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A different error estimator is based on the difference between the maximum and minimum of an elementwise-selected principal stress at the integration points in the elements belonging to one and the same node . It is triggered by selecting ERR underneath the *EL FILE keyword card.

The elementwise-selected principal stress is either the smallest or the largest principal stress (first or third). It is the largest principal stress if the maximum over all integration points in the element of the absolute value of the largest principal stress is larger than the maximum over all integration points in the element of the absolute value of the smallest principal stress. Else, it is the smallest principal stress.

A node usually belongs to several elements. The stresses are available (and most accurate) at the integration points of these elements. If the largest difference between the elementwise-selected principal stress at all integration points within an element is small, the stresses vary little across the element and the element size is deemed adequate to yield an accurate stress prediction. From the absolute value of the largest difference a relative element value is calculated. The relative element value is the absolute value divided by the absolute value of the largest elementwise-selected principal stress within the element.

To obtain the relative value at the nodes the maximum is taken of the relative element value across all elements belonging to the node. In a strict sense this is not an error estimator, it is just a measure for the variation of the elementwise-selected principal stress across all elements belonging to the node.

By applying this concept to a large number of examples for which the stress error was known a heuristic relationship was deduced. It allows for a given element type to determine the error in the elementwise-selected principal stress in a node (called STR in the frd file; it is obtained by selecting ERR underneath the *EL FILE or *ELEMENT OUTPUT card) from the relative measure just defined (describing the relative change of the elementwise-selected principal stress in the adjacent elements). If a node belongs to several element types the worst value is taken. The STR-value is in %.

For heat transfer a similar error estimator was coded for the heat flux. It is triggered by selecting HER underneath the *EL FILE keyword card. It represents the variation of the size of the heat flux vector across all elements belonging to one and the same node. For thermal problems too heuristic relationships connecting the largest temperature gradient in the adjacent element to a node and the temperature error in the node have been established. The temperature error is called TEM in the frd file and is in %. It is obtained by selecting HER underneath the *EL FILE or *ELEMENT OUTPUT card.

Next: Output variables Up: Error estimators Previous: Zienkiewicz-Zhu error estimator   Contents
guido dhondt 2018-12-15