Asymptotic analysis of a rod with small bending stiffness
Author:
Peter Wolfe
Journal:
Quart. Appl. Math. 49 (1991), 53-65
MSC:
Primary 73K05; Secondary 73G05, 73H05, 73K03, 73R05
DOI:
https://doi.org/10.1090/qam/1096232
MathSciNet review:
MR1096232
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Abstract: In this paper we consider a model problem for the deformation of a rod with small bending stiffness. We show that this problem can be considered as a singular perturbation of the problem in which the rod is replaced by a string with no resistance to bending. We construct an approximate solution to this problem. As the bending stiffness tends to zero this solution tends to the solution of the string problem away from the ends of the rod which are assumed to be clamped. However, as one would expect, there is a boundary layer near each end of the rod. The main point of the paper is to show how to construct the boundary layer corrections.
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- Thomas I. Seidman and Peter Wolfe, Equilibrium states of an elastic conducting rod in a magnetic field, Arch. Rational Mech. Anal. 102 (1988), no. 4, 307–329. MR 946963, DOI https://doi.org/10.1007/BF00251533
- Peter Wolfe, Bifurcation theory of an elastic conducting wire subject to magnetic forces, J. Elasticity 23 (1990), no. 2-3, 201–217. MR 1074676, DOI https://doi.org/10.1007/BF00054803
S. S. Antman and J. E. Dunn, Qualitative behavior of buckled nonlinear elastic arches, J. Elasticity 10, 225–239 (1980)
J. E. Flaherty and R. E. O’Malley, Singularly perturbed boundary value problems for nonlinear systems, including a challenging problem for a nonlinear beam, Theory and Applications of Singular Perturbations (W. Eckhaus and E. M. deJager, eds.), Lecture Notes in Math., no. 942, Springer, Berlin-New York, 1982, pp. 170–191
T. Seidman and P. Wolfe, Equilibrium states of an elastic conducting rod in a magnetic field, Arch. Rational Mech. Anal. 102, 307–329 (1988)
P. Wolfe, Bifurcation theory of an elastic conducting wire subject to magnetic forces, J. Elasticity (to appear).
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Article copyright:
© Copyright 1991
American Mathematical Society