2026 Hesch Space Time Exact Beams

This study formulates the dynamics of a straight-reference geometrically exact Cosserat beam as a directed world sheet in non-relativistic space–time. The central aim is to integrate spatial force and moment resultants with temporal linear and intrinsic angular momenta into common space–time fluxes, represented through a co-normal boundary operator. A mixed configuration–momentum system was discretized using continuous tensor-product finite elements and stabilized by implementing a future-directed Petrov–Galerkin perturbation. The findings indicate that the developed time-aligned Q2/Q2 method, which retains the interior momentum trace as free terminal outflow, successfully verifies terminal flux treatment against an exact rigid-motion state. Furthermore, it establishes monotone convergence for a uniform manufactured shear–bending solution and elucidates the pre-response–accuracy trade-off under delayed loading. Despite the stabilization not confirming strict domain-of-dependence causality, it does favor global space–time approximation in the future direction. In addition, the study highlights the challenges of consistently applying higher order P2/P2 simplex spaces. The comparative analysis with an over-resolved implicit-midpoint time-marching technique emphasizes that the recommended aligned Q2/Q2 discretization provides a practical realization of the proposed formulation.