I Question regarding actual computation of tensor at point (Self Study)

Amateur659
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Hello all,

I am hoping to get some feedback on the manner in which I performed computations towards solving the following problem.

question.PNG


There are a couple specific points which I am not confident of:
1. Did I properly account for the manifold structure in my computation of the nonzero components?
2. Is the general process by which I compute each tensor component correct?
IMG_20220213_010056272.jpg


Finally, please let me know if I am making a mistake posting such questions here.

Thank you for your time and feedback!
 

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It looks fine.
 
Awesome, thanks for the feedback.
 

Thread 'Strain Tensor Based on Clifford Algebra'

Let u=u_i e_i be the displacement field of a continuum body. Then the displacement gradient tensor H based on classical formulation is given by H=grad u = u_{i,j} e_i \otimes e_j, where \otimes represents tensor product.H is decomposed intro two parts. Namely, H=epsilon+Omega. The infinitesimal strain tensor is given by epsilon=(H+H^t)/2, where H^t=transose(H). In component form, we have epsilon_{ij}=(u_{i,j}+u_{j,i})/2. On the other hand, Omega=(H-H^t)/2 describes the rigid body rotation...
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