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Numerical model of a pine in a wind. (English) Zbl 1060.74668

The authors found motivation for their study in the paper by D. F. Winter [SIAM Rev. 35, No. 4, 567-579 (1993; Zbl 0791.34011)] where the question why the pine resists the impact of a strong wind was discussed mathematically. Contrary to that paper, the problem is solved here numerically in full generality. The stem of the pine is modelled as a thin homogeneous isotropic truncated cone, whereas the canopy of the pine is idealized as a sphere. The elastic model developed in the paper uses the Bernoulli-Euler approximation of the bending moment and, after dimensional reduction, leads to an initial value problem for a system of nonlinear ordinary differential equations. The numerical procedure used in the simulations is based on the standard RKF45 solver and interpolation by cubic splines. The solvability of the problem is discussed, the numerical properties of the used algorithm are analyzed, and the results are compared with the real situation.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74K10 Rods (beams, columns, shafts, arches, rings, etc.)

Citations:

Zbl 0791.34011
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Full Text: DOI EuDML

References:

[1] D. F. Winter: On the stem of a tall palm in a strong wind. SIAM REWIEW 35 (December 1993), no. 4, 567-579. · Zbl 0791.34011 · doi:10.1137/1035135
[2] E. Hájek, P. Reif, F. Valenta: Elasticity and Strengh of Materials I. (In Czech: Pružnost a pevnost I.). SNTL, Praha, 1988.
[3] I. Vicena, J. Pařez, J. Konopka: Forest protection against windfallen trees (In Czech: Ochrana lesa proti polomům). SZN, Praha, 1979.
[4] I. Vicena: Management of forest demaged by peeling (In Czech: Hospodaření v porostech poškozených loupáním). Lesnická práce, 95 (Praha 1995), no. 5, 14-15.
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