DISCRETE TIMOSHENKO BEAM MODEL FOR MODELING BEAMS WITH NON-UNIFORM CROSS-SECTIONAL AREA, CURVATURE, AND LARGE DEFLECTION

The Timoshenko beam theory is widely used in various fields due to its ability to accurately model the behavior of beams with specific characteristics. However, when it comes to analyzing large deflection beams, the Timoshenko beam theory becomes less precise. This paper introduces a proposed discrete Timoshenko beam model to predict the mechanical behavior of slender beams subjected to large deflections under various loadings. A mathematical analysis was developed and validated using finite element analysis in conjunction with a compliant mechanism. The modeling results demonstrate that the force-displacement behavior of a bistable mechanism can be accurately captured by the discrete Timoshenko beam model. In particular, when comparing the discrete Timoshenko beam model and finite element analysis, the maximum and minimum forces exhibited a strong agreement, with a percentage difference of less than 3% and 5%, respectively. In terms of the total elastic strain energy and maximum principal stress, the deviations between the discrete Timoshenko beam model and finite element analysis were approximately 2% and 7%, respectively. The proposed model can be integrated into an optimization algorithm for designing compliant mechanisms.