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

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.