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.

翻译：本文研究具有温度依赖材料属性和正交周期构型的非均匀壳体非线性时变热力方程的多尺度计算与收敛性。首要贡献在于，通过多尺度渐近技术和泰勒级数方法，严格构建了一种用于异质壳体高精度模拟的新型高阶宏微观耦合计算模型。得益于高阶修正项，该高阶多尺度计算模型在非线性热力模拟中保持了局部能量与动量守恒。此外，本文首次在能量范数意义下导出了具有显式收敛阶的高阶多尺度解全局误差估计。进一步详细阐述了包含离线与在线阶段的高效时空数值算法。通过充分的数值实验验证了所提多尺度方法的竞争优势，不仅展现了卓越的计算精度，还降低了异质壳体的计算开销。