Area and volume elements normally compute results most accurately at the integration points. The location of these data, which includes structural stresses, elastic and thermal strains, field gradients, and fluxes, can then be moved to nodal or centroidal locations for further study. This is done with extrapolation or interpolation, based on the element shape functions or simplified shape functions given in Table 12.12: Assumed Data Variation of Stresses.
Table 12.12: Assumed Data Variation of Stresses
| Geometry | No. Integration Points | Assumed Data Variation |
|---|---|---|
| Triangles | 3 | a + bs + ct |
| Quadrilaterals | 4 | a + bs + ct + dst |
| Tetrahedra | 4 | a + bs + ct + dr |
| Hexahedra | 8 | a + bs + ct + dr + est + ftr + gsr + hstr |
where:
a, b, c, d, e, f, g, h = coefficients s, t, r = element natural coordinates
The extrapolation is done or the integration point results are simply moved to the nodes, based on the user's request (input on the ERESX command). If material nonlinearities exist in an element, the least squares fit can cause inaccuracies in the extrapolated nodal data or interpolated centroidal data. These inaccuracies are normally minor for plasticity, creep, or swelling, but are more pronounced in elements where an integration point may change status.
Adjustments and special cases exist, as follows:
SOLID90 uses only the eight corner integration points.
Uniform stress cases, like a constant stress triangle, do not require the above processing.