Zur Theorie der Elastizität flacher rotationssymmetrischer Schalen

Geckeler, J. W.

doi:10.1007/bf02079933

Cited by 9 publications

(1 citation statement)

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“…This approach is usually referred to as 'asymptotic integration' in the thin-shell literature and it amounts to exploiting the presence of the ubiquitous parameter 0 < (h/R) 1 (see Figure 1) in order to derive WKB-type approximations for the corresponding thin-shell equations. Blumenthal [3,4], Geckler [27,28], and Hetényi [34] are some of the key names associated with fundamental developments in this area. The case of non-axisymmetric deformations in thin spherical shells was originally tackled by Havers [32] (see also Flügge's account in [24]), who also discovered that Blumenthal's earlier approach was still relevant to deformations lacking radial symmetry provided that some small mathematical adjustments were introduced.…”

Section: Introductionmentioning

confidence: 99%

Singular Perturbations and Torsional Wrinkling in a Truncated Hemispherical Thin Elastic Shell

Coman

Bassom

2022

J Elast

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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.

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Section: Introductionmentioning

confidence: 99%

Singular Perturbations and Torsional Wrinkling in a Truncated Hemispherical Thin Elastic Shell

Coman

Bassom

2022

J Elast

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An Accuracy Study of the Marguerre‐Vlasov Equations

Gradowczyk¹

1966

Z Angew Math Mech

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An accuracy study of the linearized Marguerre‐Vlasov equations is presented. For this purpose a system of equations for thin elastic shallow shells is obtained by means of a series expansion of Novozhilov's theory. these new equations for shallow shells are used as the departure point of the accurate analysis, which is given with the help of an order of magnitude analysis. This analysis shows that in general, good agreement with the more accurate equations should be expected. For a special class of shallow shells, however, the differences may be of importance.

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Lineare Schalenbiegetheorie

Başar

Krätzig

1985

Mechanik Der Flächentragwerke

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Zur Theorie der Elastizität flacher rotationssymmetrischer Schalen

Cited by 9 publications

References 0 publications

Singular Perturbations and Torsional Wrinkling in a Truncated Hemispherical Thin Elastic Shell

Singular Perturbations and Torsional Wrinkling in a Truncated Hemispherical Thin Elastic Shell

An Accuracy Study of the Marguerre‐Vlasov Equations

Lineare Schalenbiegetheorie

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