On the parametric large deflection study of Euler–Bernoulli cantilever beams subjected to combined tip point loading

Abstract

The problem of determining the parametric large deflection components of Euler–Bernoulli cantilever beams subjected to combined tip point loading is studied in this paper. We introduce the characteristic equation of the beam's deflection and, with employing the recently developed automatic Taylor expansion technique (ATET), present deflection solutions in terms of the loading parameters to the Euler–Bernoulli boundary value problem. The obtained ATET deflection solutions, verified by comparison with the numerical solutions, are valid for the entire beam length, and independently and efficiently adaptable for the very large loading conditions, and easily implementable for engineering analyses and syntheses. Exploiting these solutions as theoretical tools we study the beam's angular and axial deflections behavior for several tip point loading conditions. Besides the widely known beam's axial inflection points, we also recognize beam's angular inflection points for the mixed loading condition and show that the parametric solutions are intelligent in recognizing the right deflection branch for both inflection types.