Stiffness of an elastic circular cylinder of finite length

An analytical solution is proposed to determine the stiffness of an elastic circular cylinder clamped at one end, while the other end undergoes any rigid-body displacement; the lateral surface is stress-free. The validity of Saint Venant's principle has been assessed by computing the solution of this problem for cylinders having different aspect ratios. On the other hand, the solution agrees with the thin layer theory when the aspect ratio becomes infinitely small. Therefore, the solution proposed fills up the gap between beam theory and thin layer theory.