The influence of interpolation errors on finite-element calculations involving stress-curvature proportionalities

The presence of non-linear axial gradients of pressure/temperature in a finite-element model can invoke an often overlooked proportionality between the resulting curvature and bending stresses. Because these stresses can be significant, the use of polynomials and cubic-splines to interpolate any gradients to a finite-element mesh must be carefully weighed against their tendency to undulate through the data. As shown for a test case involving an interpolated pressure-distribution with artificially induced errors, the resulting polynomial oscillation can indeed induce significant variations of both sign and magnitude in the finite-element calculations. In contrast, a constrained B-spline with smoothing provided more reasonable stress predictions.