  In this work, an efficient and robust isogeometric three-dimensional
solid-beam finite element is developed for large deformations and finite
rotations with merely displacements as degrees of freedom. The finite strain
theory and hyperelastic constitutive models are considered and B-Spline and
NURBS are employed for the finite element discretization. Similar to finite
elements based on Lagrange polynomials, also NURBS-based formulations are
affected by the non-physical phenomena of locking, which constrains the field
variables and negatively impacts the solution accuracy and deteriorates
convergence behavior. To avoid this problem within the context of a Solid-Beam
formulation, the Assumed Natural Strain (ANS) method is applied to alleviate
membrane and transversal shear locking and the Enhanced Assumed Strain (EAS)
method against Poisson thickness locking. Furthermore, the Mixed Integration
Point (MIP) method is employed to make the formulation more efficient and
robust. The proposed novel isogeometric solid-beam element is tested on several
single-patch and multi-patch benchmark problems, and it is validated against
classical solid finite elements and isoparametric solid-beam elements. The
results show that the proposed formulation can alleviate the locking effects
and significantly improve the performance of the isogeometric solid-beam
element. With the developed element, efficient and accurate predictions of
mechanical properties of lattice-based structured materials can be achieved.
The proposed solid-beam element inherits both the merits of solid elements e.g.
flexible boundary conditions and of the beam elements i.e. higher computational
efficiency.
