Nonlinear topology optimization of layered shell structures

Topology stiffness (compliance) design of linear and geometrically nonlinear shell structures is solved using the SIMP approach together with a filtering scheme. A general anisotropic multi-layer shell model is employed to allow the formation of through-the-thickness holes or stiffening zones. The finite element analysis is performed using nine-node Mindlin-type shell elements based on the degenerated shell approach, which are capable of modeling both single and multi-layered structures exhibiting anisotropic or isotropic behavior. The optimization problem is solved using analytical compliance and constraint sensitivities together with the Method of Moving Asymptotes (MMA). Geometrically nonlinear problems are solved using iterative Newton–Raphson methods and an adjoint variable approach is used for the sensitivity analysis. Several benchmark tests are presented in order to illustrate the difference in optimal topologies between linear and geometrically nonlinear shell structures.