Numerical solution of problems involving the statics of geometrically nonlinear anisotropic multilayer shells of revolution

Influence of anisotropy on the stress state of multilayer reinforced shells

“…In analyzing the stress--strain state of multilayer reinforced shells, nonclassical theory is used [3,4], with the following basic hypotheses.…”

“…In [3,4], it was shown that the use of a mixed variational principle allows these contradictions to be resolved and, together with the equilibrium equations and boundary conditions, the following additional relations may be introduced…”

“…In the case of axisymmetric deformation of multilayer anisotropic shells of revolution, normal systems of ordinary nonlinear differential equations were obtained in [3,4] …”

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539.3On the basis of two refined theories of multilayer shells [3,4], a comparative analysis is given of anisotropy in cross-reinforced shells. As is known, investigating anisotropy in problems of axisymmetric deformation of anisotropic shells reduces to integrating a system of ordinary differential equations of eighth order in classical Kirchhoff--Love theory [6,7, 9], of tenth order in Timoshenko-type theory [3, 8, ii], and of twelfth-order in the generalized Timoshenko theory [4].

i.

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Equivalent single-layer models in deformation analysis of laminated multilayered plates

“…The authors are grateful to the three anonymous reviewers for their insightful and constructive comments that improved the manuscript. As a great surprise, we took one of those comments saying that already in 1981 Grigolyuk and Kulikov [53] analyzed anisotropic multilayer shells of revolution using the mixed variational formulation in a very similar fashion as described 3 years later by Eric Reissner in his well-recognized paper [26]. One should regret that the contribution of Grigolyuk and Kulikov [53] has not received proper recognition in the worldwide scientific literature.…”