Space-time method models moving curved beams with shear effects
A space-time finite element formulation for geometrically exact shear-deformable beams
Computational Engineering, Finance, and Science
Summary
Modeling how beams bend, twist, and move over time is important for many engineering problems. The authors developed a new approach that treats space and time together as one unified problem, allowing more accurate simulation of beams that can bend, shear, and even move along their length. Their method can handle complicated shapes, joints, and changing boundaries directly in the math. Tests showed their approach matches established methods but offers new flexibility and stability. They also demonstrated it on a problem involving a beam sliding like spaghetti, showing it works for moving structures.
What this means in practice
- •For structural engineers: Analyze complex curved beam structures that undergo bending, twisting, and axial movement with shear effects included, improving transient response predictions.
- •For mechanical simulation developers: Implement stable space-time finite element methods that handle moving geometries and non-material boundaries explicitly for advanced beam simulations.
Authors
Ivo Steinbrecher, Alexander Humer
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.