Effect of Boundary Conditions on the Stability of a Viscoelastic Von Mises Truss

This research aims to analyze the stability of bistable dome-shaped structures represented as a lumped parameter viscoelastic von Mises truss under different boundary conditions. Traditionally, the stability of these lumped parameter systems has been studied under pin-pinned boundary conditions. However, a closer investigation of the deformation of the dome reveals that the contact between the dome and the surface is not fixed. Instead, it slides outwards as the dome is indented. This phenomenon raises the question of whether the stability will alter if the boundary conditions are altered. With this motivation, we explore two alternate boundary conditions: (1) symmetric and (2) asymmetric. We demonstrate how relaxing or constraining the contact surface leads to change in the bifurcation point. This work allows us to gain some fundamental insights in modeling and controlling the spatiotemporal behavior of engineering structures.