  Shell structures are generally modeled based on kinematic hypotheses, where
certain involved parameters have to be evaluated phenomenologically. In this
article, we propose an isogeometric-based asymptotic analysis scheme aimed at
achieving a rational modeling and interpretation about the deformation
behaviors of multi-layered thin shells (MTSs). Asymptotic analysis of the
three-dimensional governing elasticity equations allows us to gain a deeper
insight over shell theories in three aspects. Firstly, the intrinsic hierarchy
lying in the displacement field, stress components, constitutive law, and
momentum conservation, resulting from the shell thinness, is naturally
suggested through asymptotic analysis, and not only the overall stiffness but
also the key stress components can be formulated in a fully rational manner.
Secondly, through detailed discussion on the order of non-dimensional maximum
principal curvature, it is shown that a shell must deform in one of the
following two deformation modes. One regime exhibits a mode resembling that of
thin plates, while the other corresponds to a piecewise linear distribution of
local transverse shear stresses along the thickness. And the specific orders of
the key quantities are determined for both cases. Thirdly, in contrast with the
existing arguments where an applied shear load on the shell surface
necessitates the inclusion of transverse shear stresses for analysis, it is
demonstrated that a leading-order shell theory derived from asymptotic analysis
should suffice to output satisfactory predictions over the shell stiffness, as
well as its internal stress distribution. Numerical examples of the deformation
and strength analysis for the MTS are also presented to show the reliability of
the proposed method for shell modeling.
