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The motion of a body is given by X; = X, +aX,! X, = X, +aX,t with a constant x; = X; with (x1, x2, X3) being the coordinates of a material point M in the current configuration at a time "t", while (X1, X2, X3) are the coordinates at t=0 (initial configuration) a) Determine the displacement vector u(X1, X2, X3), the velocity vector v(X1, X2, X3) in the Lagrangian description. b) Determine the displacement vector u(x1, x2, X3), the velocity vector v(x1, x2, X3) in the Eulerian description. ôx; ôx , c) Calculate the deformation gradient F (F, -).

The motion of a body is given by X; = X, +aX,! X, = X, +aX,t with a constant x; = X; with (x1, x2, X3) being the coordinates of a material point M in the current configuration at a time "t", while (X1, X2, X3) are the coordinates at t=0 (initial configuration) a) Determine the displacement vector u(X1, X2, X3), the velocity vector v(X1, X2, X3) in the Lagrangian description. b) Determine the displacement vector u(x1, x2, X3), the velocity vector v(x1, x2, X3) in the Eulerian description. ôx; ôx , c) Calculate the deformation gradient F (F, -).

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Problem: Lagrangian and Eulerian Description The motion of a body is given by X = X, +aX,t x, = X, +aX,t x; = X; with a constant with (x1, x2, X3) being the coordinates of a material point M in the current configuration at a time "t", while (X1, X2, X3) are the coordinates at t=0 (initial configuration) a) Determine the displacement vector u(X1, X2, X3), the velocity vector v(X1, X2, X3) in the Lagrangian description. b) Determine the displacement vector u(x1, x2, X3), the velocity vector v(x1, X2, X3) in the Eulerian description. ôx, c) Calculate the deformation gradient F (F, ). d) Calculate the right Cauchy Green strain tensor C and the finite strain tensor E
Transcribed Image Text:Problem: Lagrangian and Eulerian Description The motion of a body is given by X = X, +aX,t x, = X, +aX,t x; = X; with a constant with (x1, x2, X3) being the coordinates of a material point M in the current configuration at a time "t", while (X1, X2, X3) are the coordinates at t=0 (initial configuration) a) Determine the displacement vector u(X1, X2, X3), the velocity vector v(X1, X2, X3) in the Lagrangian description. b) Determine the displacement vector u(x1, x2, X3), the velocity vector v(x1, X2, X3) in the Eulerian description. ôx, c) Calculate the deformation gradient F (F, ). d) Calculate the right Cauchy Green strain tensor C and the finite strain tensor E
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