Modeling nonlinear deflections of initially curved beams with large curvatures

Understanding and modeling nonlinear deflections of compliant components are the major challenges of designing compliant mechanisms. Initially curved beams, can exhibit diverse mechanical behaviors, serving as useful alternatives to straight beams in compliant mechanisms. This paper presents a closed-form model for intermediate deflections of circular beams with normalized curvatures up to ±π/4, in which Taylor series expansion and truncation are employed. By combining this model with the chained scheme, it can capture large deflections of initially curved beams with a very small discretization number, considerably reducing the computational complexity. An experimental validation and the results comparison of the proposed model with nonlinear finite element models and the previous chained beam constrained model on three examples are provided, demonstrating its accuracy and efficiency. The model presented in this work offers a parameterized tool for designing the compliant mechanisms containing initially curved beams with large curvatures and constant sections.