Development of a novel phase-field method for local stress-based shape and topology optimization

• A phase field based method for local stress topology optimization is developed.
• The Augmented Lagrange multiplier method is developed in the phase field.
• The locality helps to solve difficult structural optimization problems.
• The topological derivatives of the local stress constraints are derived.

This research develops a stress-based topology optimization method (STOM) using the phase-field method representing topological changes. This research shows that to apply the phase field method, regional and localized stress constraints should be addressed. Thus, we use an Augmented Lagrange multiplier approach for the stress constraints and present a new numerical solution for the Lagrange multipliers inside the Allen–Cahn equation with the topological derivatives. Through several two dimensional illustrative problems, the results of the phase-field method have larger objective values, but are robust from a stress point of view compared with the results of the STOM by the density method.