On a version of the nonlinear dynamical theory of thin multilayered shells: PMM vol. 40, n≗1, 1976, pp. 180–185

Abstract

A version of the geometrically nonlinear theory of elastic multilayered shells subjected to a nonconservative load is proposed. Transverse shear strains in the layers and strains in the direction of the normal to the middle surface are taken into account. As a rule, a description of the nonstationary dynamical processes associated with shell buckling can be performed on the basis of a geometrically nonlinear theory [1]. The behavior of multilayered plates and shells under large deflections has been examined in [2–5], A variational formulation, which is valid for conservative loads acting on a shell, is used in [5] to derive the geometrically nonlinear equations. The variational principle is formulated in this paper in a form also applicable in the case of no potential of the external forces. One of the advantages of the approach developed here as compared with the results of [5] is the additional possibility of describing the local dynamical buckling of the shell in modes associated with the change in its thickness.