A newly developed qp-relaxation method for element connectivity parameterization to achieve stress-based topology optimization for geometrically nonlinear structures

The aim of this work is to present a novel computational approach to employ the stress-based topology optimization method (STOM) to minimize the volume subject to the locally defined stress constraints of a geometrically nonlinear structure in the framework of the element connectivity parameterization (ECP) method. Considering the locally defined stress constraints in topology optimization (TO) is a classic and challenging engineering problem, and successful optimization procedures have recently been developed using the density-based TO method for linear elastic structures. However, no study has yet considered the static failure constraint when using TO for a geometrically nonlinear structure. Therefore, the present study develops a novel computational approach for the STOM for a geometrically nonlinear structure. To successfully optimize a geometrically nonlinear structure, the unstable element issue must be properly addressed, in addition to the stress singularity issue, the existence of a large number of constraints, and the highly nonlinear behavior of the local stress constraints. To effectively resolve these issues, this research adopts the ECP method to interpolate and optimize the connectivities among solid finite elements. Furthermore, we find that a stress singularity issue linked to the local optima issue arises in the ECP method that is different from that of the density-based TO. By investigating the singularity behavior in detail, we develop a new qp-relaxation method that is suitable for the ECP method. To demonstrate the improved capability of the proposed ECP method with the modified qp-relaxation, several two-dimensional TO problems are solved.