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| Analysis of the Large-Deflection Mechanical Behavior of a Cantilever Beam Loaded via a Transmission Mechanism |
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Abstract To investigate the large-deflection mechanical response mechanism of elastic components under the load exerted by a transmission mechanism, this paper selects the elastic cantilever beam as the research object and conducts both theoretical analysis and verification research on large-deflection beams subjected to such loads. First, based on the equilibrium equation of curved beams and incorporating geometric nonlinearities, the governing differential equation that describes the large-deflection deformation of the elastic beam under the action of the transmission mechanism is derived and established. Subsequently, considering the strong nonlinearity of the governing differential equation and the coupling relationship between load and deformation, a numerical solution scheme integrating the shooting method with the Newton–Raphson iteration method is developed. Through iterative convergence calculations, the deflection distribution and stress state of the elastic beam are obtained. Finally, the theoretical results are compared and analyzed against finite element simulation results under various working conditions. The results demonstrate that the deflection values and stress states obtained from theoretical calculations are in excellent agreement with those from finite element simulations, thereby effectively validating the accuracy of the established mechanical model and the reliability of the numerical solution method. This model can accurately characterize the large-deflection deformation behavior of elastic beams under the influence of transmission mechanisms and provides theoretical support for structural analysis and performance prediction in engineering applications such as the design of flexible nozzles in wind tunnel test sections and railway track turnouts. It holds significant academic value and broad application prospects.
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Received: 31 October 2025
Published: 27 December 2025
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2025, Vol. 46 
