Bifurcation state and rational design of three-layer reinforced compound cone-cylinder shell structure under combined loading

Heading: 
Space-Rocket Complexes
1Grishchak, VZ, 2Hryshchak, DV, 3Dyachenko, NM, 4Sanin, AF, 5Sukhyy, KM
1Dnipro University of Technology, Dnipro, Ukraine
2The Ministry for Strategic Industry of Ukraine, Kyiv, Ukraine
3Zaporizhzhia National University, Zaporizhzhia, Ukraine
4Oles Honchar Dnipro National University, Dnipro, Ukraine
5Ukrainian State University of Chemical Technology, Dnipro, Ukraine
Space Sci. & Technol. 2023, 29 ;(6):026-041
https://doi.org/10.15407/knit2023.06.026
Publication Language: English
Abstract: 
An analytical-numerical approach to solving the problem of state bifurcation in terms of local and overall stability of a three-layer cone-cylinder shell structure discretely supported by intermediate rings, in particular of modern launch vehicles, under static combined loading by external pressure, axial forces, and torque is proposed in the paper taking into account the stiffness parameters of the intermediate rings in the plane of the initial curvature and for torsion.
          Corresponding solving equations for the problem are ordinary differential equations of the sixth order (for a cylindrical compartment with constant coefficients and for a conical one with variable coefficients along the axial coordinate). Differential relations that determine the conditions of conjugation through the intermediate ring are used.
          For the numerical solution, the finite difference method is used with central finite differences of the third and second order at the inner points of the shell determination segments and at its ends, respectively, and the second order differences with one step backward or forward at the conjugation points through the ring.
           The agreement of the calculation results with the known data for three-layer conical and cylindrical shells is shown, as well as in the limiting case, it is done when passing to a single-layer compound cone-cylinder structure.
For the considered class of cone-cylinder shell structures, boundary surfaces are constructed that separate the stability region of the structure being under study, depending on the geometric and stiffness parameters of the compartments, reinforcing elements, and the external load condition.
          The external load effect on the parameter of the post-critical wave formation for the structure under investigation is studied, providing the visualization of the deformation behavior.
          The analysis of the calculation results has shown that this approach to solving the problem of bifurcation and equistability of the compound structure compartments in relation to the local and overall forms of protrusion allows choosing rational geometric and stiffness parameters of the shell components and force elements in terms of improving the weight characteristics of the structure.
Keywords: boundary surface, combined loading, compound cone-cylinder structure, local and overall forms of protrusion, ring, three-layer shell, visualization of post-critical forms of buckling
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