High-order shell theory based on the analytical continuum dynamics formalism

Abstract eng:
A new variational formulation for the general theory of thick anisotropic shells is proposed. The dimensional reduction approach is combined with the Lagrangian formalism of analytical dynamics of continua. The shell model is defined on the two-dimensional manifold and consists in the configuration space with a set of field variables, the Lagrangian density, and the constraint equations. Here the field variables of the first kind are defined as biorthogonal expansion coefficients of the displacement vector with respect to the normal coordinate, the dimensional reduction of Lagrangian volumetric density results its surface density, and the constraint equations are derived from the boundary conditions on shell’s faces. The equations of motion are formulated as Lagrange equations of the second kind. The low-order theories are constructed using the presented formalism, and their correspondence with the classical theories is shown.

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