Design of a transversely layered rod of minimum weight with stability constraint

We consider a problem of synthesis of a transversely layered, axially compressed straight rod of minimum weight from a finite set of elastic homogeneous materials with specified constraint imposed on the critical buckling load. To describe the bending of the rod, we use the classical theory of beams based on the hypothesis of plane cross sections. The necessary optimality conditions are obtained, a computational algorithm is developed, and an example of calculation of the optimal rod is given.