- Finite Elasticity Exercises And Solutions Exercise 1 Let 4 V And T Be A Scalar A Vector And A 2nd Order Tensor Fie 1 (32.44 KiB) Viewed 53 times
Finite Elasticity - Exercises and Solutions Exercise 1 Let 4. v, and T be a scalar, a vector, and a 2nd order tensor field, respectively, on a deforming body, and let F-Grad Ə. J=det F, ox, E, where the Einstem notation that repeated indices represent summation is used, and X = (X1; X2, X3) are the reference (Lagrangian) coordinates, <= (1923) are the current Evlerian) coordinates, {E1, Es, Es} are the unit vectors in Cartesian coordinates in the reference configuration, and {el, ez, es} are the unit vectors in Cartesian coordinates in the current configuration. Shorq that (a) Grad = "grad , (6) Grad v = (grad v)F, (e) Div = - Jdivo-Fu). (d) Div T-Jdiv(Tp) where using Einstein notation): δυ, E Grad u = e E grad y = e grad v= ax ax Grad - ap 80 aus 3x Ох, au; Div u = ax T1/8X Div T= 8Tx/aX 873/ax div = ou Ty/ diy T =8T2/, T3/8 da;