On FEM analysis of Cosserat-type stiffened shells: static and stability linear analysis
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O R I G I NA L A RT I C L E
Stanisław Burzynski ´
On FEM analysis of Cosserat-type stiffened shells: static and stability linear analysis
Received: 6 July 2020 / Accepted: 18 September 2020 © The Author(s) 2020
Abstract The present research investigates the theory and numerical analysis of shells stiffened with beams in the framework based on the geometrically exact theories of shells and beams. Shell’s and beam’s kinematics are described by the Cosserat surface and the Cosserat rod, respectively, which are consistent including deformation and strain measures. A FEM approximation of the virtual work principle leads to the conforming shell and beam FE with 6 DoFs (including the drilling rotation for shells) in each node. Examples of static and stability linear analyses are included. Novel design formulas for the stability of stiffened shells are included. Keywords Stiffened shell · Cosserat shell · Cosserat beam · Shell stability · Finite element method · Drilling rotation 1 Introduction Shells are commonly used as a part of various structures. They are considered as an economical, efficient, and aesthetic choice since are able to bear high loads with low weight kept. Additional reinforcement could be achieved by using locally placed stiffeners. Stiffened shells have various applications, like structural elements in vessels, aircraft, and aerospace vehicles. They are also used as bridge decks and as floor slabs in buildings. Inspiration for this type of structures might be found in nature: leaves and insects’ wings are often membranes enforced with veins. Over the years, great effort has been done to investigate and understand stiffened plates and shell behaviour in various circumstances: under static and dynamic loading, deformation in thermal environment, free vibration, etc. Nevertheless, still novel contributions are provided to better understand their behaviour and capabilities in up-to-date applications. The current study is focused on the employment geometrically exact shell and beam theories to stiffened shells analysis as the original contribution. This approach results in compatible kinematics’ formulations of a shell as the Cosserat surface and beam as the Cosserat rod. The virtual work principle, applicable to the stiffened shell as an unseparated structure, is used to develop the finite element method (FEM) approximate solution. Consistency of shell and beam finite elements (FE) is achieved. In the present paper, the static linear analysis and stability analysis of various stiffened homogenous shells are conducted, including curved and branched shells. Since stiffened shells are widely used in engineering design, current parametric studies consist not only of rare data (e.g. displacements and critical load factors), but also a proposition of approximate design formulas given. Communicated by Marcus Aßmus. S. Burzy´nski (B) Department of Mechanics of Materials and Structures, Gda´nsk University of Technology, Narutowicza 11/12, 80-233 Gda´nsk, Poland E-mail: [email protected]
S. Burzy´n
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