Nonlinear Complementary Strain Energy Formulation for Planar Beam Flexures Undergoing Intermediate Deflection

Abstract

The previously presented beam constraint model (BCM) successfully captures pertinent nonlinearities to predict the constraint characteristics of beam flexures. This has been followed by multiple attempts to construct a more comprehensive framework comprising strain energy (SE) principles and complementary strain energy (CSE) principles. However, comprehensive results are still lacking in the current literature, especially in the validation of the CSE definition, fundamental relations between beam coefficients, further relationships between the SE and the CSE, and suitable examples. This article addresses all these gaps. The nonlinear CSE is derived using the principle of complementary virtual work for a planar beam undergoing intermediate deflections. This result is shown to be consistent with the load—displacement relations and the nonlinear strain energy formulation in the BCM. Furthermore, the current article also demonstrates for the first time that the SE and the CSE are interrelated through the gap energy, which is derived and formulated in terms of tip loads. Finally, this CSE expression is employed in the analysis of a fixed-guided mechanism. All results are validated to a high degree of accuracy via nonlinear finite element analysis.