A shell-in-shell homogenization approach for internally resolved structures

Abstract In this work we introduce a numerical framework for a multiscale shell-in-shell homogenization. It represents internally resolved shell structures, where on both scales structural shell elements are employed. In contrast to classical shell homogenization strategies, which employ shell elements with displacement degrees of freedom, the present approach considers additionally rotational degrees of freedom. A central novelty is the development of periodic boundary conditions enriched with rotational degrees of freedom so that representative volume elements (RVEs) may contain shell intersections or lack a continuous thickness. In addition, an internal constraint, the so-called moment reduction constraint, and its associated finite element formulation are introduced to ensure that the effective stiffness is independent of the size of the RVE. Furthermore, integration by parts techniques are employed to eliminate rigid body motions and rotations. The proposed approach is validated through linear-elastic benchmark tests. Several linear examples, including corrugated plates and honeycomb structures, are analyzed and compared with corresponding three-dimensional reference solutions.