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Analytical expression of elastic rods at equilibrium under 3D strong anchoring boundary conditions
Analytical expression of elastic rods at equilibrium under 3D strong anchoring boundary conditions
- Source :
- Journal of Computational Physics, Journal of Computational Physics, 2018, 373, pp.736-749. ⟨10.1016/j.jcp.2018.07.021⟩, Journal of Computational Physics, Elsevier, 2018, 373, pp.736-749. ⟨10.1016/j.jcp.2018.07.021⟩
- Publication Year :
- 2018
- Publisher :
- Elsevier BV, 2018.
-
Abstract
- A general-purpose method is presented and implemented to express analytically one stationary configuration of an ideal 3D elastic rod when the end-to-end relative position and orientation are imposed. The mechanical equilibrium of such a rod is described by ordinary differential equations and parametrized by six scalar quantities. When one end of the rod is anchored, the analytical integration of these equations lead to one unique solution for given values of these six parameters. When the second end is also anchored, six additional nonlinear equations must be resolved to obtain parameter values that fit the targeted boundary conditions. We find one solution of these equations with a zero-finding algorithm, by taking initial guesses from a grid of potential candidates. We exhibit the symmetries of the problem, which reduces drastically the size of this grid and shortens the time of selection of an initial guess. The six variables used in the search algorithm, forces and moments at one end of the rod, are particularly adapted due to their unbounded definition domain. More than 850 000 tests are performed in a large region of configurational space, and in 99.9% of cases the targeted boundary conditions are reached with short computation time and a precision better than 10 − 5 . We propose extensions of the method to obtain many solutions instead of only one, using numerical continuation or starting from different initial guesses.
- Subjects :
- 0301 basic medicine
Mechanical equilibrium
equilibrium of elastic rods
Physics and Astronomy (miscellaneous)
search algorithm
01 natural sciences
Domain (mathematical analysis)
law.invention
03 medical and health sciences
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]
Position (vector)
law
0103 physical sciences
Boundary value problem
010306 general physics
Mathematics
Numerical Analysis
Applied Mathematics
Mathematical analysis
Scalar (physics)
Computer Science Applications
Computational Mathematics
Nonlinear system
030104 developmental biology
Numerical continuation
boundary value problem
Modeling and Simulation
Ordinary differential equation
Subjects
Details
- ISSN :
- 00219991 and 10902716
- Volume :
- 373
- Database :
- OpenAIRE
- Journal :
- Journal of Computational Physics
- Accession number :
- edsair.doi.dedup.....07c5105c7299a1874f14e05abd3ec834
- Full Text :
- https://doi.org/10.1016/j.jcp.2018.07.021