Why does the finite element method need a physical law after defining shape functions?

Conditions

• Requires a governing physical principle for the problem class.
• The mathematical statement must be valid locally within elements and globally over the domain.

Reasoning, step by step

1. Define the domain using elements and nodes.
2. Use shape functions to describe displacement variations within elements.
3. Impose a governing physical law, such as minimum potential energy.
4. Solve the resulting mathematical statement to find the actual displacements and stresses.

Example

The speaker says a law from the physics book is needed to make the mathematical statement. He mentions “minimum potential energy” as an example and says the statement should be valid within the element and over the entire domain.

Common misconceptions

• Assuming shape functions alone are sufficient to solve the problem without physical constraints.
• Thinking the physical law only needs to be satisfied globally and not within individual elements.

Watch the explanation

Explore next

• What is the definition of discretization?
• How does the video derive the element equation for a chord?
• What is the circumference of a circle?