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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