Novel Model with Three Curvature Variables for Euler Beam under Large Deflection and Its Application in Planar Compliant Mechanisms

doi:10.3901/JME.2021.13.144

Abstract

Abstract: A novel model with three curvature variables for Euler beam under large deflection is proposed based on the quadratic Bernstein polynomials. The three curvature variables are considered as generalized coordinates for bending equilibrium configuration of the beam. Then, the rotation equation and the deflection curve equation in integral form are formulated using the curve theory of differential geometry. By the virtual work principle, the nonlinear geometric equilibrium equation of Euler beam is derived in which three curvature parameters are unknown variables. At the same time the numerical formulation of the equilibrium equation is shown using Gaussian quadrature and Newton-Raphson iteration method. Finally, through the typical numerical examples of straight and curved cantilever beams and the partially compliant crank rocker mechanism, the curvature model proposed above is fully proved to have high accuracy, high calculation efficiency, general applicability to curved beams and intuitive and rich expressions for deformation measurements. The calculation and analysis results show the obvious advantages and application prospects of the proposed method in the design and analysis of compliant mechanisms.

Key words: Euler beam, large deflection, curvature, parametric model, planar compliant mechanisms

CLC Number:

TH112

XIE Dan, HUANG Yonggang. Novel Model with Three Curvature Variables for Euler Beam under Large Deflection and Its Application in Planar Compliant Mechanisms[J]. Journal of Mechanical Engineering, 2021, 57(13): 144-152.

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