A new director-based finite element formulation for geometrically exact beams is proposed by weak enforcement of the orthonormality constraints of the directors. In addition to an improved numerical performance, this formulation enables the development of two more beam theories by adding further constraints. Thus, the paper presents a complete intrinsic spatial nonlinear theory of three kinematically different beams which can undergo large displacements and which can have precurved reference configurations. Moreover, the hyperelastic constitutive laws allow for elastic finite strain material behavior of the beams. Furthermore, the numerical discretization using concepts of isogeometric analysis is highlighted in all clarity. Finally, all presented models are numerically validated using exclusive analytical solutions, existing finite element formulations, and a complex dynamical real-world example.

No abstract

Based on more than three decades of rod finite element theory, this publication combines the successful contributions found in the literature and eradicates the arising drawbacks like loss of objectivity, locking, path‐dependence and redundant coordinates. Specifically, the idea of interpolating the nodal orientations using relative rotation vectors, proposed by Crisfield and Jelenić in 1999, is extended to the interpolation of nodal Euclidean transformation matrices with the aid of relative twists; a strategy that arises from the SEfalse(3false)$$ SE(3) $$‐structure of the Cosserat rod kinematics. Applying a Petrov–Galerkin projection method, we propose a rod finite element formulation where the virtual displacements and rotations as well as the translational and angular velocities are interpolated instead of using the consistent variations and time‐derivatives of the introduced interpolation formula. Properties such as the intrinsic absence of locking, preservation of objectivity after discretization and parameterization in terms of a minimal number of nodal unknowns are demonstrated by representative numerical examples in both statics and dynamics.

No abstract

A 2D-continuum model describing finite deformations in plane of discrete bi-pantographic fabrics has been recently obtained by applying an asymptotic procedure based on a set of local generalized coordinates. Rectangular bi-pantographic prototypes were additively manufactured by selective laser sintering using polyamide as raw material. Displacement-controlled bias extension tests were performed on such specimens for total elastic deformations up to ca. 25%. Experimental force measurements, complemented by discrete displacement measurements obtained by local digital image correlation, were used to fit the continuum model. In the present paper, a global and minimal set of generalized coordinates, alternative to the one used for the homogenization, is introduced for the discrete model. The mechanical constitutive parameters appearing in the discrete model are then found by means of collected experimental data. Finally, a comparison between experiments, the discrete and the continuum model is presented. It is concluded that (a) the discrete model and the experimental data are in excellent agreement, and that (b) the continuum retains the relevant phenomenology of the discrete system even for a rather low number of cells.