Mumbai University > Mechanical Engineering > Sem 6 > Finite Element Analysis

Marks: 5M

Year: May 2015

In the finite element method, an element's Jacobian matrix relates the quantities wrote in the natural coordinate space and the real space. The bigger the element is distorted in comparison with a ideal shape element, the worse will be the transformation of the quantities from the natural space to the real space. In fact, it means that the distortion on the element shape will introduce error in the mathematical transformation from natural space to the real space.

In a FE software, the Jacobian is a measure of the deviation of a given element from an ideally shaped element. The Jacobian value ranges from - 1.0 to 1.0, where 1.0 represents a perfectly shaped element. The ideal shape for an element depends on the element type. The check is performed by mapping an ideal element in parametric coordinates onto the actual element defined in global coordinates.