What is dimension for element?

To perform finite element analysis, understanding dimensions is crucial.

In this content, we will explore the concept of dimension in a simple and straightforward manner.

Dimension is a concept that represents the extent to which space or a figure widens.

The ancient Greek mathematician Euclid defined the following in his work "Elements of Geometry" regarding points, lines, planes, and solids :

A point is something without any part.

A line is a length without width.

A plane is something with only length and width.

A solid is something with length, width, and height.

Modern scientists have provided more detailed and clear definitions. The French philosopher Descartes (1596-1650) defined dimension as "the number of quantities needed to determine the position of a point."

0 Dimension → Point

: Since zero quantities are needed to determine the position, the degrees of freedom are also 0.

1 Dimension → Line

: One quantity is needed to determine the position, so the degrees of freedom are 1.

2 Dimensions → Plane

: Two quantities, X and Y, are needed to determine the position, so the degrees of freedom are 2.

3 Dimensions → Solid

: Three quantities, X, Y, and Z, are needed to determine the position, so the degrees of freedom are 3.

Understanding dimensions as the number of vectors in which a point can move within a simply constructed element might be simpler, as illustrated in the figure below.

Make it a little easier to understand with the shorts below.

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