An improved geometrically exact planar beam finite element for curved steel and steel-concrete composite beams

This paper presents an extension of the computationally efficient geometrically exact 2D Euler-Bernoulli beam finite element proposed in [1], which can account for steel plasticity and concrete cracking/crushing. The novel aspects are: (i) the formulation is consistently extended to beams with arbitrary initial curvature, (ii) an efficient procedure to obtain the beam initial configuration is proposed, (iii) slope compatibility between elements (i.e., at nodes) is enforced through a single non-linear constraint equation and a similar approach is employed to enforce fixed rotation boundary conditions, and (iv) a strategy to avoid mesh-dependent problems due to concrete softening is included. As in the previous formulation, the element is quite easy to implement and, due to the Euler-Bernoulli constraint, only requires uniaxial material laws. Several numerical examples are presented to demonstrate the capabilities of the proposed finite element.