Stability Bounds and Optimal Shape of Elastic Rods

摘要

In these Lecture notes we treat two problems of determining stability boundary for elastic rods (columns) and two optimization problems in which we determine the shape of the lightest rod, stable against buckling. In the problems of determining stability boundary we shall use generalized rod equations (corresponding to planar and spatial deformations) mat take into account both shear deformation and axis extension and examine the influence of these effects on the stability boundary.