<br />
= 0, ˙ <br />
<br />
δ7 = 0 ˙Δ1 = Δ0<br />
<br />
˙δ<br />
∗ = { ˙ δ1, Δ1, ˙ Δ2, ˙ ˙ δ4, ˙ δ5, ˙ δ6, ˙ <br />
δ7}<br />
˙δ ∗ = { ˙ δ1, Δ0, ˙ Δ2, ˙ δ4, ˙ δ5, 0, 0}.<br />
<br />
˙δ = { ˙ δ1, ( ˙ δ4 − Δ0), ( ˙ δ5 − ˙ Δ2), ˙ δ4, ˙ δ5, 0, 0}.<br />
<br />
⎫<br />
⎪⎬<br />
Δ0.<br />
⎪⎭
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