A general higher-order shell theory based on the analytical dynamics of constrained continuum systems

摘要

The new variational formulation of higher-order shell theories is based on the Lagrangian formalism of analytical dynamics of constrained continuum systems. The shell model is defined on the two-dimensional manifold within the configuration space, the set of field variables, the density of Lagrangian, and the constraints. The field variables appear as a result of the dimensional reduction as displacement expansion coefficients. The boundary conditions shifted from the shell faces onto the base surface and expressed through the field variables and their covariant derivatives become the constraint equations. The obtained hierarchy of shell theories contains the asymptotically consistent Kirchhoff's model with properly defined bending stiffness as the first-order approximation constructed without any supplementary assumption.