1.1. Representation of gradient

Try these first

1. 1.

   What is the formula for the gradient in cylindrical coordinates?

   Hint

   Think of how each term corresponds to a direction.

2. 2.

   Define radial strain.

   Hint

   It's related to changes in distance from the center in a cylindrical structure.

3. 3.

   What is the primary purpose of a gradient?

   • To find maxima
   • To determine the direction of change
   • To calculate area

   Hint

   Think about how the shape of a hill indicates steepness.

4. 4.

   True or False: The displacement vector in cylindrical coordinates can have three unique components.

   • True
   • False

   Hint

   Recall the terms used in cylindrical representation.

5. 5.

   If a hollow cylinder experiences a radial displacement of 5 cm and a hoop displacement of 3 cm, calculate the strains ε_rr and ε_θθ assuming initial lengths were 50 cm.

   Hint

   Use the formula for strain: ε = ΔL / L₀.

6. 6.

   A cylindrical structure shows a non-uniform displacement due to varying internal pressure. Describe how this affects the overall strain calculations and what assumptions might need adjusting.

   Hint

   Think about how pressure changes can result in different strain responses.