Iso Parametric Coordination System Of Elements Example

Apart from local and global coordination systems for elements, there is another system based on isoparametric formulation/representation, which is used extensively in finite element method. In BFE also in many places instead of local coordinate system, the iso parametric coordination is used.

Iso Parametric Coordination system for BarElement with two nodes

../../_images/bar-iso-coord1.png

Based on

At the beginning point of the element, where x=0 the iso parametric coordinate is ξ=-1

At the central point of the element, where x=L/2, and L is length of elements, the iso parametric coordinate is ξ=0

At the end point of the element, where x=L, and L is length of elements, the iso parametric coordinate is ξ=1

In bar element with two nodes the relation between isoparamtric ξ coordinate and local x coordinate is:

x = (ξ + 1)*L/2 and subsequently

ξ = (2*x-L)/L