As a math student I though that all 3D Finite Elements are Tetras.

On the second day at Daimler-Benz I was told "Tetras do not work" for all solvers ( Nastran, Abaqus, Permas, crash..)

In 1994 suddenly nearly all Engineers changed their mind "quadratic Tetras (midnode) work well, linear Tetras do not work" Automatic TET Meshing has aarived at the engineer's desks and it worked.

Guido Dhondt
linear elements experience locking phenomena such as shear locking and volumetric locking, or hourglassing in case of reduced integration. Please consult my book for more details (Wiley 2004).


CalculiX User's Manual: USE QUADRATIC ELEMENTS


stiffness matrix


Transforming each Integaral to the reference element.
linear elements, 3x3 Matrix, the determinant is part of the LFE error-criterion


replace the integral by sums


Zienkiewicz: List of 3 formula for tetra. Order of accuracy 1 to 3


Ciarlet:


Does reduced Integration save computation time?
If we cannot apply linear tetras and take quadratic tetras and keep the midnodes on the mid of the edges we loose the quadratic geometric approximation power.
Which Integration formula is used? Do we loose quadratic approx power by using an inaccurate integration formula?


numerical experiments CalculiX, Nastran, Abaqus