Effects of element distortions on the performance of isoparametric elements

We discuss the effects of element distortions on the performance of displacement-based isoparametric quadrilateral finite elements. Suitable example problems for both the Lagrangian and the serendipity types of elements are used to show numerically the effects of element distortions. The effects of angular and curved-edge distortions are evaluated analytically in terms of the abilities of the elements to represent exactly various polynomial displacement fields. We then solve a plane stress problem adaptively to demonstrate the effect of element distortions on the accuracy of the stress distribution. The conclusion is that the Lagrangian elements are not affected by angular distortions and are therefore the more reliable elements for general use.