Modeling and Stress Analysis of a Pre-Shaped Curved Beam: Influence of High Modes of Buckling

In this paper, we investigate the effect of high modes of buckling on the mechanical behavior of a pre-shaped curved beam. In a first stage, the presented modeling develops further the snapping forces solution and bistability conditions in order to include high modes of buckling. In a second stage, we develop the analytical solution of the stresses inside the beam during deflection between the two sides of buckling. The buckling with or without mechanical conditions on antisymmetric modes, the force characteristics, bistability conditions and stresses are described in this paper based on mathematical approach in order to provide a clear physical understanding of the curved beam behavior and its design parameters. The accurate knowledge of the design parameters is important in order to achieve the best integration of the curved beam in a complete microstructure. The analytical results are compared with and without considering high modes of buckling and have shown to be in excellent agreement with FEM simulations. The results show the importance of the high modes in calculating stresses and snapping forces.