Nonlinear closed-form model for beam flexures subject to large axial loads

Abstract

Closed-form models are important because they offer more design insights, require less computing time and prevent convergence problems in modeling compliant mechanisms. However, most of the available closed-form models, e.g., beam constraint models, are only appropriate for beam flexures within the intermediate deflection range. In this paper, a method for developing closed-form models based on the chained beam constraint model through the combined use of strain energy and Castigliano's first theorem is proposed. A closed-form model for beam flexures with a large prediction range is derived using this method. By modeling simple beams and compliant mechanisms using the proposed closed-form model, it is shown that the model has a significantly broader prediction range than the beam constraint model and is more efficient than the chained beam constraint model. The large prediction range and high efficiency of the proposed closed-form model make it potentially useful for optimizing compliant mechanisms.