A 1.000 m by 1.500 m by 2.000 m cube of a continuous solid is deformed...

 

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A 1.000 m by 1.500 m by 2.000 m cube of a continuous solid is deformed (dashed line in the figure) into a shape by the movement of point E to E'. Considering small deformations, the displacement field can be given as: u=Cxyz, v=Cxyz, and w=C3xyz. a) Find expressions for displacement u, v, and w for E' with coordinates of (1.504, 1.002, 1.996). b) Determine the state of strain at point E when the coordinates of this point after deformation are (1.504, 1.002, 1.996). All 6 components should be calculated. c) Determine the normal strain at E in the direction of Line EA. (Hint: use the 3D strain transformation equations with I, m, n direction cosines) d) Determine the shear strain at Point E for the undeformed orthogonal lines EA and EF. (Hint: use the 3D strain transformation equations with direction cosines for two unit-vectors) 1.000 m 2.000 m 1.500 m A 1.000 m by 1.500 m by 2.000 m cube of a continuous solid is deformed (dashed line in the figure) into a shape by the movement of point E to E'. Considering small deformations, the displacement field can be given as: u=Cxyz, v=Cxyz, and w=C3xyz. a) Find expressions for displacement u, v, and w for E' with coordinates of (1.504, 1.002, 1.996). b) Determine the state of strain at point E when the coordinates of this point after deformation are (1.504, 1.002, 1.996). All 6 components should be calculated. c) Determine the normal strain at E in the direction of Line EA. (Hint: use the 3D strain transformation equations with I, m, n direction cosines) d) Determine the shear strain at Point E for the undeformed orthogonal lines EA and EF. (Hint: use the 3D strain transformation equations with direction cosines for two unit-vectors) 1.000 m 2.000 m 1.500 m