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From:
http://web.mit.edu/preis/www/research.html
Elasticity, Geometry & Statistics (EGS) Laboratory, MIT, Understanding the mechanics of thin objects
The blogger (Arnoud Lazarus) writes:
"We have developed a novel continuation method to calculate the equilibria of elastic rods under large geometrically nonlinear displacements and rotations. To describe the kinematics we exploit the synthetic power and computational efficiency of quaternions. The energetics of bending, stretching and torsion are all taken into account to derive the equilibrium equations which we solve using an asymptotic numerical continuation method. This provides access to the full set of analytical equilibrium branches (stable and unstable), a.k.a bifurcation diagrams. This is in contrast with the individual solution points attained by classical energy minimization or predictor-corrector techniques. "
Publications:
A. Lazarus, J.T. Miller and P.M. Reis "Continuation of equilibria and stability of slender elastic rods using an asymptotic numerical method" J. Mech. Phys. Solids., 61(8), 1712(2013) .
A. Lazarus, J.T. Miller, M. Metlitz and P.M. Reis "Contorting a heavy and naturally curved elastic rod", Soft Matter, 9 (34), 8274 (2013) [html, pdf]. (Special themed issue on "Geometry and Topology of Soft Materials").
T. Su, J. Liu, D. Terwagne, P.M. Reis and K. Bertoldi "Buckling of an elastic rod embedded on an elastomeric matrix: planar vs. non-planar configurations" Soft Matter, 10, 6294-6302 (2004).
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