Local Coordinates and Global Coordinates in Finite Element Analysis

Local Coordinates

A local coordinates system whose origin is located within the element in order to simplify the algebraic manipulations in the derivation of the element matrix.

• The use of natural coordinates in expressing approximate functions is advantageous because special integration formulas can often be applied to evaluate the integrals in the element matrix.
• Natural coordinates also play a crucial role in the development of elements with carved boundaries.

Natural Coordinates

It is a local coordinate system that permits the specification of a point within the element by a dimensionless parameter whose absolute magnitude never exceeds unity.

• It is dimension less.
• They are defined with respect to the element rather than with reference to the global coordinates.

Global Coordinates

Global coordinates are convenient for specifying the location of each node, the orientation of each element, the boundary conditions and the loads for the entire domain.

• The solution to the field variable is generally represented with respect to the global coordinates.