Rotationally invariant distortion resistant finite-elements

•The accuracy of the finite-element solution deteriorates as elements become distorted.•New rotationally invariant and mesh distortion-resistant element.•Applied to both linear and geometrically non-linear analysis.•Predictive capabilities demonstrated using geometrically non-linear analyses.•Important step in overcoming the problem of mesh distortion sensitivity.

The predictive capability of conventional iso-parametric finite-elements deteriorates with mesh distortion. In the case of geometrically non-linear analysis, changes in geometry causing severe distortion can result in negative Jacobian mapping between the local and global systems resulting in numerical breakdown. This paper presents a finite-element formulation that is resistant to irregular mesh geometries and large element distortions whilst remaining invariant to rigid body motion. The predictive capabilities of the family of finite-elements are demonstrated using a series of geometrically non-linear analyses including an elastic cantilever beam and an elasto-plastic double notched specimen.