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

• Published in: Applied mathematical modelling Vol. 130; pp. 676 - 692
• Main Authors: Bai, Ruiyu, Li, Bo, Chen, Guimin
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.06.2024
• Subjects: Beam constraint model; Beam flexures; Castigliano's first theorem; Closed-form model; Compliant mechanisms; Beam flexures; Castigliano's first theorem; Beam constraint model; Compliant mechanisms; Closed-form model
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2024.03.018

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. •A method to develop closed-form models for beam flexures is proposed.•A closed-form model for CBCM with 3 discretized elements is obtained.•Closed-form load-displacement relations for beam flexures are obtained.•The proposed molded is demonstrated to reduce the computational time.