Understanding how results are computed

Node-based field output variables are written to the output database at each node, along with any nodal transformations applied during model creation. For the display of nodal field output variables, Abaqus/CAE reads the required values from the output database for each node included in the plot. By default, these values are displayed in the global coordinate system; you can choose to apply the nodal transformations to the results or to apply a user-specified coordinate system transformation. The final values are then used to produce contours, nodal probe values, display groups or color coding based on results, or X–Y data along a path.

Element-based field output variables are written to the output database at the integration points, the element centroid, or the element nodes, depending on the variable. For the display of element-based field output variables, Abaqus/CAE reads values from the output database for all elements connected to all nodes included in the plot. Computations are then applied to these values to produce contours, nodal probe results, display groups or color coding based on results, or X–Y data along a path.

For results saved to the output database at the integration points or at the element centroid, the first computation applied is extrapolation. (Results saved at the element nodes do not require extrapolation.) For contour plots only, you can choose quilt-type extrapolation, in which case the remaining computations discussed below do not apply. To learn more about quilt-type extrapolation, see Understanding how contour values are computed. For all other methods of results display, Abaqus/CAE extrapolates results to the nodes using weighting appropriate for the element type and shape.

Extrapolated values are generally not as accurate as the values calculated at the integration points. Therefore, adequately detailed meshing is recommended around nodes where accurate nodal values of such element results are needed. You should be particularly careful interpreting output variables extrapolated to the nodes for second-order elements with midside nodes outside the quarter-point region, such as when one edge is collapsed in two dimensions or one face is collapsed in three dimensions.

Extrapolation of element tensor quantities is performed on the individual tensor components in the local material coordinate system. Nodes common to two or more elements receive extrapolated values from all contributing elements. Depending on the characteristics of your model, these contributions may originate from more than one result region. If all contributions at a node originate from a single result region, the values are combined as necessary in further computations. If contributions are received from more than one result region, you can choose to respect the region boundary and keep the contributions separate in further computations or to ignore the region boundary and combine the values. The default result regions in an output database duplicate the regions that were used to assign section properties to the model prior to analysis. Alternatively, you can select element sets or display groups to use as result regions. For more information, see Controlling computations at region boundaries.

If invariants or components are requested, you can specify whether Abaqus/CAE should use the extrapolated data from each element or the combined data from all contributing elements to compute the invariants. By default, invariants are computed before the extrapolated results are combined (averaged). Contour plots of invariants or components may be affected by the order in which Abaqus performs the computations. For example, values for the von Mises stress may exceed the yield stress of inelastic materials; in addition, the invariant results may not take into account situations where the material orientations vary within a finite element in a non-isoparametric fashion. If invariants are computed after averaging, Abaqus determines the orientations at a node by averaging the contributing element orientations; component values will be affected if the orientations differ between contributing elements.

If you select element sets to define the result regions and invariants will be computed after averaging, the element sets that you select must contain compatible elements. Compatible elements

• share the same basic element type (continuum, shell, beam, etc.),

• use interpolation functions of the same order (first-order elements versus second-order elements), and

• have the same integration scheme (reduced integration, full integration, etc.).

Finally, computations depend on whether you choose to display the field output values or discontinuities; discontinuities are the differences in field output values between adjacent elements.

• Field Output: For the display of field output values, the calculated invariants or components at nodes common to two or more elements are averaged conditionally, depending on the compatibility of contributing result regions and on options you select. For more information, see Understanding result value averaging.

• Discontinuities: For the display of discontinuities, the calculated invariants or components at nodes common to two or more elements are compared to determine the greatest difference, depending on the compatibility of contributing result regions and on options you select. Nodes associated with only one element and nodes receiving equivalent values from all contributing elements will show a value of zero in a plot of discontinuities.

For more information, see Displaying field output values or discontinuities.

Both node- and element-based results can be transformed into a user-specified coordinate system, and angular transformations can be applied to coordinate- and distance-based nodal vector results; see Transforming results into a new coordinate system, for information on applying a transformation to your results.

Element-based results for three-dimensional continuum elements and all node-based results are transformed into the specified coordinate system based on the locations of the results. The 1-, 2-, and 3-directions for the transformed results correspond to the X-, Y-, and Z-directions of a rectangular coordinate system; the R-, $\theta$-, and Z-directions of a cylindrical coordinate system; and the R-, $\theta$-, and $\varphi$-directions of a spherical coordinate system.

Element-based results for two-dimensional continuum elements, shell elements, and membrane elements are transformed by rotating the results about the element normal at the element result location. The 2-direction for the transformed results is determined by the projection of the rectangular Y-direction or the cylindrical or spherical $\theta$-direction onto the element plane. If the Y- or $\theta$-direction of the user-defined coordinate system forms an angle less than 30° with the element normal, the next axis that follows the Y- or $\theta$-axis in a cyclic permutation of the axes is projected on the element plane instead to form the local material 2-direction, and a warning message is displayed. This method of results transformation is different from the method used by Abaqus/Standard and Abaqus/Explicit to compute local orientations (see Orientations).

Element-based results for beam and truss elements cannot be transformed; they are always displayed in the local element orientation system. In addition, element results for rebar and for CAXA, SAX, or SAXA elements are not transformed.

When you transform results to a user-specified coordinate system, you can control the following additional aspects of the coordinate system transformation:

• You can include or exclude the effects of the current deformation in the transformation calculations. Deformation effects are not scaled; Abaqus/CAE performs these calculations using a deformation scale factor of 1.0. Including deformation effects in a transformation can change the orientation of node-based coordinate systems, the projection of coordinate systems on shell and membrane elements, and the orientation of location-dependent cylindrical and location-dependent spherical coordinate systems.

• You can adjust the results to account for the rigid body transformation of the coordinate system. You can adjust the display of primary variable results or results from both the primary and deformed variables.

  Rigid body transformation helps you to understand relative displacements when large rigid body displacements are present. Rigid body transformation applies a transformation to the model to negate the displacement and rotation of a user-specified coordinate system that follows nodes (see Creating coordinate systems during postprocessing, for more information) as these nodes deform from frame to frame. The rigid body transformation is determined as the translation and rotation necessary to transform the nodes of the specified coordinate system from their current locations back to their original locations.

You can apply angular transformations for coordinate- and distance-based nodal vector results. The angular transformation computes components in terms of R, $\theta$, and Z for cylindrical coordinate systems and in terms of R, $\theta$, and $\varphi$ for spherical coordinate systems.

You can apply layup orientation transformations for results that include output from the field output variable SORIENT and include composite sections. This transformation computes tensor and vector fields using the orientation of elements on each individual ply rather than using a single orientation for the entire composite layup.