Homogenisation for macroscopic shell structures with application to textile‐reinforced mesostructures

In the analysis of textile-reinforced shell structures full-scale models are often impractical due to complex nature meso-structure. The structure is assumed be globally periodic which allows definition a representative volume element (RVE). this contribution, RVE embedded within first-order homogenisation framework, where meso-to-macro transition governed by Hill-Mandel condition. coupled multiscale approach macroscopic scale analysed using elements. Each integration point linked an accounts for total thickness shell. strains applied on means suitable boundary conditions. On mesoscopic scale, value problem solved in order obtain equivalent material parameters returned scale. Here, discrete model textile-reinforcement mesostructure obtained adapting from scaled finite method (SBFEM) solids described their surfaces. These into one central point, so-called scaling center. required star-shaped domains subdivision. Combination with isogeometric (IGA) directly facilitate NURBS (Non-Uniform Rational B-Splines) functions describing boundaries commonly used CAD software. A key choice conditions RVE. contribution set will presented. proposed validated numerical examples.