Question

The mid node should not be outside of the triangular element this condition should ensures that det J does not attain a value ____

(a) Constant

(b) Zero

(c) Unity

(d) Infinite

I had been asked this question in a national level competition.

My question is taken from Four Node Quadrilateral for Axis Symmetric Problems in chapter Two Dimensional Isoparametric Elements and Numerical Integration of Finite Element Method

Answer 1

Correct answer is (b) Zero

To elaborate: The Mid-Node Admissible Spaces (MAS) [1,2] for two-dimensional quadratic triangular finite elements are extended to three-dimensional quadratic tetrahedral finite elements (3DQTE). The MAS concept for 3DQTE postulates a bounded 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 determinant value at any point of the element.