A Synthesis Module for Designing Shallow Bistable Arches using COMSOL®
COMSOL®, like other finite element analysis software, enables analysis of an object of given geometry, material properties, boundary conditions, and loading. In this paper, we present a synthesis module for a class of structures called shallow bistable arches. Bistable arches have two force-free stable equilibrium states. They deform nonlinearly to switch between their as-fabricated stress-free and toggled stressed states. There exists a correspondence between the arch-profiles of these two states. In our past work, we have derived analytical bilateral relationships between the two stable arch-profiles for pinned-pinned and fixed-fixed shallow bistable arches. A shallow arch is one whose height is much smaller than the span. The shallow arch assumption was necessary to derive the analytical bilateral relationships that help obtain one stable arch-profile from another.
Obtaining the toggled arch-profile from the as-fabricated profile is analysis and it can be done using the nonlinear structural mechanics module of COMSOL®. However, when one wants to design or synthesize a bistable arch for applications such as circuit breakers, switches, valves, snap-connectors, etc., certain profile of the stressed toggled state may be of interest. Repetitive analysis of user-conceived arches using COMSOL®’s nonlinear mechanics module is one way but it depends on user’s intuition. It is also time-consuming and it does not guarantee the result, especially when there are requirements on the shape of the arch profile along with the travel of a certain point between the two stable states as well as switching and switch-back forces. To address such a need, we present a synthesis module in COMSOL using aforementioned bilateral relationships.
Our module works as follows. A designer specifies a set of points in the module to prescribe the required toggled arch-profile. The given points are fitted to a curve and an arch-profile is displayed. Then, using analytical relationships, the as-fabricated profile of the arch is obtained. Using cross-section parameters, 2D or 3D models of the as-fabricated arch is automatically created. In the next step, we analyze the obtained geometry using COMSOL nonlinear mechanics module. Arch-profiles of the specified toggled stable state and the one obtained from COMSOL are juxtaposed for comparison by the user. The user can evaluate switching and switch-back forces and choose the location of actuation. There exist multiple pathways between the two states depending on the actuation point and direction of the force. Furthermore, the module recognizes the user-specifications that are not realizable as bistable arches. The utility of the module is illustrated through examples for the design of a wide range of bistable arches with pinned-pinned and fixed-fixed boundary conditions, for an on-off valve, a micro-machined switch, and a miniature circuit breaker.
Keywords: Synthesis, nonlinear structural mechanics, valve, switch, circuit breaker