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In the present work, we consider multi-scale computation and convergence fornonlinear time-dependent thermo-mechanical equations of inhomogeneous shellspossessing temperature-dependent material properties and orthogonal periodicconfigurations. The first contribution is that a novel higher-order macro-microcoupled computational model is rigorously devised via multi-scale asymptotictechnique and Taylor series approach for high-accuracy simulation ofheterogeneous shells. Benefitting from the higher-order corrected terms, thehigher-order multi-scale computational model keeps the conservation of localenergy and momentum for nonlinear thermo-mechanical simulation. Moreover, aglobal error estimation with explicit rate of higher-order multi-scalesolutions is first derived in the energy norm sense. Furthermore, an efficientspace-time numerical algorithm with off-line and on-line stages is presented indetail. Adequate numerical experiments are conducted to confirm the competitiveadvantages of the presented multi-scale approach, exhibiting not only theexceptional numerical accuracy, but also the less computational expense forheterogeneous shells.

Higher-order multi-scale method for high-accuracy nonlinear thermo-mechanical simulation of heterogeneous shells