In general, when the axial compressive load is applied on thin cylindrical shells, the dent deforms radially inward further, and also two ridges are formed near the dent tips along with two inclined trough surfaces extending from each ridge one above and one below the dent tips as shown in Figure 9 (a) (The line diagram of the same is shown in Figure 9 (b) to illustrate the terminologies used to represent the buckling behavior). Two bridge surfaces one of which bridges the trough surfaces above the dent and the other bridges the trough surfaces below the dent; also bend radially inward along the longitudinal edges of the dent as shown in Figure 9. Similar ridge-trough surfaces formation was noticed by Wullschleger and Piening Mayer (2002) for a horizontal dent on composite cylindrical shell subjected to axial compression. It is well known that the order of membrane strain energy stored in thin shell structures will be more than the order of bending energy stored. Any deviation from the perfect geometrical shape of the structure will cause storing of bending energy instead of membrane energy and thereby cause failure of thin cylindrical shell much earlier. This formation of local elastic deformation (ridge-trough surfaces formation) around the dent increases the strength of the cylindrical shell around the dent region. The extent of area over which the local deformation effect realized is known as Dent Effective Region (DER). As the load applied increases further, the amplitude of deformations of ridge-trough formation gets increased.
This and the next two slides are from:
B. Prabu, A.V. Raviprakash, N. Rathinam (Dept. of Mechanical Engineering, Pondicherry Engineering College, Pondicherry, India), “Parametric study on buckling behaviour of thin stainless steel cylindrical shells for circular dent dimensional variations under uniform axial compression”, International Journal of Engineering, Science and Technology Vol. 2, No. 4, 2010, pp. 134-149.
ABSTRACT: It is well known that thin cylindrical shell structures have wide applications as one of the important structural elements in many engineering fields and its load carrying capacity is decided by its buckling strength which in turn predominantly depends on geometrical imperfections present in it. Geometrical imperfections can be classified as local and distributed geometrical imperfections. But in this work, only local geometrical imperfection namely dent is considered for analysis. The main aim of this study is to determine the more influential dimensional parameter out of two dent dimensional parameters, one is the extent of dent present over a surface area and the other is dent depth, which affect the buckling strength of the cylindrical shells drastically. To account for the parameter “extent of dent present over an area”, the dent is considered as circular dent and its amplitude is considered as dent depth. For this purpose, finite element (FE) models of cylindrical shells with a circular dent at half the height of cylindrical shells having different dent sizes are generated. These FE models are analyzed using ANSYS non-linear buckling analysis. It is concluded that extent of dent present over an area is more influential than dent depth. To verify this conclusion further, FE models of cylindrical shells with two circular dents at half the height of cylindrical shell placed at 180 ̊ apart having different dent sizes are generated and analyzed.
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