Analysis of Planar Bistable and Snap-through Arches for Contact and Dynamic Loads

Abstract

We present the concept of using an array of dynamically snapping arches as a self-offloading diabetic footwear mechanism. To develop such a mechanism, we study the nonlinear behavior of the pinned-pinned and fixed-fixed shallow arches for contact and dynamic loads, respectively. First, we analyze the contact interaction of a pinned-pinned arch with a rigid flat edge by posing it as an energy minimization problem. The point contact, line contact, and bifurcation of the line contact into two point contacts are considered as three cases in the contact analysis. In each case, we calculate the critical force required during transition from one type of contact to another. Second, the snap-through dynamic buckling of a fixed-fixed arch is analyzed and a closed-form solution for dynamic critical buckling load is found for two special cases. These results are compared with those from the finite element simulations.