A Finite Difference Scheme for the Large-Deflection Analysis of Non-Prismatic Cantilever Beams - Shahriar, Adnan; Khodadadi, Hamid; Majlesi, Arsalan; Montoya, Arturo (Discontinuity, Nonlinearity, and Complexity, 2026)
The analysis of a cantilever beam at any level is a mature subject, and there are a lot of elegant numerical techniques to perform large deflection analysis of non-prismatic cantilever beams. This work aims to develop a straightforward and computationally efficient method to solve large deflection problems of non-prismatic cantilever beams subjected to transverse loading. The modeled beams are assumed to be naturally straight, slender, inextensible, and follow a linear elastic material behavior. The governing differential equation obtained from Euler--Bernoulli beam theory, where the exact curvature expression is preserved, has been discretized using the first-order forward finite difference method. When the deflection is very high, the discretized equation results in a system of highly non-linear equations, and an iterative solution method must be used to solve the problem. This paper employs the bisection method to satisfy the fixed-end boundary condition, which consists of enforcing a slope angle of zero. The method is illustrated through a numerical example of a cantilever beam with a rectangular cross-section subjected to both concentrated and distributed loads. The results provided by this method were shown to be in excellent agreement with the results from alternative numerical methods found in the literature, which verifies the validity of the proposed method.