Studies of nonlinear deformation and stability of oval and elliptic cylindrical shells under axial compression |
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Authors: | D V Boiko L P Zheleznov V V Kabanov |
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Institution: | 1.Chaplygin Siberian Research Aviation Institute,Novosibirsk,Russia |
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Abstract: | The stability of noncircular shells, in contrast to that of circular ones, has not been studied sufficiently well yet. The
publications about circular shells are counted by thousands, but there are only several dozens of papers dealing with noncircular
shells. This can be explained on the one hand by the fact that such shells are less used in practice and on the other hand
by the difficulties encountered when solving problems involving a nonconstant curvature radius, which results in the appearance
of variable coefficients in the stability equations. The well-known solutions of stability problems were obtained by analytic
methods and, as a rule, in the linear approximation without taking into account the moments and nonlinearity of the shell
precritical state, i.e., in the classical approximation. Here we use the finite element method in displacements to solve the
problem of geometrically nonlinear deformation and stability of cylindrical shells with noncircular contour of the transverse
cross-section. We use quadrilateral finite elements of shells of natural curvature. In the approximations to the element displacements,
we explicitly distinguish the displacements of elements as rigid bodies. We use the Lagrange variational principle to obtain
a nonlinear system of algebraic equations for determining the unknown nodal finite elements. We solve the system by a step
method with respect to the load using the Newton-Kantorovich linearization at each step. The linear systems are solved by
the Kraut method. The critical loads are determined with the use of the Silvester stability criterion when solving the nonlinear
problem. We develop an algorithm for solving the problem numerically on personal computers. We also study the nonlinear deformation
and stability of shells with oval and elliptic transverse cross-section in a wide range of variations in the ovalization and
ellipticity parameters. We find the critical loads and the shell buckling modes. We also examine how the critical loads are
affected by the strain nonlinearity and the ovalization and ellipticity of shells. |
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