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.

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