2. LMB Formulation

Try these first

1. 1.

   Define the cylindrical coordinate system and name its components.

   Hint

   Think about how these dimensions describe a point in 3D space.

2. 2.

   What is a basis vector?

   Hint

   Relate this to how you define directions in 2D or 3D.

3. 3.

   What is the primary coordinate system discussed in this section?

   • Cartesian
   • Cylindrical
   • Spherical

   Hint

   Recall the distinct features of each system.

4. 4.

   True or False: The basis vectors in cylindrical coordinates change direction with angular position.

   • True
   • False

   Hint

   Think about how these vectors relate to angular changes.

5. 5.

   A cylindrical tank has varying stresses at different heights. If the stress at height z is represented as σ(z) = 3z², compute the total force acting on the top face of the cylindrical element given radius r = 2.

   Hint

   Utilize integration techniques for polynomial functions.

6. 6.

   Create a simulation model of a cylindrical structure under varying loads. How would the stress distribution change as you alter the radial distance?

   Hint

   Consider software that can visualize stress under loads.