Optimal shape of a twisted and compressed rod

✍ Scribed by Valentin B Glavardanov; Teodor M Atanackovic

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 127 KB
• Volume: 20
• Category: Article
• ISSN: 0997-7538
• DOI: 10.1016/s0997-7538(01)01165-2

✦ Synopsis

We formulate and solve the problem of determining the shape of an elastic rod stable against buckling and having minimal volume. The rod is loaded by a concentrated force and a couple at its ends. The equilibrium equations are reduced to a single nonlinear second-order equation. The eigenvalues of the linearized version of this equation determine the stability boundary. By using Pontryagin's maximum principle we determine the optimal shape of the rod.