Quantifying the strength of stability of multi-stable structures: A new design perspective

Abstract

In recent years the use of multi-stable components for designing adaptive structures and energy harvesting systems has been broadly investigated. Most of these studies have concentrated on analyzing the equilibrium shapes and the snap-through loads of the bi/multi-stable elements. However, there is minimal work on quantifying the strength of these stable equilibrium shapes. The strength of stable states is a measure of the ease or difficulty of the transition between the different stable states of any multi-stable system. Quantifying the strength of stability becomes paramount while designing adaptive structures which integrate multi-stable elements. Previous studies have argued that snap-through loads represent the goodness of stability; however, the magnitude of the snapthrough load highly depends on the boundary conditions of the structure and the loads’ application point. This work presents a mathematical framework that quantifies the strength of stability of the stable equilibrium shapes of multi-stable elements and identifies the minimum energy path (MEP) between two stable states. The method is based on finding, either with an analytical approach or finite element (FE) models, the stable and transition points of the energy landscape. Results prove that the method provides a quantitative measure of stability, a key parameter when designing adaptive structures. In addition, the minimum energy path between two stable states provides a tool to simplify the design of efficient actuation strategies for multi-stable systems. Four numerical examples are detailed to demonstrate the robustness of the approach.