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Parabolic elements can map curved geometry much more accurately than linear
elements of the same size. The mid-side nodes of the boundary edges of an
element are placed on the actual geometry of the model. In extremely sharp or
curved boundaries, placing the mid-side nodes on the actual geometry can result
in generating distorted elements with edges crossing over each other. The
Jacobian of an extremely distorted element becomes negative. An element with
negative Jacobian causes the analysis program to stop.
In the course of calculating the element stiffness matrix, the program performs
integration processes over the domain of the element. The integration process is
simplified by evaluating the function of interest at prescribed locations inside the
element. These locations are called Gaussian points. For the purpose of checking
the quality of parabolic elements, COSMOS/Works gives you a choice to base the
Jacobian check on 4, 16, or 29 Gaussian points.
The Jacobian ratio of a parabolic tetrahedral element, with all mid-side nodes
located exactly at the middle of the straight edges is 1.0. The Jacobian ratio
increases as the curvatures of the edges increase. The Jacobian ratio at a point
inside the element provides a measure of the degree of distortion of the element at
that location. COSMOS/Works calculates the Jacobian ratio at the selected
number of Gaussian points for each tetrahedral element. Based on stochastic
studies, it is generally seen that a Jacobian ratio of 40 or less is acceptable.
COSMOS/Works adjusts the locations of the mid-side nodes of distorted elements
automatically to make sure they pass the Jacobian check.
Thank`s for your great explanation....