21.17. Application in Finite Element Method (FEM)

Try these first

1. 1.

   What does the stiffness matrix (K) represent in FEM?

   Hint

   Think about how it relates to how structures resist forces.

2. 2.

   What does the displacement vector (u) indicate?

   Hint

   Relate it to the movement of parts of the structure under load.

3. 3.

   What does the symbol [K] represent in the FEM matrix equation?

   • Force matrix
   • Stiffness matrix
   • Displacement matrix

   Hint

   Think about the properties of the material.

4. 4.

   True or False: The displacement vector [u] is derived from applying the stiffness matrix [K] to the force vector [F].

   • True
   • False

   Hint

   Remember the equation structure.

5. 5.

   Given a simple two-dimensional structure described by the stiffness matrix K = [[4, -2], [-2, 4]], calculate the eigenvalues.

   Hint

   Use the formula for the characteristic equation.

6. 6.

   Using a given force vector F = [10, 20] and the stiffness matrix K = [[3, -1], [-1, 2]], find the displacement vector u.

   Hint

   Consider how to isolate u.