Stress-based topology optimization method for steady-state fluid–structure interaction problems

Abstract

This research developed a new stress-based topology optimization method (STOM) for a steady-state fluid–structure interaction (FSI) problem that minimizes the volume subject to the local stress constraints. Despite numerous studies on STOM, challenging optimization issues related to stress-based topology optimization (TO) procedures for fluid–structure multiphysics systems still exist. Critical issues involved in creating a successful TO for an FSI structure include: the interpolation approach between the fluid equation and the structure equation with respect to locally defined design variables, the mutual multiphysics coupling boundary conditions at dramatically evolving interfacing boundaries, and a clear interpretation of the governing equations and the interaction boundary conditions for spatially varying intermediate design variables. In addition to these three issues, which are related to multiphysics equations, there are three important considerations related to the STOM: the stress singularity issue, the issues of multiple constraints and the highly nonlinear behavior of the stress constraints. To resolve all of the aforementioned issues, we applied a monolithic analysis, integrating the qp-relaxation method and the global p-norm approach. Using the present method, we created optimal layouts that minimize the volume constraining local stress values for a steady-state fluid and structural interaction system.