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The solution of a nonlinear problem of stability of a multi-layer shell of revolution made from a composite material of low shear rigidity

Knyazev A.A., Trushin S.I., Zhavoronok S.I.

#### Abstract:

When stability problems for thin-walled structured are considered in a non-linear statement, it is necessary to determine critical points and points of bifurcation on the curve of equilibrium configurations and to study the post-critical behavior of a structure. Methods of continuation of a solution with respect to a parameter are of great effectiveness for constructing curves of equilibrium configurations and studying stability properties of equilibrium modes of shells. From the analysis of solutions of non-linear problems of the theory of plates and shells it follows that the method of continuation can get good results when it is used in collaboration with the Newton-Raphson and Runge-Kutta procedures. At that, it is necessary to use the length of the arc of a curve of equilibrium configurations. This procedure should includes an auxiliary equation for iterations on a sphere. Using a length of the arc of the curve as a parameter of continuation, we can construct a uniform procedure for regular and limiting points as well as for points of bifurcation. Based on the method of continuation on a parameter, we obtain a solution for a problem of geometrically non-linear elastic deformation of a thin-walled multi-layer anysotropic shell. We present examples of the solution of the problem on post-critical behavior of spherical and conical shells.

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