Fragile points method for Euler–Bernoulli beams

Abstract

In this paper, the recently introduced Fragile Points Method (FPM) is extended to study the static bending, free vibration, and mechanical buckling of isotropic and homogeneous case as well as functionally graded Euler–Bernoulli beams. The beam kinematics is based on the Euler–Bernoulli theory that assumes plane sections remain plane and perpendicular to the neutral axis of the deformed beam. The salient feature of the FPM is that it is a truly meshless method that employs simple local point-based polynomial test and trial functions. The key distinction is that the polynomial test and trial functions are discontinuous and constructed using radial basis functions, in contrast to the conventional Galerkin framework. Further, as the trial and test functions are discontinuous, the continuity requirement imposed by the continuous Galerkin framework is circumvented. The discontinuous trial and test functions lead to inconsistency; to alleviate this, we employ numerical flux corrections inspired by the discontinuous Galerkin method. The efficiency and robustness of the approach are tested with a few standard benchmark examples.