Open access: An objective isogeometric mixed finite element formulation for nonlinear elastodynamic beams with incompatible warping strains

We have released the open access publication, "An objective isogeometric mixed finite element formulation for nonlinear elastodynamic beams with incompatible warping strains", which is part of the journal "Multibody System Dynamics" by Springer Nature.

The article is written by: M.-J. Choi, S. Klinkel, S. Klarmann and R. A. Sauer.

Abstract:
We present a stable mixed isogeometric finite element formulation for geometrically andmaterially nonlinear beams in transient elastodynamics, where a Cosserat beam formulationwith extensible directors is used. The extensible directors yield a linear configuration spaceincorporating constant in-plane cross-sectional strains. Higher-order (incompatible) strainsare introduced to correct stiffness, whose additional degrees of freedom are eliminated byan element-wise condensation. Further, the present discretization of the initial director fieldleads to the objectivity of approximated strain measures, regardless of the degree of basisfunctions. For physical stress resultants and strains, we employ a global patch-wise ap-proximation using B-spline basis functions, whose higher-order continuity enables usingmuch fewer degrees of freedom than an element-wise approximation. For time-stepping, weemploy implicit energy–momentum consistent scheme, which exhibits superior numericalstability in comparison to standard trapezoidal and mid-point rules. Several numerical ex-amples are presented to verify the present method.

You get full access here:

https://link.springer.com/article/10.1007/s11044-024-10037-x