  In the present work, we consider multi-scale computation and convergence for
nonlinear time-dependent thermo-mechanical equations of inhomogeneous shells
possessing temperature-dependent material properties and orthogonal periodic
configurations. The first contribution is that a novel higher-order macro-micro
coupled computational model is rigorously devised via multi-scale asymptotic
technique and Taylor series approach for high-accuracy simulation of
heterogeneous shells. Benefitting from the higher-order corrected terms, the
higher-order multi-scale computational model keeps the conservation of local
energy and momentum for nonlinear thermo-mechanical simulation. Moreover, a
global error estimation with explicit rate of higher-order multi-scale
solutions is first derived in the energy norm sense. Furthermore, an efficient
space-time numerical algorithm with off-line and on-line stages is presented in
detail. Adequate numerical experiments are conducted to confirm the competitive
advantages of the presented multi-scale approach, exhibiting not only the
exceptional numerical accuracy, but also the less computational expense for
heterogeneous shells.
