Investigating the buckling behaviour of imperfection sensitive conical composite structures subjected to Single Perturbation Load Approach

The stability of shell structures has been an object of studies for more than a century. Thin walled cylindrical and conical structures are widely used in aerospace, offshore, marine, civil and other industries. The importance of taking into account geometric imperfections for cylindrical and conical thin-walled structures in buckling had been already recognized a long time ago. In spite of a multitude of publications on buckling of imperfect shells, such structures are still today generally designed at the preliminary design phase according to the NASA SP-8007 [1] for cylinders and the NASA SP-8019 [2] for truncated cones. Both guidelines date from 1960’s and they are based on a lower bound curve which does not consider important mechanical characteristics of laminated composite shells, such as the stacking sequence. Several authors have proven that this guideline does not take into account some important mechanical characteristics of laminated shells generated by the different angles of orthotropic plies along the stacking sequence, producing configurations that are over-conservative or even non-conservative for some cases. The running EU project DESICOS (New Robust DESIgn Guideline for Imperfection Sensitive COmposite Launcher Structures, cf. [3]) contributes to lighter and cheaper structures by a new design procedure for imperfection sensitive composite launcher structures, exploiting the worst imperfection approach efficiently. The goal of the DESICOS project is to obtain a new design guideline combining probabilistic and deterministic approaches. Koiter in 1945 [4] was the first who theoretically demonstrated the already experimentally observed imperfection sensitivity that affects the buckling behavior of thin-walled structures. Nowadays, with the everyday increasing computational power, it becomes easier to consider imperfections in numerical simulations. However, in the early design stage the real geometric imperfection pattern of a new type of structure is not available. The Single Perturbation Load Approach (SPLA), a design method developed by Hühne, is a deterministic approach where a lateral load is applied prior to the axial compression (Figure 1), stimulating a single dimple [5]. At this dimple the buckling process will start and a single buckle is produced, which will then propagate until the structure collapses. Esslinger, 1970 [6], using high speed cameras observed that the buckling mechanism of imperfection sensitive shells always started with a single-buckle, and therefore this imperfection of this shape could be though as a “worst-case” imperfection. Deml and Wunderlich [7] also came to this conclusion using a modified finite element procedure in which the nodal coordinates where included in the set of degrees of freedom, allowing the solver to find not only the nodal displacements but also the worst nodal positions that, within a given mobility tolerance (i.e. the maximum imperfection amplitude), would produce the minimum non-linear buckling load. In this paper a numerical investigation about the SPLA applied to characterize the buckling process of imperfection sensitive composite conical structures of different heights under axial compression will be presented. Buckling behavior of the structures subjected to the SPLA will be compared with the buckling behavior of the structures with initial geometric imperfections. Knock down factors calculated with the SPLA will be presented and compared with the NASA knock down factors. The study is part of the European Union (EU) project DESICOS