12.18. Use in Finite Element Method (FEM)

Try these first

1. 1.

   What does the Dirac delta function represent mathematically?

   Hint

   Think about where it is non-zero.

2. 2.

   How does the Dirac delta function aid in achieving weak formulations in FEM?

   Hint

   Focus on point evaluation.

3. 3.

   What is the integral of the Dirac delta function over its entire domain?

   • 0
   • 1
   • Infinity

   Hint

   Think about what the function captures in its behavior.

4. 4.

   True or False: The Dirac delta function is a traditional continuous function.

   • True
   • False

   Hint

   Recall the definition we discussed.

5. 5.

   Derive the weak form of a simple differential equation using the Dirac delta function as a point source.

   Hint

   Review the definitions of weak formulations and point evaluations.

6. 6.

   Create a FEM model for a cantilever beam subjected to a point load at its free end using delta functions.

   Hint

   Think about your boundary conditions and how the delta function influences load applications.