Geometrically exact isogeometric Bernoulli–Euler beam based on the Frenet–Serret frame

A novel geometrically exact model of the spatially curved Bernoulli–Euler beam is developed. The formulation utilizes Frenet–Serret frame as reference for updating orientation a cross section. weak form consistently derived and linearized, including contributions from kinematic constraints configuration-dependent load. nonlinear terms with respect to cross-sectional coordinates are strictly considered, obtained constitutive scrutinized. main features invariance rigid-body motion, path-independence, improved accuracy strongly beams. new reduced conceived special case, by omitting rotational DOF. Although rotation-free, includes torsion axis, which allows simulations spatial beams that predominantly bent binormal. applicability isogeometric finite element verified via set standard academic benchmark examples. able accurately have well-defined frames.