1.3. Representation of displacement gradient

Try these first

1. 1.

   What is the formula representation of displacement in cylindrical coordinates?

   Hint

   Consider breaking it down into its components.

2. 2.

   Define a gradient in physical terms.

   Hint

   Think about how it relates to direction and rate of change.

3. 3.

   What is a displacement gradient?

   • A measure of total force
   • A measure of how displacement varies
   • A type of strain

   Hint

   Think about how displacement is analyzed in various materials.

4. 4.

   True or False: The basis vectors in cylindrical coordinates do not change with respect to the angle θ.

   • True
   • False

   Hint

   Recall how the basis system is defined.

5. 5.

   A hollow cylinder experiences a radial displacement of 2 mm and circumferential displacement of zero. Calculate the components of the displacement gradient matrix and discuss its significance.

   Hint

   Focus on substituting into the gradient definitions.

6. 6.

   Consider a cylindrical shell with a displacement gradient matrix showing significant shear terms. Discuss what these terms imply about the internal forces occurring within the cylinder during deformation.

   Hint

   Think about the implications of shear stress.