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October 28, 2004, 02:51
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How to calculate these tensor term ?
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#1 |
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Guest
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There is 2 tensor that i don,t know how to calculate! 1: S_ij*S_ij = ?
2: S_ij*S_jk*S_ki= ? there : i=1,2,3,j=1,2,3 Who can give me an exact formula about these calculations (in terms S_11,S_12,....)?? thaks! |
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October 28, 2004, 04:27
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Re: How to calculate these tensor term ?
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#2 |
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Guest
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Repeated indices imply summation. So
S<sub>ij</sub> S<sub>ij</sub> = Σ<sub>i</sub> Σ<sub>j</sub> S<sub>ij</sub> S<sub>ij</sub> which is a scalar. |
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October 29, 2004, 07:59
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Re: How to calculate these tensor term ?
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#3 |
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Guest
Posts: n/a
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If you have S11=2.*DU/DX, S22=2.*DVDY, S33=2.*DW/DZ, S12=DUDY+DVDX, S23=DV/DZ+DW/DY, S31=DW/DX+DU/DZ,
THEN SIJ*SIJ=S11**2+S22**2+S33**2+2.*(S12**2+S23**2+S31 **2) SIJ*SJK*SKI=S11**3+S22**3+S33**3+6.*S12*S23*S31+ 3.*[S12**2*(S11+S22)+S23**2*(S22+S33)+S31**2*(S33+S11)] |
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October 29, 2004, 15:48
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Re: How to calculate these tensor term ?
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#4 |
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Guest
Posts: n/a
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Thank you 2 very much!
In chinese : ллÄãÃÇ£¡·Ç³£¸Ðл£º£© |
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