Bistable Buckled Beam-Like Structures by One-Dimensional Hierarchical Modeling

Abstract

In the last few years, great interest has been shown in harnessing bistability, or more generally multistability, as a source of energy and motion in engineering applications, both at micro-scale (such as switches, relays, valves or pumps) and macro-scale (shape-changing aerodynamic panels, variable geometry engine exhausts and reconfigurable airplane wings). Bistability is a highly non-linear phenomenon relying on the snap-through buckling, an elastic instability in which a structure passes from one equilibrium configuration to another nonadjacent equilibrium state by means of a sudden displacement jump. The theoretical understanding of such phenomenon plays a key role in the structural design optimization for practical applications. To this aim, the development of accurate yet efficient computational models for the analysis of bistable composite structures represents an important and up-to-date research topic. This chapter addresses the development of a hierarchical framework based on the Carrera Unified Formulation that allows the derivation of several kinematic models by arbitrarily setting the polynomial order approximation of the displacement field. The proposed approach is assessed towards reference and commercial software finite elements solutions for the analysis of bistable buckled beam-like structures, showing the capability of accurately yet efficiently predicting stable configurations, snap-through load, force-displacement curves and stress evolution in the geometrically non-linear regime.