A technique to develop mesh-distortion immune finite elements

Three sufficient conditions are proposed for an iso-parametric finite element formulation to be immune to mesh-distortion effects, even for extremely distorted element geometries for which the Jacobian geometric mapping goes negative! Illustrative element formulations are presented to test the sufficiency of the proposed conditions. Numerical results confirm that the illustrative elements are indeed capable of giving mesh-distortion immune solution for extreme mesh distortions. This has been possible partly because the stiffness integral is free of the Jacobian term in the new formulation.