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Green–Lagrange strain for Shell: transformation from curvilinear coordinate to local Cartesian coordinate

Submitted by phdggg on

Hello all:

      I am confused about how to transform Green–Lagrange strain defined using  curvilinear coordinate to local Cartesian coordinate.  

      In a paper on "Nonlinear shell models with seven kinematic parameters", published in Comput. Methods Appl. Mech. Engrg. 194 (2005) 2336–2362. Since I am trying to implement this method, I have a question on Eqs. (63) and (64), where the strain defined in curvilinear coordinate system is converted to the local Cartesian coordinate.  I think there is a typo in Eq.(63) since i is not defined. If so, what should be the correct form? Also, should T be the inverse of that matrix or not take the inverse?

     In another paper on "Nonlinear shell problem formulation accounting for through-the-thickness stretching and its finite element implementation" published in Computers and Structures 80 (2002) 699–717. In Eq. (89), T does not take the inverse. I am confused. Could you please clarify?

Thanks,

Mengda