Node Values Versus Element Values

Stress results are first calculated at certain locations, called Gauss or quadrature points, located inside each element. Simulation calculates stresses at the nodes of each element by extrapolating the results available at the Gauss points.

After a successful run, nodal stress results at each node of every element are available in the result database.

node_red.gif Element nodes

gauss_blue.gif Gauss points

First order tetrahedral elements (draft quality) have one Gauss point in their volume. Second order tetrahedral elements have four Gauss points. First order shell elements have one Gauss point. Second order shell elements have three Gauss points.

For a node common to several elements, each element gives stress results that are slightly different. For example, if a node is common to three elements, there can be three slightly different values for every stress component at that node.

When you plot nodal stresses, the program averages the stress values from all adjacent elements contributing to the stresses at that node.

nodal_values_a.gif nodal_values_b.gif
Stress values extrapolated from Gauss points to nodes of each element. Nodal stress values averaged at each node.

Alternatively, you can report a single element stress value as the arithmetic average (mean) from all Gauss points within each element. Although these stresses are averaged between Gauss points, they are called non-averaged stresses (or element stresses) because the averaging is done internally within the same element only.

Element stress values averaged within the element.

Element stresses and nodal stresses are always different, but too large a difference indicates that the mesh is not sufficiently refined in that location.

The variation between the element and nodal stress values on an element basis is used to estimate the energy error distribution over the whole model. Based on strain energy principles, Simulation estimates the energy norm error for every element.

To reduce the stress errors, refine the mesh at the areas with high values of energy norm error.

Energy norm error (element) = 1 /3 * strainerror * stresserror * (Element volume)

The strainerror is the difference between the nodal strain and element strain on an element basis. The stresserror is the difference between the nodal stress and element stress on an element basis.

To plot the energy norm error, in the Stress Plot PropertyManager, under Advanced Options, select Element Values. Under Component plot-deformation.png, select ERR: Energy Norm Error.