Structural topology optimization with simultaneous stress and displacement constraints considering multiple load cases

In this paper, a structural topology optimization approach is presented considering stress and displacement constraints using different load cases. This is motivated by structural engineering applications. A short review on different types of constraints is presented, distinguishing respective measures on a global and local basis. It is identified that local stress and displacement constraints represent common engineering problems most closely and allow for a wide variety of applications, especially different displacement limits for different structural regions. In order to solve the proposed multiconstrained formulation, stress-constrained optimization with the Augmented Lagrangian method is extended to include displacement constraints simultaneously. The implementation of multiple load cases is discussed. This leads to a highly modular approach that can easily be adapted to different engineering problems. The corresponding gradient is derived and the optimization is performed using a steepest descent method. The effectiveness of this approach is proven based on the example of an L-shaped structure and a two-span beam.