Structural Topology Optimization based on Augmented Lagrangian Method to consider Stress and Displacement Constraints
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In structural topology optimization, different types of constraints can be considered based on stress, displacement or strain energy in terms of global or local measures. However, local stress and displacement constraints represent common structural engineering applications most closely and allow for a wide variety of applications, especially taking into account different displacement limits for different structural regions. Therefore, a topology optimization problem is formulated using stress and displacement constraints simultaneously. To address this formulation, the optimization process for stress constraints based on the Augmented Lagrangian method is extended for the simultaneous integration of displacement constraints. The corresponding gradient can be derived such that the optimization can be performed using a steepest descent method. This leads to a highly modular approach that can easily be adapted to different engineering problems. To investigate the effectiveness of this approach, optimized topologies for an L-shaped structure are presented. Furthermore, the implementation of multiple load cases is discussed for the topology optimization of a two-span beam.
