Shape detemination of a cantilever column subjected to follower force.

Abstract

This paper deals with the shape determination problem of the cantilever column, i. e. Beck's column, subjected to the follower force. The objective is to maximize the critical load under constraints of volume constancy and lower limit of design variables, under the influence of internal and external damping. The governing equation of motion is transformed into a matrix system by the finite element method with the adjoint variational principle based on the Lagrange multiplier method. The shape improvement process is formulated by the gradient projection method based on the sensitivity of critical load to the design. Numerical results show that improved shape has a higher critical load than the initial shape (uniform) and makes three eigenvalues achieve a critical point simultaneously.