۱- Introduction

۲- Geometrical description of shells with special shapes

۳- Geometrical description of shells with special shapes with corrugated middle surfaces

۴- Linear buckling

۵- Nonlinear buckling

۶- Conclusions

References

Abstract

The problem of elastic stability of the shells with special shapes with corrugated middle surfaces under external pressure is debated in the presented paper. Solution of the problem is based on FEM study. Corrugated barrelled, pseudo-barrelled, and cylindrical shells of constant mass are considered. Geometrical modification of the middle surface geometry is based on sine wave along principal directions. Middle surface of the corrugated shells are described referring to differential geometry of surfaces by parametric functions in three-dimensional Euclidean space. Linear and nonlinear buckling analyses are conducted. Examples of buckling modes are presented, which differ significantly from those typical for shells of revolution with positive or zero Gaussian curvature. It is proven that corrugation may lead to serious increase or decrease of critical load for all types of presented shells.

Introduction

Continuous search for optimal technical solutions creates the need to develop more efficient structures. Due to the wide spectrum of shells applications in the industry, many authors devoted their efforts towards description of stress state and stability analysis of shells. In conjunction with thin-walled nature of those structures the most vivid branch of structural analysis of shells is stability problem. Among many monographs concerning structural stability one can distinguish the following: [1–۵]. There are also many papers devoted to analytical and numerical solutions of buckling behaviour, concerning shells with unique geometrical forms. Due to practical limitations, shapes are usually narrowed to cylinders [6,7], spheres [8], and cones [9,10]. However, more often further complex shapes are being topics of consideration, for example: barrels [11], pseudo-barrels [12], pseudo-spheres [13], bi-segmented spherical shells [14], multi-segmented spherical shells [15], clothoidal-spherical shells [16] and egg-shaped shells [17]. Zingoni [18] presented a review work concerning liquid-containment shells of revolution including non-conventional shapes. Additionally various shell panels are being objects of intensive studies. Post-buckling problems of multiple shell panels are discussed in [19,20] using higherorder theories. The most effective way of increasing load-carrying ability of shell structures is modification of their geometrical form. This fact can be assumed due to the number of diverse types of shells shapes that have been developed in recent decades. In this work the effect of corrugation of shells with positive, negative, and zero Gaussian curvature on stability is considered. Some of corrugated structures, mainly longitudinally corrugated cylinders have been already studied. Malinowski et al. [21] presented the buckling problem of sandwich cylindrical shell with corrugated main core, subjected to uniformly distributed external pressure. Iwicki et al. [22,23] investigated numerous stability problems of silos composed of corrugated sheets and columns. Jongpradist et al. [24] considered a corrugated food can design in terms of stability and strength, by experimental studies and response surface method. Dickson et al. [25] performed an analytical study of buckling problem of ringstiffened corrugated cylinders and compared results with experimental data. Liu et al. [26] studied numerically the problem of axial-impact on meridionally corrugated tubes with a view to improve the energy absorption aspect of standard circular tubes. Hao et al. [27,28] performed an analytical study to resolve a similar problem considering progressive buckling and dynamic response of such structures. The Authors verified the analytical solution with a numerical FEM study. Ghazijahani et al. [29] performed an experimental study on equivalent structures and compared obtained results with theoretical predictions. Ning and Pellegrino [30] extensively described the problem of axially compressed, circumferentially corrugated cylindrical shells. Malek [31] et al. investigated the effect of corrugation along two directions of the surface of barrelled vault. The authors have proven such modification can lead to a great increase of the buckling load. Malek and Williams [32] presented conceptual design of corrugated plates and shells. Using analytical approach, a closed-form solution of equilibrium state of such structures was obtained.