On the Shape Determination of Non-Conservative System: A Case of Column Under Follower Force

The shape of a column subject to dissipative and follower forces is determined by the response-based procedure using the space-time finite element scheme. The shape improvement process is derived from the inverse problem of the adjoint variational principle combined with the energy-ratio method. By shifting the time domain included in the functional, the shape is determined in a step-by-step procedure suggesting the possibility of an adaptive shape improvement. The case study shows that the response of improved column is remarkably calm even in unstable region for the uniform column.