Topology optimization of ultra high resolution shell structures

摘要

This work presents a high performance computing framework for ultra large scale, shell-element based topology optimization. The shell elements are formulated using a linear elastic, small strain assumption and are of the solid type, meaning that each quadrilateral shell element is extruded and assigned 24 degrees of freedom. The resulting linear system is solved using a fully parallelized multigrid preconditioned Krylov method, tailored specifically for unstructured quadrilateral shell meshes. The multigrid approach is shown to have good parallel scaling properties and is able to efficiently handle the ill-conditioning arising from the ‘Solid Interpolation of Material Properties’ (SIMP) method. For the optimization, the classical minimum compliance design problem with multiple load cases, prescribed minimum length scale and a local volume constraint is investigated. The latter is implemented through efficient PDE-filtering in contrast to usual local image filtering based implementations. Finally, the framework is demonstrated on two idealized examples from civil and aerospace engineering, solving shell optimization problems with up to 11 million shell elements on 800 cores. As an example, this resolution corresponds to a minimum feature size of 1.5 cm on a high-riser of height 80 m.