Theoretical Analysis on Nonlinear Buckling, Post-Buckling of Slender Beams and Bi-Stable Mechanisms

Abstract Compliant mechanisms (CMs) are used to transfer motion, force, and energy, taking advantages of the elastic deformation involved compliant members. A branch special type phenomenon called (post) buckling has been widely considered in CMs: avoiding for better payload-bearing capacity utilizing post-buckling produce multi-stable states. This paper digs into essence beam’s behaviors where we start from famous Euler–Bernoulli beam theory then extend mentioned linear geometrically nonlinear one handle multi-mode problems via introducing concept bifurcation theory. Five representative cases studied this paper, followed by detailed theoretical investigations their multi-state property proved. We finally propose a novel bi-stable termed as pre-buckled (PBMs) that integrate features both rigid mechanisms. The insights PBMs presented detail. To best our knowledge, is first study on derivation kinematic models PBMs, which could be an important contribution field.