Higher-order semi-layerwise models for doubly curved delaminated composite shells
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O R I G I NA L
András Szekrényes
Higher-order semi-layerwise models for doubly curved delaminated composite shells
Received: 13 January 2020 / Accepted: 17 August 2020 © The Author(s) 2020
Abstract This work deals w ith the development and extension of higher-order models for delaminated doubly curved composite shells with constant radii of curvatures. The mechanical model is based on the method of four equivalent single layers and the system of exact kinematic conditions. A remarkable addition of this work compared to some previous ones, is a modified and improved continuity condition between the delaminated and undelaminated parts of the shell. Using the principle of virtual work, the equilibrium equations of the shell systems are brought to the stage and solved by using the classical Lévy plate formulation under simply supported conditions. Four different scenarios of elliptic and hyperbolic delaminated shells are investigated providing the solutions for the mechanical fields as well as for the J-integral. The analytical results are compared to 3D finite element calculations, and excellent agreement was obtained for the displacement components and normal stresses. On the contrary, it was found that the transverse shear stresses are captured quite differently by the proposed method and the finite element models. Although the role of shear stresses should not be underrated, they seem to be marginal because the distributions of the J-integral components are in very good agreement with the numerically determined energy release rates. Keywords Delamination · Mixed mode II/III fracture · First-order shell theory · Second-order shell theory · Energy release rate
1 Introduction Laminated plates and shells are the quite important parts of engineering structures (e.g., ship body, car bodywork, helmets, pressure vessels) [1–6]. The heterogeneous nature of laminated composite materials makes them susceptible to many types of damage modes. Delamination or interlaminar fracture is one of the primary failure modes in such materials [7–9]. Delamination physically means that the neighboring layers partially or entirely get separated from each other reducing significantly the stiffness and strength of the laminate [10], respectively. Apart from that even the dynamic properties of the structure alter significantly [11–13]. It is therefore very important to develop models which are able to capture adequately the mechanical behavior of delaminated composite structures. The literature offers numerous classic and improved models for the computational analysis of laminated plates and shells. The so-called equivalent single layer (ESL) theories are two-dimensional theories based on suitable assumptions of kinematics and stress state along the thickness direction compared to those of threedimensional models. Obviously, the classical laminated plate and shell theories (CLPT and CST) [14,15] are quite essential in this field. Eventually, the CLPT and CST theories are useful only if the structure does not contain imperfections at all.
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