Perturbation methods and nonlinear stability analysis. (English) Zbl 1011.74021
Fu, Y. B. (ed.) et al., Nonlinear elasticity: Theory and applications. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 283, 345-391 (2001).
The author uses perturbation approach to study the stability of elastic bodies subjected to large deformations. Bifurcations at a non-zero and zero critical mode number are analyzed separately. Each case is introduced by a model example, and an infinite elastic rod supported by array of nonlinear elastic springs and necking of an elastic plate are considered in detail. The method presented could be used to examine the nonlinear wave propagation by a suitable change of variable. The paper is well written and presents important results in nonlinear stability theory.
For the entire collection see [Zbl 0962.00003].
For the entire collection see [Zbl 0962.00003].
Reviewer: Teodor Atanackovic (Novi Sad)
MSC:
| 74G60 | Bifurcation and buckling |
| 74B20 | Nonlinear elasticity |
| 74G10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics |
