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Theoretical investigation of the strength and stability of special pseudospherical shells under external pressure
Affiliation:1. National Key Laboratory of Precision Hot Processing of Metals, Harbin Institute of Technology, Harbin 150001, China;2. Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621900, China;1. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland;2. Department of Vehicles, Warsaw University of Technology, 84 Narbutta Str., 02-524 Warsaw, Poland;3. Cybernetic Institute, National Research Tomsk Polytechnic University, 30 Lenin Avenue, 634050 Tomsk, Russian Federation;4. Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, 77 Politehnicheskaya Str., 410054 Saratov, Russian Federation;5. Department of Mathematics and Modeling, Saratov State Technical University, 77 Politehnicheskaya Str., 410054 Saratov, Russian Federation;1. School of Engineering and Design, Brunel University, UB8 3PH Uxbridge, UK;2. University of Naples ‘Federico II’, Via Claudio 21, 80125 Napoli, Italy
Abstract:The paper is devoted to a new shape of a shell of revolution with negative Gaussian curvature. The main part of the meridian of the shell is a plane curve of the Huygens tractrix. Geometrical properties of the middle surface of the shell of revolution are presented. The membrane state of stress for a family of shells with constant capacity and constant mass under uniform external pressure is analysed. The critical pressure, buckling modes and equilibrium paths for the family of shells are calculated with the use of the FEM (the ANSYS system). Results of the analytical and numerical investigations are presented in tables and figures. A stable post-critical behaviour of presented shells is pointed out which is not typical for most shell structures.
Keywords:Shell of revolution  Elastic buckling  Equilibrium paths  Negative Gaussian curvature
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