An Exploration of Buckling Modes and Deflection of a Fixed-Guided Beam

This paper explored the deflection and buckling of fixed-guided beams. It uses an analytical model for predicting the reaction forces, moments, and buckling modes of a fixed-guided beam undergoing large deflections. One of the strengths of the model is its ability to accurately predict buckling behavior and the buckled beam shape. The model for the bending behavior of the beam is found using elliptic integrals. A model for the axial deflection of the buckling beam is also developed based on the equations for stress and strain and the buckling profile of the beam calculated with the elliptic integral solution. These two models are combined to predict the performance of a beam undergoing large deflections including higher order buckling modes. The force vs. displacement predictions of the model are compared to the experimental force vs. deflection data of a bistable mechanism and a thermomechanical in-plane microactuator (TIM). The combined models show good agreement with the force vs. deflection data for each device. The paper’s main contributions include the addition of the axial buckling model to existing beam bending models, the exploration of the deflection domain of a fixed-guided beam, and the demonstration that nonlinear finite element models may incorrectly predict a beam’s buckling mode unless unrealistic constraints are placed on the beam.