Non-material finite elements for spatial deformations of belts. (English) Zbl 1520.74080
Altenbach, Holm (ed.) et al., Contributions to advanced dynamics and continuum mechanics. Dedicated to the 65th birthday of Prof. Alexander K. Belyaev. Cham: Springer. Adv. Struct. Mater. 114, 227-242 (2019).
Summary: We present a novel mixed Eulerian-Lagrangian beam finite element formulation. Large spatial deformations of shear-rigid, but extensible rods with natural curvature are considered. The three-dimensional deformation of a thin strip clamped at both ends is computed with this novel method and compared with semi-analytic solutions of the boundary value problem of the incremental rod theory as well as with the finite element solution for an equivalent shell model. Stability of the straight clamped beam in the absence of gravity is considered analytically for the sake of comparison and the critical value of the natural curvature is found. Finally, the contact problem of a belt spanned between two pulleys is discussed.
For the entire collection see [Zbl 1422.74009].
For the entire collection see [Zbl 1422.74009].
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74M15 | Contact in solid mechanics |
Keywords:
nonlinear mixed Eulerian-Lagrangian beam model; frictionless contact; critical natural curvatureReferences:
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