Non-Axisymmetrically Loaded Cylindrical Shell
The non-axisymmetrical loading of a cylindrical shell induces a basically non-symmetric deformed state. The cylindrical shell is maximally deformable in circumferential direction, and the bending components close to eigenmodes develop prevailingly under a
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Non-Axisymmetrically Loaded Cylindrical Shell
Abstract The non-axisymmetrical loading of a cylindrical shell induces a basically non-symmetric deformed state. The cylindrical shell is maximally deformable in circumferential direction, and the bending components close to eigenmodes develop prevailingly under a growing load. The concept of variability allows revealing the interaction of deformed shapes induced by the load and of shell eigenforms manifesting itself at shell buckling. Two typical loads are considered—external pressure and axial compression. For the case of external pressure, the ‘‘wind’’-type diagram, the cyclic diagram and locally applied pressure are investigated. For the case of axial compression, attention is paid mainly to cyclic compression. The effect of initial deformed shape transformation (by development of the components with higher wave numbers) is investigated. The correlation between load and initial deformed shape variability, on the one hand, and critical loads and general shell behaviour, on the other hand, is revealed, and the resonance effects are studied. The influence of nonuniform load component upon critical load and type of behaviour is investigated. The applicability of simplified (membrane) models of stability analysis is discussed.
5.1 General Considerations. Linear Problem Numerous investigations of the stability of shells subjected to non-symmetric external pressure (Andreev et al. 1988; Biagi and del Medico 2008; Blachut 2010; Chen and Rotter 2012; Huang and Han 2010; Kabanov et al. 1978; Kumarpanda and Ramachandra 2010; Li and Lin 2010; Liew et al. 2012; Ohga et al. 2005; Rodriguez and Merodio 2011; Schneider et al. 2005; Sosa and Godo 2009) are presented in the literature. In these researches only small nonuniformities and the simplest membrane model to describe the initial stress-strain state were considered. The minimal eigenvalue of the linearized problem was considered to be the buckling load.
N. I. Obodan et al., Nonlinear Behaviour and Stability of Thin-Walled Shells, Solid Mechanics and Its Applications 199, DOI: 10.1007/978-94-007-6365-4_5, Ó Springer Science+Business Media Dordrecht 2013
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5 Non-Axisymmetrically Loaded Cylindrical Shell
Buckling modes were presented by trigonometric series. Further researches, based on such a model, showed that the critical amplitude of nonuniform external pressure exceeds the classical critical value of uniform pressure (3.14). Namely, the peak of ‘‘aerodynamic’’ critical pressure appeared to be 30 % higher than the critical level for uniform loading. In fact, the membrane model of the prebuckling state provides one with Euler critical load for circumferentially averaged stress level. More sophisticated shell models take into account the prebuckling bending (Andreev et al. 1988) and its dependence upon membrane forces [quasilinear model (Kabanov et al. 1978)]. Furthermore, these researches revealed the importance of bending factors and non-monotonous dependence of critical load k upon the load circumferential variab
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