Validity Limits

Equivalent-stiffness homogenization is a scale-separated approximation. It is most appropriate when stiffener height and pitch are small relative to curvature and response length scales:

\[ \frac{h_s}{R_\text{min}} \ll 1, \qquad \frac{p}{R_\text{min}} \ll 1, \qquad \frac{p}{L_\text{response}} \ll 1. \]

Tensyl's default warning thresholds are:

\[ \frac{h_s}{R_\text{min}}\ge 0.05, \qquad \frac{p}{R_\text{min}}\ge 0.05, \qquad \frac{p}{L_\text{response}}\ge 0.05. \]

Tensyl also reports a membrane-bending coupling ratio:

\[ \frac{\|\mathbf B\|_F} {\sqrt{\|\mathbf A\|_F\|\mathbf D\|_F}}. \]

The default warning threshold is 0.10. Read this ratio as: how much of the stiffness's behavior is membrane-bending cross-talk, relative to the membrane and bending stiffness it sits between. A large value means strain and curvature are strongly coupled — usually a sign of eccentric stiffeners or an offset reference surface, and a hint that a scalar "equivalent modulus" would throw away something real.

Interpreting Warnings

Warnings are not pass/fail certification criteria. They are prompts for engineering review. A warning means the ABD stiffness should not be used blindly for the intended response without checking assumptions, comparing against a detailed model, or changing the model family.

So a warning fired — now what? In practice:

  • re-read the assumptions and confirm the geometry actually matches a scale-separated model (is pitch really small next to your response length?);
  • compare the homogenized result against a detailed finite-element model of the same geometry and loading before trusting it downstream;
  • or change the model family entirely if the separation of scales simply does not hold.

None of these steps is optional. They are how you find out whether the approximation actually holds for your geometry. This is the boundary drawn in "What Tensyl Is Not".

Out of Scope for the First Model Family

The current tangent-plane family does not model:

  • local skin buckling between stiffeners;
  • stiffener crippling;
  • joints, welds, fasteners, or bondlines;
  • stiffener intersection stress concentrations;
  • local load introduction;
  • geometric imperfections;
  • nonlinear material response;
  • nonlinear postbuckling;
  • response modes with wavelength comparable to stiffener pitch.