Topology Optimization of Shell Structures using Element Connectivity Parameterization

This paper considers the application of Element Connectivity Parameterization (ECP) to shell topology optimization problems. In the ECP method, a topology is not realized by modifying the properties of individual elements, but by controlling the connections between adjacent elements. This concept is implemented by the use of zero-length one-dimensional inter-element links, whose stiffnesses are controlled by the design variables. The ECP approach is particularly attractive in problems involving geometrical and/or physical nonlinearities. However, for shell problems, the regular ECP approach has difficulty converging to crisp solid and void designs. This study clarifies the reason for this behavior, and proposes a novel approach involving two sets of links per element. A distinction is made between links associated with membrane and bending deformations of the shells, which resolves the convergence problems. The effectiveness of the proposed approach is illustrated by compliance minimization topology optimization of several linear elastic shell problems. In comparison to the conventional density-based approach using SIMP, equivalent or better objective values are obtained. Keywords: topology optimization, shell structures, shell elements, element connectivit6y parameterization.