A further study on the postbuckling of extensible elastic rods

Abstract

The postbuckling of extensible elastic rods is studied using non-linear geometric models. Accordingly the kinematics and equilibrium are stated. Nine different strain-stress relationships are analyzed. The classical Strength of Materials approach is compared and discussed with other eight constitutive laws stated with Lagrangian and Eulerian descriptions. The well-known Cauchy and Green methods in Continuum Mechanics are alternatively employed. Four of the approaches are worked out until an explicit solution of the secondary equilibrium path is obtained. The analysis is applicable to small strain problems. The linearized problem is presented for all the laws together with numerical results for rods with various values of the extensibility parameter. The secondary equilibrium paths are numerically evaluated to illustrate the degree of discrepancy. A speciffic example that displays unexpected unstable behavior is shown. Both critical loads and postbuckling curves are coincident when the theoretical problem of an inextensible rod is solved. It is shown that even when small strains are addressed, the extensibility in#uence gives rise to disagreement of the postbuckling response when using the different alternatives.