E. Tertel, P. Kuryło Stabilnost konusne panel oplate slojevite konstrukcije – analiza stanja naprezanja Tehnički vjesnik 24, Suppl. 1(2017), 55-60 55 ISSN 1330-3651 (Print), ISSN 1848-6339 (Online) DOI: 10.17559/TV-20140912102638 THE STABILITY OF THE SANDWICH CONICAL SHELL PANEL – THE STRESS STATE ANALYSIS Edward Tertel, Piotr Kuryło Original scientific paper The paper presents an analysis of the stress state in a sandwich open conical shell panel. The shells under consideration consist of two face-layers (facings, claddings) and a core layer. The facings are load-carrying, a core layer is lightweight and it resists transverse shear only. The facings are made of isotropic, compressible, work-hardening materials. The core is the greater part of the whole shell thickness (over 80 %). The shell under consideration is two-parametrical loaded. Pre-buckling deformation of the shell could occur within the elastic, elastic-plastic or plastic range. In order to determine the stress state which occurs during stability loss, the constitutive relations of the Nadai-Hencky deformation (NHd) theory, alongside the HMH (Huber- Mises-Hencky) yield condition, are accepted. The results obtained from the analysis show that during stability loss, the effective stress may temporarily decrease. Then the unloading and hardening phenomena could occur and this should be taken into consideration. Keywords: buckling; deformation; sandwich shell; stability; stress Stabilnost konusne panel oplate slojevite konstrukcije – analiza stanja naprezanja Izvorni znanstveni članak U radu se daje analiza stanja naprezanja konusne panel oplate slojevite konstrukcije. Analizirana oplata sastavljena je od dva vanjska sloja (obloge) i srednjeg sloja. Obloge podnose opterećenje, srednji sloj je male težine i odupire se samo poprečnom smiku. Obloge su od izotropnih, stlačivih materijala za otvrdnjivanje zbog obrade. Središnji sloj zauzima veći dio debljine čitave oplate (preko 80 %). Razmatrana oplata je dvo-parametarski opterećena. Do deformacije pred-izvijanja oplate može doći u okviru elastičnog, elastično-plastičnog ili plastičnog područja. Kako bi se odredilo stanje naprezanja do kojeg dolazi tijekom gubitka stabilnosti, prihvaćeni su konstitutivni odnosi Nadai-Hencky teorije deformacije uz Huber-Mises-Hencky(HMH) uvjet popuštanja. Dobiveni rezultati pokazuju da tijekom gubitka stabilnosti može doći do privremenog smanjenja efektivnog naprezanja. Tada može doći do pojave rasterećenja i kaljenja i treba ju uzeti u obzir. Ključne riječi: deformacija; izvijanje; naprezanje; panel oplata; stabilnost 1 Introduction Thin-walled structures consisting of three layers have features that make them interesting for designers and builders of lightweight, modern constructions. The most important feature is a structural efficiency which is high. Layered, light-weight structures are more often used to design different constructions (e.g. fuselages, tanks, pipes, buildings elements). For this reason, these structures are well recognized and widely examined in the scientific study. An analysis of different thin-walled, layered structures (shells and plates) under the action of various loading is presented in [1÷4]. The main advantage of such structures is relatively high value of the load-to-weight ratio. The designed structures are characterized by advantageous compressive buckling strength as well as bending stiffness while they also have a relatively low weight. An interesting analysis of a structural behaviour of sandwich panels with construction cut-outs is presented in [5]. Certain types of engineering shell structures (e.g. train bodies, aircraft fuselages) are quite often in the shape of a cone. Therefore, in specified applications, an analysis of the three-layer, cone-shaped shell panel under certain type of external loads (longitudinal force and perpendicular pressure) may be interesting case studies. Strength and stability of cylindrical, conical and rectangular structures are considered by many authors. Scientific papers refer to different kinds of shell structures. The single-layer shells are considered in [6, 7], whereas the bi-layered in [9] and sandwich ones in [9÷13]. Works [3, 4] present different approaches and methods of sandwich structures analysis and the authors give large reference lists there. The empirical results of buckling analysis of thin-walled conical shells under external pressure are presented in [7]. An interesting new method of empirical measurement of strains and stress fields in loaded structures is presented in [14]. A majority of publications accept some initial assumptions concerning changes in stress values. Most publications assume the active loading process (Shanley approach) [9÷12]. This article shows a way to determine stress changes during stability loss. This allows adopting an appropriate method of loading of a construction (constant load or active load approaches).A theoretical investigation of the stress changes in the three-layered conical shell under the action of complex loading is the main aim of presented study. 1.1 The initial assumptions At the beginning of the considerations, some initial assumptions have to be adopted. The object under consideration is a three-layer conical shell segment. The shell consists of two thin face-layers and one core layer (Fig. 1a). In this consideration the face-layers are of equal thicknesses and are made of the same material which is compressible and isotropic. Other considerations, especially for unsymmetrical shells, could be seen in the previous publications [10, 11]. The internal-core layer is made of a foam plastic that is assumed to be elastic, and incompressible in the radial (z-axis) direction. For this layer the transverse shear is the only stress that it resists. The analysed shell is geometrically and physically symmetrical. The coordinate system adopted in the brought to you by CORE View metadata, citation and similar papers at core.ac.uk