FEM Clarification: What is a Linear Element?

[Niles]

Hi

In my book on FEM they talk about "linear elements" (in 1D). My question is: When is a finite element considered linear?

Is it when the shape (interpolation) functions are linear in the 1D variable?
Is it when the trial function is linear in the 1D variable?

 

[serbring]

Hi

In my book on FEM they talk about "linear elements" (in 1D). My question is: When is a finite element considered linear?

Is it when the shape (interpolation) functions are linear in the 1D variable?
Is it when the trial function is linear in the 1D variable?

interesting question, but I cannot help you. Just a guess...when the material is fully elastic?

 

[AlephZero]

It could mean several different things

1. The element is geometrically a straight or curved line (for example a rod or beam) not a surface or solid element.
2. The element shape functions are linear.
3. The element formulation only works for linear elastic materials (no plasticity, creep, etc).
4. The element formulation only works for small strain, small displacement problems.

Without more context, it's hard to give a good answer.

 

[prost22]

"Linear element" normally just mean that the shape functions used to map the geometric element (the element as it looks in the body you are meshing) to the parent element are linear (1D), bilinear (2d), or trilinear (3d). This is sometimes called "p=1" (for polynomial level = 1) elements. Normally they aren't talking at all about the linearity of the material constitutive relation. In 1D, two shape functions completely define the behavior of the computed variable (in structures, that would be the displacement field); in 2D, four shape functions, and 3D, 8 shape functions--you'll often read that an element is defined by the number of nodes, though that's confusing sometimes, as in p=2 (quads) and higher p-levels, you have shape functions assigned to element edges and the middle of the element.

 

[Niles]

Thanks for all the suggestions!

Cheers!

Niles.