1.10.1. Finite Difference Method (FDM)

Try these first

1. 1.

   What does FDM stand for in the context of numerical methods?

   Hint

   What do you call the method that breaks apart continuous data into pieces?

2. 2.

   What is the purpose of discretization in FDM?

   Hint

   Think about what happens when we divide time into smaller segments.

3. 3.

   What is the purpose of the Finite Difference Method?

   • To solve patterns in static loads
   • To approximate solutions of differential equations
   • To create structural designs

   Hint

   Think about its main uses in dynamic analysis.

4. 4.

   True or False: FDM can only be used for linear equations.

   • True
   • False

   Hint

   Consider what types of equations you’ve learned about.

5. 5.

   Calculate the displacement of a mass subjected to a harmonic force using FDM for five time steps considering initial displacement and velocity.

   Hint

   Use the governing equation for FDM and remember to apply initial conditions correctly.

6. 6.

   Assess the computational efficiency of solving a complex MDOF system using FDM and suggest methods to optimize performance.

   Hint

   Think about how larger time increments affect precision and resource requirements.