Singular perturbations and torsional wrinkling in a truncated hemispherical thin elastic shell. (English) Zbl 1495.74018
Summary: The work described in this paper is concerned with providing a rational asymptotic analysis for the partial wrinkling bifurcation of a thin elastic hemispherical segment in which the upper rim experiences in-plane circular shearing relative to the other circular edge. The mathematical structure of the associated complex-valued boundary eigenvalue problem is revealed by using the method of matched asymptotic expansions. Our key result is a three-term asymptotic formula for the critical load in terms of a suitable small parameter proportional to the ratio between the thickness and the radius of the shell. Comparisons of this formula with direct numerical simulations provide further insight into the range of validity of the results derived herein.
MSC:
| 74G60 | Bifurcation and buckling |
| 74K25 | Shells |
| 74G10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics |
Keywords:
partial wrinkling; boundary layer; method of matched asymptotic expansions; complex-valued boundary eigenvalue problem; three-term asymptotic critical load formulaReferences:
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