Idea for a new static output result: Material utilization

[stfnp]

From the maximum permissible stresses of the materials in the bow (#64, #232) and the volumes of the layers we can compute the amount of elastic energy that the limbs could theoretically store if they were perfectly evenly stressed to their maximum permissible stress. See also Resilience (Wikipedia). On the other hand we know from the static simulation how much energy actually gets stored in the bow limbs during the draw.

Computing the ratio between actually stored energy and this theoretical limit gives us a measure of how well the materials in the bow are utilized. A bow where the stresses are evenly distributed might reach a utilization of up to 50% (limited by the stress distribution in a beam's cross section). Low utilization values on the other hand would point to a bow where significant volumes of material are not stressed as much as they could handle -> possible improvements by using less material and/or distributing stresses more evenly.

Having a single numerical measure of how good the stress distribution in the bow is would be especially nice for numerical optimization. Having an optimization algorithm adjust width and/or height of a bow limb in order to maximize material utilization could eventually become the basis for some kind of "auto-tiller" functionality.

Complications:

• If the actual stresses in the bow exceed the permissible stresses, the material utilization obviously increases since more energy is being stored. The material utilization result would be meaningless in this case. Maybe only compute it if all stresses are within their limits (Add some facility or output result for detecting material failure #64) and set it to 0% otherwise.

• Tension and Compression: Materials in VirtualBow will get a tensile and a compressive stress limit (Extend material definition with additional fields #232). Which one should be used for computing the maximum amount of energy that the material can store?

  1. Always use maximum tensile stress: Seems "unfair" if the material is used in compression and the maximum compressive stress is lower
  2. Use the maximum absolute value between tensile and compressive limit: This way the bow designs will get "punished" for using materials in tension that would be better in compression and vice versa, which is already better
  3. Don't use energies for the calculation but actually analyze the stress distribution in the bow. Compare tensile stresses to the tensile limits and compressive stresses to compressive limits.