Compliant structure under follower forces and any combined loading: Theoretical and experimental studies.

Highlights • A robust numerical approach has been proposed to solve for follower forces in compliant mechanisms. • Linear and nonlinear finite element methods have been adopted to solve for large deflection with complicated geometries and forces. • Experiments have been performed for beams with follower forces and are validated with the simulated results based on the proposed model. • The efficacy of the presented algorithms in the design of compliant structures is shown through a wing morphing example. Graphical abstract Abstract A linear finite element and a nonlinear finite element solution scheme have been proposed to obtain the deflection of a compliant structure, modeled as a cantilever beam, under the action of a follower force acting at the end, in addition to any additional arbitrary loading. The developed techniques have been compared with a numerical technique available in literature, wherein, nonlinear Euler–Bernoulli beam theory is used in an iterative scheme. It was found that the results of the nonlinear finite element algorithm exactly match the solution from the available scheme; while on the other hand, the linear finite element gives fairly close results at a higher rate of convergence. Experiments are carried out to validate the two proposed solution techniques. Two example problems have been solved, which show the practical application of this numerical scheme, in the design of mechanisms actuated by smart materials like shape memory alloys (SMA) and macro fiber composites (MFC), in the process, obviating the limitations of the available techniques in solving such problems. [ABSTRACT FROM AUTHOR]