Element

An element is just a subdivision of the initial domain of definition.

It can be 0 dimensional (point), 1d (edge), 2d (triangle/square) or 3d (tetrahedron, cubes…)

Order of an element

The order of an element correspond to the number of points that define the said element. More order allows better computation (because the interpolation is more accurate) but more cost as well.

Degree of freedom

Every displacement or rotation applied to an element is called a “degree of freedom”

Here, there’s 6 degrees of freedom for a 1D element in 3 dimension

Here, there’s 12 degrees of freedom for a 2D element

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Here, the rotation counts as a degree of freedom as the behavior is significantly influenced by bending moments, which cause rotation

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Check out this example for further explanation.

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A 3D elements has 24 degrees of freedom (rotations are induced by translation of nodes)