A transition element for uniform strain hexahedral and tetrahedral finite elements

A transition element is presented for meshes containing uniform strain hexahedral and tetrahedral finite elements. It is shown that the volume of the standard uniform strain hexahedron is identical to that of a polyhedron with 14 vertices and 24 triangular faces. Based on this equivalence, a transition element is developed as a simple modification of the uniform strain hexahedron. The transition element makes use of a general method for hourglass control and satisfies first-order patch tests. Example problems in linear elasticity are included to demonstrate the application of the element.