Abstract:

The elliptic integral method (EIM) is an efficient analytical approach for analyzing large deformations of elastic beams. However, it faces the following challenges. First, the existing EIM can only handle cases with known deformation modes. Second, the existing EIM is only applicable to Euler beams, and there is no EIM available for higher-precision Timoshenko and Reissner beams in cases where both force and moment are applied at the end. This paper proposes a general EIM for Reissner beams under arbitrary boundary conditions. On this basis, an analytical equation for determining the sign of the elliptic integral is provided. Based on the equation, we discover a class of elliptic integral piecewise points that are distinct from inflection points. More importantly, we propose an algorithm that automatically calculates the number of inflection points and other piecewise points during the nonlinear solution process, which is crucial for beams with unknown or changing deformation modes.

Key words: elastic beam, elliptic integral, deformation mode transition, equilibrium path, high-precision algorithm