Asymptotic analysis of sponge spicules’ sensitivity to geometric imperfection regarding to buckling instability.

Keyword: asymptotic analysis, marine sponge Tethya aurantia, (tapered) spicule, geometric imperfection, buckling, post-buckling

• Abstract
• Introduction
  • Why studying biological structure is important? Investigation of biological structure will give inspiration to mechanical design.
  • The importance of buckling resistance of imperfection sensitivity in engineering and structural design.
  • Background introduction of Tethya aurantia and strongyloxea (Sxa) spicules.
  • Propose our hypothesis that Clausen profile is less sensitive to geometric imperfection than the other two profiles we are considering in this paper. This justifies the deviation of the actual Sxas from the Clausen profile and the imperfection of the Sxas.
  • The paragraph organization of the following sections.
• Review that the spicules resemble Clausen column which has optimal shape against buckling
  • Introduce the boundary value problem under assumption of EB beam theory, buckling load
  • Introduce the Clausen profile and other profiles such as constant and ellipse cross-section
  • Clausen profile describes the Sxas’ tapers the best out of the different profiles that we considered (citing Scientific Report paper)
  • Show the pics of all kinds of imperfection of Sxas.
• Numerical experiments. (need to get more details from Max)
  • Justification of the assumptions for the perturbations: no volume constraint, in L2 space.
  • explain the algorithm (Rayleigh–Ritz method, step function perturbation)
  • show the numerical cloud
• Theoretical estimation of the lower bound of the numerical clouds.
  • Perturbation expansions (Kellar’s technique)
  • Derive expression of first order perturbation of the eigenvalue using Sturm–Liouville theory
  • Derive the eigenvalue change for the worse perturbation
  • Calculate the slope of lower bound line for different shape of columns
  • Comparison between the numerical cloud and the theoretical curve
• Discussion and conclusion
  • Some insights on the worst perturbations, e.g. bad perturbation typically takes off volume from the original column, etc.
  • Our hypothesis that Clausen column has optimal buckling strength, also is least sensitive to geometric imperfection among the shapes we are considering is true.
  • limitation of this work: This is an asymptotic analysis which only valid for imperfection of small norm. The imperfection is limited to be axisymmetric. We are not able to get the formula of the profile which is least sensitive to imperfection.
  • Future work: try to make this work better or explore other properties of Sxas.