A Second-Order Reduced Multiscale Approach for Non-linear Axisymmetric Structures with Periodic Configurations

Abstract An effective second-order reduced multiscale (SORM) approach is proposed for axisymmetric inelastic heterogeneous structures with periodic configurations. The axisymmetric structures studied in this work are periodical in radial and axial directions and homogeneous in circumferential directions. At first, the high-order linear and non-linear local solutions at microscale are gotten by solving distinct multiscale auxiliary functions. Further, the homogenized parameters are introduced, and the related non-linear homogenization equations defined on global domain are given. The significant feature of the presented approaches are (i) high-order homogenization solutions that do not require high-order continuities of the coarse-scale solutions, (ii) a novel reduced-model form based on transformation field analysis (TFA) to analyze non-linear local cell problem with less computing time compared with direct numerical simulations and (iii) a new SORM algorithm derived for simulating the axisymmetric inelastic structures. Finally, by some representative examples, the effectiveness and accuracy of the presented algorithm are confirmed.