Bi-stable Concepts for Reconfigurable Structures

This study is concerned with novel bi-stable structures, which are proposed for enabling reconfigurable structures with multiple, load-free equilibrium states. The first structure is a discrete member bi-stable module and is deformable in shear. The degree of shape change is predicted by a compatibility analysis. The stiness of the module in either state is confirmed by a modified version of Maxwell’s Rule for planar frameworks. The stiness and degree of stability of larger grid-like structures formed by interconnecting modules is also considered. The second structure is a shallow, continuous dome pressed into a thin sheet, which can be inverted by snapping through the sheet. Multiply stable shells are formed by stamping many domes in an ordered array into the complete sheet. It is shown that residual stresses are responsible for the novel, large and stable deformations, and a finite element analysis is performed to investigate the eects of the forming process upon the inversion behaviour of a single dome. I. Introduction In this paper, novel bi-stable structures are proposed for developing reconfigurable structures. The latter may be defined as a class of structures whose topology and/or shape can be altered appreciably and fixated, in order to increase their functionality and/or to enhance their performance capabilities. Deployable spacecraft structures (Pellegrino 1 ), for example, embrace both principles: their mechanistic properties permit them to be folded for stowage during transportation and to be unfolded in the first stages of deployment; they are then made sti at the end of deployment for structural integrity during operation. An alternative solution uses structures that have multiple but stable, i.e. positively sti, equilibrium states. The transition between states during reconfiguration must be enabled by higher than normal loads either applied externally or reacted internally by integrated actuators. Hence, the simplest reconfigurable structure exhibits bi-stability, and this paper introduces the behaviour of two, rather dierent concepts, which may be assembled or formed together into larger, multiply stable structures. The first concept is a pin-jointed structure although here, simple models are made from cardboard strips with frictional hinges. It has a large-displacement shearing mode and “snaps” elastically into one of two stable, free-standing configurations, as predicted by an elementary compatibility analysis. The well-known Maxwell criterion is modified to give the determinacy of the structure, and is confirmed by a mobility analysis. The method can be applied to modular grids formed by interconnecting structures to elucidate possible modes of deformation. Depending on the tessellation of structures, local, as well as global modes are possible, and simpler bi-stable structures can be found within the general layout. The second concept is a continuous, shallow axi-symmetric dome that has been pressed into hardened, flat metal sheet. The dome can be made to invert and revert by “popping” it through the sheet in either direction. The area surrounding the dome no longer remains flat by virtue of its interaction with the dome at its rim. When an array of closely-spaced domes is formed over the entire sheet, individual domes can be pushed through singly, or in localised rows and columns, and their interaction with each other creates multiple, global distortions. When all domes are in the same sense, in either direction, the sheet can adopt one of several cylindrical forms. It is shown that residual stresses are largely responsible, and is verified by novel experiments; a finite element analysis of the dome formation is then detailed.