General complete Lagrange interpolations with applications to three-dimensional finite element analysis Original Research Article

In this paper, we have first derived the interpolation polynomials for the general serendipity solid elements of rectangular shape which allow arbitrarily placed nodes along the edges. We have then presented a method to determine the interpolation functions for the general complete Lagrange elements which allow arbitrarily placed nodes. Explicit expressions for interpolation functions of the serendipity and complete Lagrange families with uniform spacing of nodes over the element domain are derived for elements of orders 4–10. We have also modified the shape functions of complete Lagrange family to correctly interpolate the complete polynomials in the global space for angular distortions of quadrilaterals over the six planar facets of linear solid hexahedron elements.