What are element shape functions in the finite element method?
Element shape functions describe how displacements vary inside a finite element. After the solid is broken into elements and element equations are written, these functions represent the internal variation of displacement within each individual element.
Conditions
- Defined within an individual finite element.
- Used after discretizing the domain into elements and identifying nodes.
Reasoning, step by step
- Discretize the domain into elements and identify the nodes.
- Write the element equations for the nodes.
- Use shape functions to mathematically represent how the displacement changes continuously within the boundaries of each element.
- Apply these functions to interpolate values between the nodal points.
Example
The speaker says element equations represent how displacements change within the element. He then says, “This is what we call as the element shape functions.”
Common misconceptions
- Thinking shape functions apply to the entire global domain rather than individual elements.
- Confusing shape functions with the governing physical laws of the problem.
Watch the explanation
3:13 – 3:25Watch this moment ↗
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