Interpolation is a result calculation performed when you wish to study results at a location where no nodes exist. For example, Path results, Surface results, and some probes result objects can consist of arbitrary (that is, non-node-based) locations. To calculate a result at these types of locations, Mechanical employs an interpolation algorithm. For a given x, y, z in the object, the algorithm identifies the element that contains x, y, z. If x, y, z is not contained in any element, the algorithm produces no results.
A Newton's Method loop, with the aid of element shape functions and their derivatives, attempts to converge to the natural (element) coordinates corresponding to the global x, y, z. Using the natural coordinates, the element shape functions, and the results at the element's nodes, Mechanical computes the interpolated result value for the global x ,y, z location.
Limitations and Conditions
Interpolation primarily applies to degree of freedom results such as temperatures, displacements, and node-based element results like thermal flux, stress, and strain.
Therefore, it is recommended that you not use interpolation for results such as node-based element reactions (EHEAT/ENFO). The application allows for these calculations, but they are not good candidates for interpolation. In addition, you should not sum interpolated results of these types; such as to calculate total heat or total force.
- Convergence
There is no assurance that convergence actually occurs. If Newton fails to converge, natural coordinates of (0, 0, 0) are chosen. Currently, no warnings are issued for convergence problems.
- High Order Elements
Contours for high-order elements are displayed by decomposing element faces into low-order primitives. This decomposition introduces extra display-only nodes at the centroids of element faces. The values at these nodes are generated by interpolating the computed results and can differ from manually calculated values, especially when dealing with expressions which introduce discontinuities in the result field, such as SX/abs(SX).
- Expression-Based User Defined Results
Interpolation should be limited to simple linear combinations of results.
If the application performs an interpolation on an expression-based User Defined Result, it generates the final result based on the order of the calculations taking place. For example, given the expression SX^3, for the cube of normal stress in the X direction, at each node the application calculates SX^3 values. The interpolation occurs next for each (x,y,z) that requires a result and the application interpolates nodal values of SX^3. The critical point is that this procedure would produce different results if it first interpolated the nodal values of SX to the x,y,z values and then calculated SX^3.
Given a complex expression, such as (SEQV / SX)^3, the final interpolated results on a line or a surface could may be counter intuitive. This is why it is recommended that interpolation be limited to simple linear combinations of results.