Brittle and ductile failure constraints of stress-based topology optimization method for fluid–structure interactions

Abstract

This study considers failure theories for brittle and ductile materials in the stress-based topology optimization method (STOM) for steady state fluid–structure interactions (FSI). In some relevant studies, the subject of the stress-based topology optimization to minimize volumes with local von Mises stress constraints has been researched. However, the various failure theories for ductile and brittle materials, such as the maximum shear stress theory, the brittle and ductile Mohr–Coulomb theory, and the Drucker–Prager theory, have not been considered. For successful STOM for FSI, in addition to alleviating physics interpolation issues between structure and fluid and some numerical issues related to STOM, the mathematical characteristics of the various failure theories should be properly formulated and constrained. To resolve all the involved computational issues, the present study applies the monolithic analysis method, the qp-relaxation method, and the p-norm approach to the failure constraints. The present topology optimization method can create optimal layouts while minimizing volume constraining local failure constraints for ductile and brittle materials for steady state fluid and structural interaction system.