Mid-node admissible space for 3D quadratic tetrahedral finite elements

The Mid-Node Admissible Spaces (MAS) [1,2] for two-dimensional quadratic tr iangular finite elements are extended to three-dimensional quadratic tetrah edral finite elements (3DQTE). The MAS concept for 3DQTE postulates a bound ed region within which a mid-side node of a curved edge of the 3DQTE can be placed to ensure maintaining a specified minimum and maximum Jacobian dete rminant value at any point of the element. The theorems that form the basis of the MAS and their mathematical proofs, followed by the procedure to con struct the MAS for 3DQTE, are presented. Based on the MAS developments, a r obust element quality metric for 3DQTE is developed. The metric is based on the Jacobian determinant over the entire element without requiring that ii actually be computed everywhere on the element. Tire metric is relatively inexpensive to compute, especially for I,mildly distorted elements. It is s hown to be able to detect elements of poor quality that other distortion me trics fail to detect It also approves good quality elements regardless of t he extent to which they may appear to be geometrically distorted.