Optimal shape of a twisted and compressed rod

We formulate and solve the problem of determining the shape of an elastic r od stable against buckling and having minimal volume. The rod is loaded by a concentrated force and a couple at its ends. The equilibrium equations ar e reduced to a single nonlinear second-order equation. The eigenvalues of t he linearized version of this equation determine the stability boundary. By using Pontryagin's maximum principle we determine the optimal shape of the rod. (C) 2001 Editions scientifiques et medicales Elsevier SAS.