The classical 8-node isoparametric serendipity element uses parametric shape functions for both test and trial functions. Although this element performs well in general, it yields poor results under severe mesh distortions. The distortion sensitivity is caused by the lack of continuity and/or completeness of shape functions used for test and trial functions. A recent element using parametric and metric shape functions for constructing the test and trial functions exhibits distortion immunity. This paper discusses the choice of parametric or metric shape functions as the basis for test and/or trial functions, satisfaction of continuity and completeness requirements, and their connection to distortion sensitivity. Also, the performances of four types of elements, viz., parametric, metric, parametric-metric, and metric-parametric, are compared for distorted meshes, and their merits and demerits are discussed.
S. Rajendran and Dr. Shankar S., “Mesh Distortion Sensitivity of 8-node Plane Elasticity Elements Based on Parametric, Metric, Parametric-metric, and Metric-parametric Formulations”, Structural Engineering and Mechanics, vol. 17, pp. 767–788, 2004.