  The paper presents a two-dimensional geometrically nonlinear formulation of a
beam element that can accommodate arbitrarily large rotations of cross
sections. The formulation is based on the integrated form of equilibrium
equations, which are combined with the kinematic equations and generalized
material equations, leading to a set of three first-order differential
equations. These equations are then discretized by finite differences and the
boundary value problem is converted into an initial value problem using a
technique inspired by the shooting method. Accuracy of the numerical
approximation is conveniently increased by refining the integration scheme on
the element level while the number of global degrees of freedom is kept
constant, which leads to high computational efficiency. The element has been
implemented into an open-source finite element code. Numerical examples show a
favorable comparison with standard beam elements formulated in the
finite-strain framework and with analytical solutions.
