Functional morphology of regular echinoid tests (Echinodermata, Echinoida): a finite element study

Abstract

Functional morphology of the calcareous test ofEchinus esculentus was investigated by parametric finite element analysis, an engineering technique developed for numerical analysis of the behaviour of complex structures responding to external forces. Finite element models of the test were generated by methods of Computer Aided Geometric Design (CAGD) to calculate the mechanical responses to different types of loading. The load cases included vertical, concentrated load at the apex, vertical, distributed load on the upper third of the test, internal pressure and tensile forces as introduced into the test by tube feet activity. The objectives were the shape of the test, the distribution of material and the alternating zones of porous and non-porous plates within the test.—Echinoid tests resist external loading without showing any specific points of failure. The thickened margins of the periproct and peristome apertures account for load-bearing capacity as well as the thickned meridional structures which carry a greater portion of stress than the thinner parts of the test. Distribution of material is not a response to concentrated loads on the apex nor to self-weight. Taken strictly, echinoid tests are not thin (or membrane) shells. Under loading, bending moments occur which influence the stress state in the entire test. The pneu hypothesis could not be confirmed. Adaptation of the test shape or of the distribution of material as a response to internal pressure does not exist. Tests of regular echinoids are especially well adapted to the mechanical activity of the ambulacral tube feet, i.e. the shape of the test, its flattening towards the substrate, the outward bulge of the ambulacra and the differential distribution of material within the test.