On the performances of parametric finite elements when geometry distortions occur

Parametric finite elements can lose their performance when distortions of the element geometry arise. Geometry distortions cause global co-ordinates to be non-linear functions of local co-ordinates when described through the co-ordinate transformation. This transformation is ruled by the inverse of the Jacobian matrix. In this paper a new method to investigate the effects of element distortions on the performance of parametric finite elements is presented. By inspecting analytically the Jacobian matrix, the proposed method investigates, on a rational basis, the relation between distortions and the interpolating functions of parametric finite elements. Common examples are employed to test the accuracy of the information provided by the method. Comparison with extant methods confirm the ability of the proposed technique to give useful information about the performance of an investigated element when geometry distortions occur.