The Lagrangian description of a deformation is given by x1 = X, + X3(e2 e-2)...

  

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The Lagrangian description of a deformation is given by x1 = X, + X3(e2 – e-2) X 2 = X,- X {e²– 1) X3 = Xze? Determine the components of the deformation matrix F;A and from it show that the Jacobian J does not vanish. Invert the mapping equa- tions to obtain the Eulerian description of the deformation. Answer: J = e? X1 = x1 – X3 (1 - e4) X2 = x2 + X3 (1 - e-2) X3 = X3 e-2 The Lagrangian description of a deformation is given by x1 = X, + X3(e2 – e-2) X 2 = X,- X {e²– 1) X3 = Xze? Determine the components of the deformation matrix F;A and from it show that the Jacobian J does not vanish. Invert the mapping equa- tions to obtain the Eulerian description of the deformation. Answer: J = e? X1 = x1 – X3 (1 - e4) X2 = x2 + X3 (1 - e-2) X3 = X3 e-2