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Orthonormalization of covariant base_Green strain tensor

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lijingyang

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Unread post Fri Dec 02, 2016 12:26 pm

Orthonormalization of covariant base_Green strain tensor

Hello,
To get the orthonormal frame of Green strain tensor from [(g0)1 g(0)2 (g0)3] to [(e0)1 (e0)2 (e0)3], which is explained in Slide 25 of lecture1109. The method used in the slide seems to assume that (e0)1 is perpendicular to (e0)3, also the expression of (e0)3 seems to be a scalar, not a vector (also is (e0)3 going to be related to rz, which is partialr/partialz, or r0z, which is partialr0/partialz?). If we follow this equation to get [(e0)1 (e0)2 (e0)3], they seem not to be orthonormalized.

Thank you for your help!
-Lijing
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recuero

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Unread post Wed Dec 07, 2016 7:00 pm

Re: Orthonormalization of covariant base_Green strain tensor

Hi Lijing,

You are right. The orthonormalization is not expressed correctly on that slide -the second set of equations is correct.
Correct expressions for orthonormalization are as follows:

(e0)1 = (g0)1/norm((g0)1)
(e0)3 = cross((g0)1,(g0)2)/norm(cross((g0)1,(g0)2))
(e0)2 = cross((e0)3 ,(e0)1)

Let me know if you still have questions. Also, you can always double-check the expressions in Chrono's shell element class.

Best,
Antonio

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