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I'm no expert on FEM but from what I understand:
1. The difference is how it plots the stress. "Nodal stress" plots the value at the nodes of the mesh element. The number of nodes that an element has depends on the order of the elements edges. A second order tetrahedral element will have ten nodes, where a first order one will have 4. This creates a prettier picture as it can plot more than a single color per mesh element.
"Elemental stress" plots the average stress value at the center of the element. This means the entire element gets one color.
2/3. For the most part I believe it is preference on how you want the results to be displayed. Theoretically, there should be no differencee between the two as the mesh size approaches 1/inf.
During the solution process, in each element, stress results are calculated at certain locations called 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.
Nodal Value Stresses in Gauss points can be extrapolated to element nodes. Most often, one node is shared by several elements, and each element reports different stresses at the shared node. Reported values from all adjacent
elements are then averaged to obtain a single value. This method of stress averaging produces averaged (or nodal) stress results.
Element values Alternately, the stress values from all Gaussian points within each element can be averaged to report a single elemental stress. Although
these stresses are averaged between Gauss points, they are called nonaveraged
stresses (or element stresses) because the averaging is done internally within the same element only.
Hi Allan: to answer your questions 2) and 3). The stresses should approach one another as the element size gets smaller (as Steven indicated) - so it can be used as a convergence criterion (along with plotting the error estimate). Beware however, of parts that connect and viewing stress results at the connection boundary - you'll normally want to uncheck the option "average stress across element boundaries", when plotting stress. Some analysts take the point of view that element stresses are the best way to assess the answer from FEA, since it's "pure", and represents the true element stress, rather than extrapolating Gauss point stresses to the nodes, then averaging the stresses from each element at that node (in effect, polluting the answer). However, the nodal stress plots certainly look pretty. We use element stress plots for convergence assessments; then use nodal stress plots as "wow" factor for audiences.