Topology Optimization for Layered Shell Structures using the Element Connectivity Parameterization

Abstract

This paper concerns itself with topological layout optimization of layered shell structures. Because shell structures have the capability to efficiently carry loads with a minimum amount of material, shells are widely used in major engineering structures such as aerospace structures, ship hulls, car bodies, etc. Given the importance of shell structures, many researchers have investigated the use of topology optimization techniques for this class of problems. The conventional approach is to use a density-based formulation.
In various challenging topology optimization problems, the recently proposed element connectivity parameterization (ECP) method was found to have significant advantages over conventional density-based approaches. Examples are increased numerical robustness under large deflections, ease of including complex nonlinear materials, and improved accuracy in certain multi-physics settings. In order to exploit these benefits also in the important class of shell structure problems, the focus of this research is on the application of the ECP approach to topology optimization of shell structures.
In our previous research, we developed an ECP-based formulation for the topology optimization of open shell structures, based on a decoupling of the bending and membrane modes of a given shell element. However, closed shell structures with local reinforcements are much more common in practice. In this contribution, we therefore extend the formulation to the reinforcement topology optimization of layered shell structures, considering both symmetric and asymmetric laminates, In addition to a detailed discussion of this new formulation, we demonstrate the effectiveness of our approach by various numerical examples.

Keywords: Topology optimization, Shell structure, ECP method