Two-dimensional elastostatic analysis using Coons-Gordon interpolation

Abstract

During the last years blending-function (Coons’) interpolation has been utilized for the construction of large 2D and 3D finite elements with degrees of freedom appearing along the boundaries of the domain. In the particular case of elasticity problems, these so-called “boundary-only Coons macroelements” have been applied to the analysis of simple structures in which adequate accuracy was remarked. This paper continues the research investigating, for the first time, the role of internal nodes in the accuracy of the numerical solution using various trial functions along the boundary in conjunction with various blending functions (piecewise-linear, cubic B-splines and Lagrange polynomials). The performance and limits of the proposed Coons-Gordon macroelements are tested in typical 2D elastostatic examples, where they are also compared with conventional four-node bilinear finite elements of the same mesh density. It was definitely found that although the ‘boundary-only formulation’ of the proposed Coons macroelements successfully pass some well-established patch tests and may be very accurate in some simple test cases, in general, it must be substituted by the ‘transfinite formulation’ (Coons-Gordon) where a sufficient number of internal nodes is necessary to ensure convergence.