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SUMMARY:A Geometrically Exact Spectral Method for Elastohydrodynamics of C
 osserat Rods - Mingjia Yan (University of Cambridge)
DTSTART:20250911T141500Z
DTEND:20250911T142000Z
UID:TALK233341@talks.cam.ac.uk
DESCRIPTION:Slender structures are ubiquitous in biological and engineered
  systems\, from bacterial flagella to soft robotic arms. The Cosserat rod 
 provides a mathematical framework for slender bodies that can bend\, twist
 \, stretch and shear across multiple length scales. In viscous fluid envir
 onments at low Reynolds numbers\, inertial effects become negligible\, and
  hydrodynamic forces are well approximated by Stokes friction. We demonstr
 ate that the resulting elastohydrodynamic equations of motion\, when formu
 lated using Cartan&rsquo\;s method of moving frames\, possess the structur
 e of a geometric field theory in which the configuration field takes value
 s in SE(3) \, the Lie group of rigid body motions. We present four differe
 nt representations\, namely\, vectorial\, moving frame\, Lie group\, and d
 ifferential form formalisms\, of the kinematics\, dynamics and constitutiv
 e law of the Cosserat rod. Then\, a spectral collocation method using Juli
 a is exploited to numerically integrate the coordinatised equations of mot
 ion as an Initial-Boundary-Value problem (IBVP)\, where the local coordina
 tes are specified by 2D translations and rotations. This IBVP is solved as
  a Differential-Algebraic Equations (DAEs)\, in which the boundary conditi
 ons are imposed as algebraic constraints. Finally\, we show that the simul
 ations of a clamped-free Cosserat rod exhibit the expected behaviours.&nbs
 p\;
LOCATION:External
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