Problem
Research questions and friction points this paper is trying to address.
geometrically exact beams
shear-deformable beams
space-time finite element
transient analysis
non-material boundaries
A space-time finite element formulation for geometrically exact shear-deformable beams
🤖 AI Summary
This study addresses the challenges of space-time coupling and non-material boundary treatment in the transient analysis of geometrically exact shear-deformable beams by proposing a unified space-time finite element framework. Based on a mixed variational principle, the method independently introduces translational and angular velocity fields, combined with nodal rotation vector parameterization and triad-based objective interpolation. Time-varying material domains are directly represented through spatial surface geometry, enabling natural handling of non-material boundaries without modifying the underlying formulation. The convergence, objectivity, and stabilization effects of the algorithm are systematically verified. Furthermore, the framework is successfully applied to axially moving continua problems such as the sliding spaghetti problem, providing an efficient and unified modeling paradigm for complex time-varying structural dynamics.
📝 Abstract
We present a space-time finite element formulation for the transient analysis of geometrically exact shear-deformable beams. The formulation treats space and time within a unified finite element framework and employs a mixed approach in which translational and angular velocities are introduced as independent fields. The rotation field is parametrized using nodal rotation (pseudo-)vectors and a suitable objective interpolation of the triad field is employed. The resulting formulation supports generally curved beam structures, including geometric kinks and rigid joints. Furthermore, time-dependent material domains can be represented directly through the geometry of the space-time surface, enabling the treatment of non-material boundaries without modifying the underlying beam formulation. Numerical examples demonstrate convergence to solutions obtained with classical time-stepping schemes, objectivity of the formulation, and the influence of the space-time stabilization. Finally, the sliding spaghetti problem illustrates the applicability of the proposed approach to axially moving continua.
Innovation
Methods, ideas, or system contributions that make the work stand out.
space-time finite element
geometrically exact beams
mixed formulation
objective interpolation
non-material boundaries
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2023-12-22StructuresCitations: 2
