Symbolic homogenization and structure optimization for a periodically perforated cylindrical shell

The main focus of this paper lies in the drastic model reduction for a complex multi-scale problem linear elasticity. core work structural optimization periodic perforated cylindrical shells under given load on small portion surface. Periodic structure shell is frame beams. Algorithm presented utilizes two our recent analysis works homogenization and dimension 3D to two-dimensional homogenized shell, then w.r.t. beam thickness auxiliary cell-problems beams, by asymptotic method. In paper, we found analytical solution orthotropic obtained limit, variable separation Fourier analysis. depends explicitly effective properties, which are computed symbolically, design variables structure. Cell-problems solved symbolic means type loading has been optimized. Moreover, yields semi-analytic practical usage underlying theoretical derivation. We stress that with holes analytic corresponding macroscopic new.